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dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "d346010a65ef6868fea4b14cf34b5d2d" } } $('.js-work-strip[data-work-id=32210967]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210967,"title":"Electrothermal characterization of large-area organic light-emitting diodes employing finite-element simulation","translated_title":"","metadata":{"grobid_abstract":"We investigated and modeled the electrothermal behavior of a 5 Â 5 cm 2 organic lightemitting diode (OLED) with electrothermal measurements and finite-element simulation. A hybrid electrothermal model consisting of finite and lumped elements was proposed. Heat distribution of large-area OLED was measured by infrared spectroscopy. We have achieved an excellent agreement of measured and simulated results. The simulation confirms a strong influence of temperature on current distribution for large-area OLED. It turns out that the design of homogeneous devices requires knowledge about electrical and thermal aspects. Another result anticipates that the switching behavior of OLED strongly correlates with thermal relaxation. The model is a valuable tool to simulate luminance distribution and local aging allowing strong improvement of device development.","publication_date":{"day":1,"month":8,"year":2011,"errors":{}},"publication_name":"Organic Electronics","grobid_abstract_attachment_id":52439619},"translated_abstract":null,"internal_url":"https://www.academia.edu/32210967/Electrothermal_characterization_of_large_area_organic_light_emitting_diodes_employing_finite_element_simulation","translated_internal_url":"","created_at":"2017-04-02T19:02:24.102-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439619,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439619/thumbnails/1.jpg","file_name":"j.orgel.2011.05.01020170402-6042-wtuacw.pdf","download_url":"https://www.academia.edu/attachments/52439619/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Electrothermal_characterization_of_large.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439619/j.orgel.2011.05.01020170402-6042-wtuacw-libre.pdf?1491185619=\u0026response-content-disposition=attachment%3B+filename%3DElectrothermal_characterization_of_large.pdf\u0026Expires=1733049543\u0026Signature=L2zRsO6TSNWsZWPzaIwStSyQIcwdPl-U~Ts4OllAGtGykJGHh81qtn982AZ680rua9jzoq0SqiGw0rFpS6of~-6ImNlTTinGpSJfxrhEyoTKQAWt-~k~GaXojoPY1lP0Kt7fAaFJkWIRqHJXhWBb~kyJ7TooRRPtf~kBw8-ik8pmxXbdWHHrbX2iXypqhvznLQtyJutxuH9~u9mvF25K1XVO0cBMKubX9M2nDXcYxd89QK-4l1YVnYULGgSs5~LcknywGeJPHaH1LDtW2JxAqkqUO7w35-z7Ewqes~p9o5vAvO4d-LusXo7vNGvkBqbHvf9mYuUM4pTGytWuR6BCnw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Electrothermal_characterization_of_large_area_organic_light_emitting_diodes_employing_finite_element_simulation","translated_slug":"","page_count":7,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael 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data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210966/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications"><img alt="Research paper thumbnail of VSP-traveltime inversion for linear-velocity constants based on nonlinear regression with survey-design applications" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210966/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications">VSP-traveltime inversion for linear-velocity constants based on nonlinear regression with survey-design applications</a></div><div class="wp-workCard_item"><span>Seg Technical Program Expanded Abstracts</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210966"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210966"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210966; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210966]").text(description); $(".js-view-count[data-work-id=32210966]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210966; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210966']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210966, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210966]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210966,"title":"VSP-traveltime inversion for linear-velocity constants based on nonlinear regression with survey-design applications","translated_title":"","metadata":{"abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","publication_date":{"day":null,"month":null,"year":1999,"errors":{}},"publication_name":"Seg Technical Program Expanded Abstracts"},"translated_abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","internal_url":"https://www.academia.edu/32210966/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications","translated_internal_url":"","created_at":"2017-04-02T19:02:23.965-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":86410,"name":"Nonlinear Regression","url":"https://www.academia.edu/Documents/in/Nonlinear_Regression"},{"id":131343,"name":"Survey design","url":"https://www.academia.edu/Documents/in/Survey_design"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210965"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210965/Invariant_properties_for_finding_distance_in_space_of_elasticity_tensors"><img alt="Research paper thumbnail of Invariant properties for finding distance in space of elasticity tensors" class="work-thumbnail" src="https://attachments.academia-assets.com/52439594/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210965/Invariant_properties_for_finding_distance_in_space_of_elasticity_tensors">Invariant properties for finding distance in space of elasticity tensors</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the distance is obtained as the minimization of corresponding expressions with respect to the action of the orthogonal group. These expressions are stated in terms of the eigenvalues of both the given tensor and the projected one. The process of minimization is facilitated by the fact that, as we prove, the traces of the corresponding Voigt and dilatation tensors are invariant under these orthogonal projections. For isotropy, cubic symmetry and transverse isotropy, we formulate algorithms to find both the orientation and the eigenvalues of the elasticity tensor that is endowed with a particular symmetry and is closest to the given elasticity tensor.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="2a3f38b19e1ace947d9ccdb30c24fb7d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439594,"asset_id":32210965,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439594/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210965"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210965"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210965; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210965]").text(description); $(".js-view-count[data-work-id=32210965]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210965; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210965']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210965, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "2a3f38b19e1ace947d9ccdb30c24fb7d" } } $('.js-work-strip[data-work-id=32210965]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210965,"title":"Invariant properties for finding distance in space of elasticity tensors","translated_title":"","metadata":{"abstract":"Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the distance is obtained as the minimization of corresponding expressions with respect to the action of the orthogonal group. These expressions are stated in terms of the eigenvalues of both the given tensor and the projected one. The process of minimization is facilitated by the fact that, as we prove, the traces of the corresponding Voigt and dilatation tensors are invariant under these orthogonal projections. For isotropy, cubic symmetry and transverse isotropy, we formulate algorithms to find both the orientation and the eigenvalues of the elasticity tensor that is endowed with a particular symmetry and is closest to the given elasticity tensor.","ai_title_tag":"Distance Measurement for Symmetric Elasticity Tensors","publication_date":{"day":null,"month":null,"year":2007,"errors":{}}},"translated_abstract":"Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the distance is obtained as the minimization of corresponding expressions with respect to the action of the orthogonal group. These expressions are stated in terms of the eigenvalues of both the given tensor and the projected one. The process of minimization is facilitated by the fact that, as we prove, the traces of the corresponding Voigt and dilatation tensors are invariant under these orthogonal projections. For isotropy, cubic symmetry and transverse isotropy, we formulate algorithms to find both the orientation and the eigenvalues of the elasticity tensor that is endowed with a particular symmetry and is closest to the given elasticity tensor.","internal_url":"https://www.academia.edu/32210965/Invariant_properties_for_finding_distance_in_space_of_elasticity_tensors","translated_internal_url":"","created_at":"2017-04-02T19:02:23.749-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439594,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439594/thumbnails/1.jpg","file_name":"0712.1082.pdf","download_url":"https://www.academia.edu/attachments/52439594/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Invariant_properties_for_finding_distanc.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439594/0712.1082-libre.pdf?1491185643=\u0026response-content-disposition=attachment%3B+filename%3DInvariant_properties_for_finding_distanc.pdf\u0026Expires=1733049543\u0026Signature=OaMVPUaaN5ePhGCMyfadyfFuC~NQOKMFtuYhxOx7TEohheUy8UFAGq14AZGyys0ZMslqIsc6xxw-frrYm7CIZD1ftZP2LHbdXroEpoJEoLkMOWZGYMgz~JJ1zqc0wDmg6iJhScZMLS7g~ZeoxXZ0Qk6N-wmooGp3marMKf9HIrHi9z7ZUJZd-~YHicJOhsrH51aLKEiXqu-0CXYo-iMNAKLNa2PKGKl2fnjHgTyYMqfh8ZFIG3XCfQBSiUvKliTBTfP81gol-Nw0h6mFEqbfQJUBm2Cqx4J6iWorHZFyHerVzJV-RzGgcTs-DC12B-PsSi-43aIS2My~mdsmVL4PxQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Invariant_properties_for_finding_distance_in_space_of_elasticity_tensors","translated_slug":"","page_count":19,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[{"id":52439594,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439594/thumbnails/1.jpg","file_name":"0712.1082.pdf","download_url":"https://www.academia.edu/attachments/52439594/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Invariant_properties_for_finding_distanc.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439594/0712.1082-libre.pdf?1491185643=\u0026response-content-disposition=attachment%3B+filename%3DInvariant_properties_for_finding_distanc.pdf\u0026Expires=1733049543\u0026Signature=OaMVPUaaN5ePhGCMyfadyfFuC~NQOKMFtuYhxOx7TEohheUy8UFAGq14AZGyys0ZMslqIsc6xxw-frrYm7CIZD1ftZP2LHbdXroEpoJEoLkMOWZGYMgz~JJ1zqc0wDmg6iJhScZMLS7g~ZeoxXZ0Qk6N-wmooGp3marMKf9HIrHi9z7ZUJZd-~YHicJOhsrH51aLKEiXqu-0CXYo-iMNAKLNa2PKGKl2fnjHgTyYMqfh8ZFIG3XCfQBSiUvKliTBTfP81gol-Nw0h6mFEqbfQJUBm2Cqx4J6iWorHZFyHerVzJV-RzGgcTs-DC12B-PsSi-43aIS2My~mdsmVL4PxQ__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"},{"id":52439593,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439593/thumbnails/1.jpg","file_name":"0712.1082.pdf","download_url":"https://www.academia.edu/attachments/52439593/download_file","bulk_download_file_name":"Invariant_properties_for_finding_distanc.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439593/0712.1082-libre.pdf?1491185645=\u0026response-content-disposition=attachment%3B+filename%3DInvariant_properties_for_finding_distanc.pdf\u0026Expires=1733049543\u0026Signature=QTYRVE1KiIWA59sbp7iyIVlibSLBc9wGNnx8JrorLTqTCkKGfcokWe1Njuy4Uzi8SeItKgBn5NSGG7jKn4AvJSV98G6K~HPG7FceXwaXH897-8C1C4cf~W0Z11guk~rBbZW8eW2Zq2elNEftiYlXVZQeoJuqCW3jVQFefFZXXSBGS2qNbMz4glJHq-1qeqbnlxj9tLftm1OdKvHN4OFJ3a~-Fd6NECqhzvTgu7h9xPsMjW7fGN~8JE67VXXBH1j1ze5OZTvYMYJLHeNMyqGbYpUPdpB8dS3DmwlxhIhB1TsczpFKcvkZECc0WOScdbaxwyEapt3WDFZ~802NMs49Iw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":73,"name":"Civil Engineering","url":"https://www.academia.edu/Documents/in/Civil_Engineering"},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":511,"name":"Materials Science","url":"https://www.academia.edu/Documents/in/Materials_Science"},{"id":48904,"name":"Elasticity","url":"https://www.academia.edu/Documents/in/Elasticity"},{"id":1555351,"name":"Euclidean Distance","url":"https://www.academia.edu/Documents/in/Euclidean_Distance"}],"urls":[{"id":8044630,"url":"http://adsabs.harvard.edu/abs/2007arxiv0712.1082b"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210964"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210964/On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet"><img alt="Research paper thumbnail of On convexity and detachment of innermost wavefront-slowness sheet" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210964/On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet">On convexity and detachment of innermost wavefront-slowness sheet</a></div><div class="wp-workCard_item"><span>Geophysics</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex,...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210964"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210964"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210964; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210964]").text(description); $(".js-view-count[data-work-id=32210964]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210964; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210964']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210964, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210964]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210964,"title":"On convexity and detachment of innermost wavefront-slowness sheet","translated_title":"","metadata":{"abstract":"ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.","publication_date":{"day":null,"month":null,"year":2009,"errors":{}},"publication_name":"Geophysics"},"translated_abstract":"ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.","internal_url":"https://www.academia.edu/32210964/On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet","translated_internal_url":"","created_at":"2017-04-02T19:02:23.564-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":409,"name":"Geophysics","url":"https://www.academia.edu/Documents/in/Geophysics"},{"id":13883,"name":"Seismology","url":"https://www.academia.edu/Documents/in/Seismology"},{"id":48904,"name":"Elasticity","url":"https://www.academia.edu/Documents/in/Elasticity"},{"id":59249,"name":"Computers","url":"https://www.academia.edu/Documents/in/Computers"},{"id":176607,"name":"Polarisation","url":"https://www.academia.edu/Documents/in/Polarisation"},{"id":191543,"name":"Polarization","url":"https://www.academia.edu/Documents/in/Polarization"},{"id":222440,"name":"Waves","url":"https://www.academia.edu/Documents/in/Waves"},{"id":1029207,"name":"Tensor","url":"https://www.academia.edu/Documents/in/Tensor"},{"id":2353926,"name":"Isotropy","url":"https://www.academia.edu/Documents/in/Isotropy"}],"urls":[{"id":8044629,"url":"http://cat.inist.fr/?aModele=afficheN\u0026cpsidt=22037089"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210963"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210963/On_Obtaining_Effective_Transversely_Isotropic_Elasticity_Tensors"><img alt="Research paper thumbnail of On Obtaining Effective Transversely Isotropic Elasticity�Tensors" class="work-thumbnail" src="https://attachments.academia-assets.com/52439616/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210963/On_Obtaining_Effective_Transversely_Isotropic_Elasticity_Tensors">On Obtaining Effective Transversely Isotropic Elasticity�Tensors</a></div><div class="wp-workCard_item"><span>Journal of Elasticity</span><span>, 2009</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ffb366455b9602baf46abf7c19d5609e" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439616,"asset_id":32210963,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439616/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210963"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210963"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210963; 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A similar problem was considered by other authors and solved analytically assuming a fixed orientation of the natural coordinate system of the transversely isotropic tensor. In this paper we formulate a method for finding the optimal orientation of the coordinate system-the one that produces the shortest distance. The optimization problem reduces to finding the absolute maximum of a homogeneous eighth-degree polynomial on a two-dimensional sphere. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210961"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210961/On_effective_elasticity_tensors"><img alt="Research paper thumbnail of On effective elasticity tensors" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210961/On_effective_elasticity_tensors">On effective elasticity tensors</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; by &quot;effective&quot;, we mean the closest in the sense of the Euclidean or log-Euclidean distance. It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. 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It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. In general, the minimization process","publication_date":{"day":null,"month":null,"year":2008,"errors":{}}},"translated_abstract":"We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; by \u0026quot;effective\u0026quot;, we mean the closest in the sense of the Euclidean or log-Euclidean distance. It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. In general, the minimization process","internal_url":"https://www.academia.edu/32210961/On_effective_elasticity_tensors","translated_internal_url":"","created_at":"2017-04-02T19:02:23.104-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_effective_elasticity_tensors","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":10981,"name":"Data Assimilation","url":"https://www.academia.edu/Documents/in/Data_Assimilation"},{"id":318537,"name":"Local minima","url":"https://www.academia.edu/Documents/in/Local_minima"},{"id":504035,"name":"Three Dimensional","url":"https://www.academia.edu/Documents/in/Three_Dimensional"},{"id":1555351,"name":"Euclidean Distance","url":"https://www.academia.edu/Documents/in/Euclidean_Distance"},{"id":2064458,"name":"Transversely Isotropic Solids","url":"https://www.academia.edu/Documents/in/Transversely_Isotropic_Solids"}],"urls":[{"id":8044626,"url":"http://adsabs.harvard.edu/abs/2008AGUFM.S41C1868S"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210960"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210960/On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors"><img alt="Research paper thumbnail of On Characterization of Elasticity Parameters in Context of Measurement Errors" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210960/On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors">On Characterization of Elasticity Parameters in Context of Measurement Errors</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this presentation, we discuss the one-to-one relation between the elasticity parameters and th...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210960"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210960"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210960; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210960]").text(description); $(".js-view-count[data-work-id=32210960]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210960; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210960']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210960, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210960]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210960,"title":"On Characterization of Elasticity Parameters in Context of Measurement Errors","translated_title":"","metadata":{"abstract":"In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic","publication_date":{"day":null,"month":null,"year":2007,"errors":{}}},"translated_abstract":"In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic","internal_url":"https://www.academia.edu/32210960/On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors","translated_internal_url":"","created_at":"2017-04-02T19:02:22.901-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":8183,"name":"Linear Elasticity","url":"https://www.academia.edu/Documents/in/Linear_Elasticity"},{"id":31477,"name":"Uncertainty Quantification","url":"https://www.academia.edu/Documents/in/Uncertainty_Quantification"},{"id":162403,"name":"Measurement Error","url":"https://www.academia.edu/Documents/in/Measurement_Error"},{"id":491689,"name":"Seismic Tomography","url":"https://www.academia.edu/Documents/in/Seismic_Tomography"},{"id":547093,"name":"Inverse Theory","url":"https://www.academia.edu/Documents/in/Inverse_Theory"},{"id":829227,"name":"Body Waves","url":"https://www.academia.edu/Documents/in/Body_Waves"},{"id":1231330,"name":"Constitutive Equation","url":"https://www.academia.edu/Documents/in/Constitutive_Equation"}],"urls":[{"id":8044625,"url":"http://adsabs.harvard.edu/abs/2007AGUFM.S34B..05S"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210959"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210959/On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial"><img alt="Research paper thumbnail of On Seismic Waves in Linearly Elastic, Anisotropic and Nonuniform Continua: Tutorial" class="work-thumbnail" src="https://attachments.academia-assets.com/52439615/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210959/On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial">On Seismic Waves in Linearly Elastic, Anisotropic and Nonuniform Continua: Tutorial</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exploration seismologists benefit from knowledge of these properties. This knowledge provides us with rock-physics information and also enables us to account for the effects of anisotropy and nonuniformity on seismic imaging. Anisotropy and nonuniformity are conveniently studied in the context of continuum mechanics. Aki and Richards (1980) at the beginning of their classic book, while referring to certain standard conjectures used in seismology, write “[t]hese conjectures, and many others that are generally assumed by seismologists to be true, are properties of infinitesimal motion in classical continuum mechanics for an elastic medium with a linear stress-strain relation”. This tutorial presents aspects of a scientific foundation for the study and interpretation of seismic wave phenomena in linearly elastic, anisotropic, nonuniform continua. It draws on continuum mechanics and the asympto...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="887d508096743a4889cfb2cd1840ff9c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439615,"asset_id":32210959,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439615/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210959"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210959"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210959; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210959]").text(description); $(".js-view-count[data-work-id=32210959]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210959; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210959']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210959, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "887d508096743a4889cfb2cd1840ff9c" } } $('.js-work-strip[data-work-id=32210959]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210959,"title":"On Seismic Waves in Linearly Elastic, Anisotropic and Nonuniform Continua: Tutorial","translated_title":"","metadata":{"abstract":"Most sedimentary rocks are anisotropic. 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It draws on continuum mechanics and the asympto...","ai_title_tag":"Seismic Waves in Elastic Anisotropic Nonuniform Continua"},"translated_abstract":"Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exploration seismologists benefit from knowledge of these properties. This knowledge provides us with rock-physics information and also enables us to account for the effects of anisotropy and nonuniformity on seismic imaging. Anisotropy and nonuniformity are conveniently studied in the context of continuum mechanics. Aki and Richards (1980) at the beginning of their classic book, while referring to certain standard conjectures used in seismology, write “[t]hese conjectures, and many others that are generally assumed by seismologists to be true, are properties of infinitesimal motion in classical continuum mechanics for an elastic medium with a linear stress-strain relation”. This tutorial presents aspects of a scientific foundation for the study and interpretation of seismic wave phenomena in linearly elastic, anisotropic, nonuniform continua. It draws on continuum mechanics and the asympto...","internal_url":"https://www.academia.edu/32210959/On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial","translated_internal_url":"","created_at":"2017-04-02T19:02:22.774-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439615,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439615/thumbnails/1.jpg","file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r.pdf","download_url":"https://www.academia.edu/attachments/52439615/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439615/On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r-libre.pdf?1491185623=\u0026response-content-disposition=attachment%3B+filename%3DOn_Seismic_Waves_in_Linearly_Elastic_Ani.pdf\u0026Expires=1733049543\u0026Signature=XvoEr4oTgefM83dwdLgcjpdKKqUQ4pz1qxghepCrf~nl2p69O-S3LeSdLxiDKpCpyJUD3QBq53JPNB9~X5L46hPFGmvNcdKfseWnvaLHeYIMR~SPQAhPklF6rGivNxNTUJQ1cuOEqVylP8D2juImB4LBq3ZmnCbzUtfpLu4Ft1kL8MlSMlicJ8lplD0dvWLooXQ3o81bVXqQNDmIyS~uvrkUqSNEnlinYWgGsDVN9pz9K1tV2TH-crqixzIIyvmJuJ0xXI1gGiUIXVkizJhXcOdxXwPH2LO6nn62VcDF1RC~FJdt1~eE7Rnx5QIRwf6KO9~EUPb0HVu7drFcegtJgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial","translated_slug":"","page_count":8,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[{"id":52439615,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439615/thumbnails/1.jpg","file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r.pdf","download_url":"https://www.academia.edu/attachments/52439615/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439615/On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r-libre.pdf?1491185623=\u0026response-content-disposition=attachment%3B+filename%3DOn_Seismic_Waves_in_Linearly_Elastic_Ani.pdf\u0026Expires=1733049543\u0026Signature=XvoEr4oTgefM83dwdLgcjpdKKqUQ4pz1qxghepCrf~nl2p69O-S3LeSdLxiDKpCpyJUD3QBq53JPNB9~X5L46hPFGmvNcdKfseWnvaLHeYIMR~SPQAhPklF6rGivNxNTUJQ1cuOEqVylP8D2juImB4LBq3ZmnCbzUtfpLu4Ft1kL8MlSMlicJ8lplD0dvWLooXQ3o81bVXqQNDmIyS~uvrkUqSNEnlinYWgGsDVN9pz9K1tV2TH-crqixzIIyvmJuJ0xXI1gGiUIXVkizJhXcOdxXwPH2LO6nn62VcDF1RC~FJdt1~eE7Rnx5QIRwf6KO9~EUPb0HVu7drFcegtJgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210958"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210958/Angle_of_Incidence_as_a_Function_of_Source_receiver_Offset_of_a_Dipping_Refractor_An_Exact_Expression_for_VSP_Apllications"><img alt="Research paper thumbnail of Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications" class="work-thumbnail" src="https://attachments.academia-assets.com/52439613/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210958/Angle_of_Incidence_as_a_Function_of_Source_receiver_Offset_of_a_Dipping_Refractor_An_Exact_Expression_for_VSP_Apllications">Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however,...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however, the angle of incidence is often difficult to establish. Partially, because of this difficulty it is more common to consider Amplitude Variations as a function of a lateral source-receiver Offset (AVO) rather than Amplitude Variations as a function of the Angle of incidence (AVA). Computational modelling and theoretical analysis, nevertheless, require the knowledge of angles of incidence in order to relate them directly to various forms of Zoeppritz equations (e.g., Aki and Richards, 1980). Furthermore, although a lateral source-receiver offset is eas-ily established based on field acquisition parameters, the angle of incidence requires a more involved calculation. This Short Note provides explicit and exact expressions which can be used in AVA studies using the Vertical Seismic Profile (VSP). The expressions can be conveniently used in planning an AVAiAVO survey while designing source-r...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ce0e975575eacb4009209bca1ee2c6b1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439613,"asset_id":32210958,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439613/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210958"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210958"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210958; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210958]").text(description); $(".js-view-count[data-work-id=32210958]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210958; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210958']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210958, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ce0e975575eacb4009209bca1ee2c6b1" } } $('.js-work-strip[data-work-id=32210958]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210958,"title":"Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications","translated_title":"","metadata":{"abstract":"Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however, the angle of incidence is often difficult to establish. Partially, because of this difficulty it is more common to consider Amplitude Variations as a function of a lateral source-receiver Offset (AVO) rather than Amplitude Variations as a function of the Angle of incidence (AVA). Computational modelling and theoretical analysis, nevertheless, require the knowledge of angles of incidence in order to relate them directly to various forms of Zoeppritz equations (e.g., Aki and Richards, 1980). Furthermore, although a lateral source-receiver offset is eas-ily established based on field acquisition parameters, the angle of incidence requires a more involved calculation. This Short Note provides explicit and exact expressions which can be used in AVA studies using the Vertical Seismic Profile (VSP). 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210957"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210957/VSP_Reflection_Points_for_Linear_Inhomogeneity_and_Elliptical_Anisotropy"><img alt="Research paper thumbnail of VSP Reflection Points for Linear Inhomogeneity and Elliptical Anisotropy" class="work-thumbnail" src="https://attachments.academia-assets.com/52439617/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210957/VSP_Reflection_Points_for_Linear_Inhomogeneity_and_Elliptical_Anisotropy">VSP Reflection Points for Linear Inhomogeneity and Elliptical Anisotropy</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">An exact analytical expression for traveltime in a medium with a constant velocity gradient and e...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">An exact analytical expression for traveltime in a medium with a constant velocity gradient and elliptical velocity dependence is used to calculate possible reflection points for a given source receiver geometry. The set of reflection points are collectively referred to as the illumination zone. Also, we give an expression that can be used to trace rays in a vertically inhomogeneous elliptically anisotropic medi-um. These expressions are applicable for both survey design and data interpretation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ee199ca5530151b57ee0bd0856539e19" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439617,"asset_id":32210957,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439617/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210957"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210957"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210957; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210957]").text(description); $(".js-view-count[data-work-id=32210957]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210957; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210957']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210957, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ee199ca5530151b57ee0bd0856539e19" } } $('.js-work-strip[data-work-id=32210957]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210957,"title":"VSP Reflection Points for Linear Inhomogeneity and Elliptical Anisotropy","translated_title":"","metadata":{"abstract":"An exact analytical expression for traveltime in a medium with a constant velocity gradient and elliptical velocity dependence is used to calculate possible reflection points for a given source receiver geometry. 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Inferring material properties of t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Geophysics—similarly to astrophysics—relies on remote sensing. Inferring material properties of the Earth’s interior is akin to inferring the composition of a distant star. In both cases, scientists rely on matching theoretical predictions or explanations with observations. Notably, obtaining a sample of a material from the interior of our planet might not be less difficult than obtaining a sample from a distant celestial object. To infer the presence and orientations of subsurface fractures, seismologists might use directional properties of Hookean solids. In other words—using such a solid as a mathematical model— seismologists match its quantitative predictions with observations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210956"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210956"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210956; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210956]").text(description); $(".js-view-count[data-work-id=32210956]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210956; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210956']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210956, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210956]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210956,"title":"On Hookean Solids in Seismology: Anisotropy and Fractures","translated_title":"","metadata":{"abstract":"Geophysics—similarly to astrophysics—relies on remote sensing. Inferring material properties of the Earth’s interior is akin to inferring the composition of a distant star. In both cases, scientists rely on matching theoretical predictions or explanations with observations. Notably, obtaining a sample of a material from the interior of our planet might not be less difficult than obtaining a sample from a distant celestial object. To infer the presence and orientations of subsurface fractures, seismologists might use directional properties of Hookean solids. In other words—using such a solid as a mathematical model— seismologists match its quantitative predictions with observations."},"translated_abstract":"Geophysics—similarly to astrophysics—relies on remote sensing. Inferring material properties of the Earth’s interior is akin to inferring the composition of a distant star. In both cases, scientists rely on matching theoretical predictions or explanations with observations. 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In other words—using such a solid as a mathematical model— seismologists match its quantitative predictions with observations.","internal_url":"https://www.academia.edu/32210956/On_Hookean_Solids_in_Seismology_Anisotropy_and_Fractures","translated_internal_url":"","created_at":"2017-04-02T19:02:22.451-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_Hookean_Solids_in_Seismology_Anisotropy_and_Fractures","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); 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The resulting effective tensor is the highestlikelihood estimate within the specified symmetry class. Given two material-symmetry classes, with one included in the other, the weighted Frobenius distance from the given tensor to the two effective tensors can be used to decide between the two models-one with higher and one with lower symmetry-by means of the likelihood ratio test.","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Journal of Elasticity","grobid_abstract_attachment_id":52439614},"translated_abstract":null,"internal_url":"https://www.academia.edu/32210955/Effective_Elasticity_Tensors_in_Context_of_Random_Errors","translated_internal_url":"","created_at":"2017-04-02T19:02:22.353-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439614,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439614/thumbnails/1.jpg","file_name":"Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3.pdf","download_url":"https://www.academia.edu/attachments/52439614/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_Elasticity_Tensors_in_Context.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439614/Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3-libre.pdf?1491185629=\u0026response-content-disposition=attachment%3B+filename%3DEffective_Elasticity_Tensors_in_Context.pdf\u0026Expires=1733049543\u0026Signature=Wk2aJ6FdiBGuE7JOs6E2eSXwkkggB1G6OopMv5sNHNjnxYxWeqtNFTgjf4pUOGTHYIu0XEYU97jyCx3z-KhGhNZFj3PiJits32nXe2QZrfoK3vWXa0EQmbZA9zPrpKC-F-5iR9upqZUjaANPu-l2fdX9lxBSA6JP4TG2atQ~10sT7hqX14VxXgzdWWB0lrTcqQCDJWLbXn0Fp5HofiWHkVPANH86G-PvXJrqW4aMF~Fht5ypNH1XsswIm5zdjxrxG1FLrtiVd74WApQYDIpBCZmTxfJDKWe6sV-5Bs1AE8JZhRUaxVfjPWaQoZl5RzkDZtuJCjV6hHSlxlGx--varA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Effective_Elasticity_Tensors_in_Context_of_Random_Errors","translated_slug":"","page_count":15,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[{"id":52439614,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439614/thumbnails/1.jpg","file_name":"Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3.pdf","download_url":"https://www.academia.edu/attachments/52439614/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_Elasticity_Tensors_in_Context.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439614/Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3-libre.pdf?1491185629=\u0026response-content-disposition=attachment%3B+filename%3DEffective_Elasticity_Tensors_in_Context.pdf\u0026Expires=1733049543\u0026Signature=Wk2aJ6FdiBGuE7JOs6E2eSXwkkggB1G6OopMv5sNHNjnxYxWeqtNFTgjf4pUOGTHYIu0XEYU97jyCx3z-KhGhNZFj3PiJits32nXe2QZrfoK3vWXa0EQmbZA9zPrpKC-F-5iR9upqZUjaANPu-l2fdX9lxBSA6JP4TG2atQ~10sT7hqX14VxXgzdWWB0lrTcqQCDJWLbXn0Fp5HofiWHkVPANH86G-PvXJrqW4aMF~Fht5ypNH1XsswIm5zdjxrxG1FLrtiVd74WApQYDIpBCZmTxfJDKWe6sV-5Bs1AE8JZhRUaxVfjPWaQoZl5RzkDZtuJCjV6hHSlxlGx--varA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":73,"name":"Civil Engineering","url":"https://www.academia.edu/Documents/in/Civil_Engineering"},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":48904,"name":"Elasticity","url":"https://www.academia.edu/Documents/in/Elasticity"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210954"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210954/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications"><img alt="Research paper thumbnail of VSP‐traveltime inversion for linear‐velocity constants based on nonlinear regression with survey‐design applications" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210954/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications">VSP‐traveltime inversion for linear‐velocity constants based on nonlinear regression with survey‐design applications</a></div><div class="wp-workCard_item"><span>SEG Technical Program Expanded Abstracts 2000</span><span>, 2000</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210954"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210954"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210954; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210954]").text(description); $(".js-view-count[data-work-id=32210954]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210954; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210954']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210954, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210954]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210954,"title":"VSP‐traveltime inversion for linear‐velocity constants based on nonlinear regression with survey‐design applications","translated_title":"","metadata":{"abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","publication_date":{"day":null,"month":null,"year":2000,"errors":{}},"publication_name":"SEG Technical Program Expanded Abstracts 2000"},"translated_abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","internal_url":"https://www.academia.edu/32210954/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications","translated_internal_url":"","created_at":"2017-04-02T19:02:22.247-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":86410,"name":"Nonlinear Regression","url":"https://www.academia.edu/Documents/in/Nonlinear_Regression"},{"id":131343,"name":"Survey design","url":"https://www.academia.edu/Documents/in/Survey_design"}],"urls":[]}, dispatcherData: dispatcherData }); 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A hybrid electrothermal model consisting of finite and lumped elements was proposed. Heat distribution of large-area OLED was measured by infrared spectroscopy. We have achieved an excellent agreement of measured and simulated results. The simulation confirms a strong influence of temperature on current distribution for large-area OLED. It turns out that the design of homogeneous devices requires knowledge about electrical and thermal aspects. Another result anticipates that the switching behavior of OLED strongly correlates with thermal relaxation. The model is a valuable tool to simulate luminance distribution and local aging allowing strong improvement of device development.","publication_date":{"day":1,"month":8,"year":2011,"errors":{}},"publication_name":"Organic Electronics","grobid_abstract_attachment_id":52439619},"translated_abstract":null,"internal_url":"https://www.academia.edu/32210967/Electrothermal_characterization_of_large_area_organic_light_emitting_diodes_employing_finite_element_simulation","translated_internal_url":"","created_at":"2017-04-02T19:02:24.102-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439619,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439619/thumbnails/1.jpg","file_name":"j.orgel.2011.05.01020170402-6042-wtuacw.pdf","download_url":"https://www.academia.edu/attachments/52439619/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Electrothermal_characterization_of_large.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439619/j.orgel.2011.05.01020170402-6042-wtuacw-libre.pdf?1491185619=\u0026response-content-disposition=attachment%3B+filename%3DElectrothermal_characterization_of_large.pdf\u0026Expires=1733049543\u0026Signature=L2zRsO6TSNWsZWPzaIwStSyQIcwdPl-U~Ts4OllAGtGykJGHh81qtn982AZ680rua9jzoq0SqiGw0rFpS6of~-6ImNlTTinGpSJfxrhEyoTKQAWt-~k~GaXojoPY1lP0Kt7fAaFJkWIRqHJXhWBb~kyJ7TooRRPtf~kBw8-ik8pmxXbdWHHrbX2iXypqhvznLQtyJutxuH9~u9mvF25K1XVO0cBMKubX9M2nDXcYxd89QK-4l1YVnYULGgSs5~LcknywGeJPHaH1LDtW2JxAqkqUO7w35-z7Ewqes~p9o5vAvO4d-LusXo7vNGvkBqbHvf9mYuUM4pTGytWuR6BCnw__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Electrothermal_characterization_of_large_area_organic_light_emitting_diodes_employing_finite_element_simulation","translated_slug":"","page_count":7,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael 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element method","url":"https://www.academia.edu/Documents/in/Finite_element_method"},{"id":24227,"name":"Organic Electronics","url":"https://www.academia.edu/Documents/in/Organic_Electronics"},{"id":24231,"name":"Organic light emitting diodes","url":"https://www.academia.edu/Documents/in/Organic_light_emitting_diodes"},{"id":32149,"name":"Numerical Method","url":"https://www.academia.edu/Documents/in/Numerical_Method"},{"id":48576,"name":"Switching","url":"https://www.academia.edu/Documents/in/Switching"},{"id":78842,"name":"Infrared spectroscopy","url":"https://www.academia.edu/Documents/in/Infrared_spectroscopy"},{"id":116059,"name":"Relaxation","url":"https://www.academia.edu/Documents/in/Relaxation"},{"id":118582,"name":"Physical sciences","url":"https://www.academia.edu/Documents/in/Physical_sciences"},{"id":254893,"name":"Finite element simulation","url":"https://www.academia.edu/Documents/in/Finite_element_simulation"},{"id":260118,"name":"CHEMICAL 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data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210966/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications"><img alt="Research paper thumbnail of VSP-traveltime inversion for linear-velocity constants based on nonlinear regression with survey-design applications" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210966/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications">VSP-traveltime inversion for linear-velocity constants based on nonlinear regression with survey-design applications</a></div><div class="wp-workCard_item"><span>Seg Technical Program Expanded Abstracts</span><span>, 1999</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210966"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210966"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210966; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210966]").text(description); $(".js-view-count[data-work-id=32210966]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210966; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210966']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210966, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210966]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210966,"title":"VSP-traveltime inversion for linear-velocity constants based on nonlinear regression with survey-design applications","translated_title":"","metadata":{"abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","publication_date":{"day":null,"month":null,"year":1999,"errors":{}},"publication_name":"Seg Technical Program Expanded Abstracts"},"translated_abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","internal_url":"https://www.academia.edu/32210966/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications","translated_internal_url":"","created_at":"2017-04-02T19:02:23.965-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":86410,"name":"Nonlinear Regression","url":"https://www.academia.edu/Documents/in/Nonlinear_Regression"},{"id":131343,"name":"Survey design","url":"https://www.academia.edu/Documents/in/Survey_design"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210965"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210965/Invariant_properties_for_finding_distance_in_space_of_elasticity_tensors"><img alt="Research paper thumbnail of Invariant properties for finding distance in space of elasticity tensors" class="work-thumbnail" src="https://attachments.academia-assets.com/52439594/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210965/Invariant_properties_for_finding_distance_in_space_of_elasticity_tensors">Invariant properties for finding distance in space of elasticity tensors</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of ...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the distance is obtained as the minimization of corresponding expressions with respect to the action of the orthogonal group. These expressions are stated in terms of the eigenvalues of both the given tensor and the projected one. The process of minimization is facilitated by the fact that, as we prove, the traces of the corresponding Voigt and dilatation tensors are invariant under these orthogonal projections. For isotropy, cubic symmetry and transverse isotropy, we formulate algorithms to find both the orientation and the eigenvalues of the elasticity tensor that is endowed with a particular symmetry and is closest to the given elasticity tensor.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="2a3f38b19e1ace947d9ccdb30c24fb7d" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439594,"asset_id":32210965,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439594/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210965"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210965"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210965; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210965]").text(description); $(".js-view-count[data-work-id=32210965]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210965; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210965']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210965, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "2a3f38b19e1ace947d9ccdb30c24fb7d" } } $('.js-work-strip[data-work-id=32210965]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210965,"title":"Invariant properties for finding distance in space of elasticity tensors","translated_title":"","metadata":{"abstract":"Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. 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The process of minimization is facilitated by the fact that, as we prove, the traces of the corresponding Voigt and dilatation tensors are invariant under these orthogonal projections. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210964"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210964/On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet"><img alt="Research paper thumbnail of On convexity and detachment of innermost wavefront-slowness sheet" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210964/On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet">On convexity and detachment of innermost wavefront-slowness sheet</a></div><div class="wp-workCard_item"><span>Geophysics</span><span>, 2009</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex,...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210964"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210964"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210964; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210964]").text(description); $(".js-view-count[data-work-id=32210964]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210964; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210964']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210964, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210964]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210964,"title":"On convexity and detachment of innermost wavefront-slowness sheet","translated_title":"","metadata":{"abstract":"ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.","publication_date":{"day":null,"month":null,"year":2009,"errors":{}},"publication_name":"Geophysics"},"translated_abstract":"ABSTRACT We have proved that the innermost wavefront-slowness sheet of a Hookean solid is convex, whether or not it is detached from the other sheets. This theorem is valid for the generally anisotropic case, and it is an extension of theorems whose proofs require the detachment of the innermost sheet. Although the Hookean solids that represent most materials encountered in seismology exhibit a detached innermost sheet, the positive definiteness of the elasticity tensor, which is its sole fundamental constraint, allows for the existence of both detached and nondetached sheets. Besides the foundational considerations, the omnipresence of computer methods requires that we investigate cases that, even if not commonly encountered, are within the realm of physical possibility, and can appear as the output of modeling. The theorem proved for a general Hookean solid, has been exemplified using a particular case of transverse isotropy. For that case, it has been shown that the innermost sheet exhibits a polarization of a quasicompressional wave. However, this need not be a general property of that sheet because the presented theorem refers to convexity of the innermost sheet, not to its polarization.","internal_url":"https://www.academia.edu/32210964/On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet","translated_internal_url":"","created_at":"2017-04-02T19:02:23.564-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_convexity_and_detachment_of_innermost_wavefront_slowness_sheet","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":409,"name":"Geophysics","url":"https://www.academia.edu/Documents/in/Geophysics"},{"id":13883,"name":"Seismology","url":"https://www.academia.edu/Documents/in/Seismology"},{"id":48904,"name":"Elasticity","url":"https://www.academia.edu/Documents/in/Elasticity"},{"id":59249,"name":"Computers","url":"https://www.academia.edu/Documents/in/Computers"},{"id":176607,"name":"Polarisation","url":"https://www.academia.edu/Documents/in/Polarisation"},{"id":191543,"name":"Polarization","url":"https://www.academia.edu/Documents/in/Polarization"},{"id":222440,"name":"Waves","url":"https://www.academia.edu/Documents/in/Waves"},{"id":1029207,"name":"Tensor","url":"https://www.academia.edu/Documents/in/Tensor"},{"id":2353926,"name":"Isotropy","url":"https://www.academia.edu/Documents/in/Isotropy"}],"urls":[{"id":8044629,"url":"http://cat.inist.fr/?aModele=afficheN\u0026cpsidt=22037089"}]}, dispatcherData: dispatcherData }); 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210961"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210961/On_effective_elasticity_tensors"><img alt="Research paper thumbnail of On effective elasticity tensors" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210961/On_effective_elasticity_tensors">On effective elasticity tensors</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; by &quot;effective&quot;, we mean the closest in the sense of the Euclidean or log-Euclidean distance. It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. In general, the minimization process</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210961"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210961"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210961; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210961]").text(description); $(".js-view-count[data-work-id=32210961]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210961; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210961']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210961, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210961]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210961,"title":"On effective elasticity tensors","translated_title":"","metadata":{"abstract":"We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; by \u0026quot;effective\u0026quot;, we mean the closest in the sense of the Euclidean or log-Euclidean distance. It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. In general, the minimization process","publication_date":{"day":null,"month":null,"year":2008,"errors":{}}},"translated_abstract":"We consider the problem of obtaining the effective orthotropic tensor that corresponds to a given generally anisotropic one; by \u0026quot;effective\u0026quot;, we mean the closest in the sense of the Euclidean or log-Euclidean distance. It is difficult to find the absolute minimum of the distance function, since the minimization process is nonlinear, exhibiting several local minima. In general, the minimization process","internal_url":"https://www.academia.edu/32210961/On_effective_elasticity_tensors","translated_internal_url":"","created_at":"2017-04-02T19:02:23.104-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_effective_elasticity_tensors","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":10981,"name":"Data Assimilation","url":"https://www.academia.edu/Documents/in/Data_Assimilation"},{"id":318537,"name":"Local minima","url":"https://www.academia.edu/Documents/in/Local_minima"},{"id":504035,"name":"Three Dimensional","url":"https://www.academia.edu/Documents/in/Three_Dimensional"},{"id":1555351,"name":"Euclidean Distance","url":"https://www.academia.edu/Documents/in/Euclidean_Distance"},{"id":2064458,"name":"Transversely Isotropic Solids","url":"https://www.academia.edu/Documents/in/Transversely_Isotropic_Solids"}],"urls":[{"id":8044626,"url":"http://adsabs.harvard.edu/abs/2008AGUFM.S41C1868S"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210960"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210960/On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors"><img alt="Research paper thumbnail of On Characterization of Elasticity Parameters in Context of Measurement Errors" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210960/On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors">On Characterization of Elasticity Parameters in Context of Measurement Errors</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">In this presentation, we discuss the one-to-one relation between the elasticity parameters and th...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210960"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210960"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210960; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210960]").text(description); $(".js-view-count[data-work-id=32210960]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210960; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210960']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210960, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210960]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210960,"title":"On Characterization of Elasticity Parameters in Context of Measurement Errors","translated_title":"","metadata":{"abstract":"In this presentation, we discuss the one-to-one relation between the elasticity parameters and the traveltime and polarization of a propagating signal in the context of the measurement errors. 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The one-to-one relationship between seismic measurements and a model postulated in the realm of the constitutive equation of an elastic continuum provides the link between the observational and theoretical aspects of seismic","internal_url":"https://www.academia.edu/32210960/On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors","translated_internal_url":"","created_at":"2017-04-02T19:02:22.901-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_Characterization_of_Elasticity_Parameters_in_Context_of_Measurement_Errors","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[{"id":8183,"name":"Linear Elasticity","url":"https://www.academia.edu/Documents/in/Linear_Elasticity"},{"id":31477,"name":"Uncertainty Quantification","url":"https://www.academia.edu/Documents/in/Uncertainty_Quantification"},{"id":162403,"name":"Measurement Error","url":"https://www.academia.edu/Documents/in/Measurement_Error"},{"id":491689,"name":"Seismic Tomography","url":"https://www.academia.edu/Documents/in/Seismic_Tomography"},{"id":547093,"name":"Inverse Theory","url":"https://www.academia.edu/Documents/in/Inverse_Theory"},{"id":829227,"name":"Body Waves","url":"https://www.academia.edu/Documents/in/Body_Waves"},{"id":1231330,"name":"Constitutive Equation","url":"https://www.academia.edu/Documents/in/Constitutive_Equation"}],"urls":[{"id":8044625,"url":"http://adsabs.harvard.edu/abs/2007AGUFM.S34B..05S"}]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210959"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210959/On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial"><img alt="Research paper thumbnail of On Seismic Waves in Linearly Elastic, Anisotropic and Nonuniform Continua: Tutorial" class="work-thumbnail" src="https://attachments.academia-assets.com/52439615/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210959/On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial">On Seismic Waves in Linearly Elastic, Anisotropic and Nonuniform Continua: Tutorial</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exp...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exploration seismologists benefit from knowledge of these properties. This knowledge provides us with rock-physics information and also enables us to account for the effects of anisotropy and nonuniformity on seismic imaging. Anisotropy and nonuniformity are conveniently studied in the context of continuum mechanics. Aki and Richards (1980) at the beginning of their classic book, while referring to certain standard conjectures used in seismology, write “[t]hese conjectures, and many others that are generally assumed by seismologists to be true, are properties of infinitesimal motion in classical continuum mechanics for an elastic medium with a linear stress-strain relation”. This tutorial presents aspects of a scientific foundation for the study and interpretation of seismic wave phenomena in linearly elastic, anisotropic, nonuniform continua. It draws on continuum mechanics and the asympto...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="887d508096743a4889cfb2cd1840ff9c" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439615,"asset_id":32210959,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439615/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210959"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210959"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210959; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210959]").text(description); $(".js-view-count[data-work-id=32210959]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210959; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210959']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210959, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "887d508096743a4889cfb2cd1840ff9c" } } $('.js-work-strip[data-work-id=32210959]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210959,"title":"On Seismic Waves in Linearly Elastic, Anisotropic and Nonuniform Continua: Tutorial","translated_title":"","metadata":{"abstract":"Most sedimentary rocks are anisotropic. 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It draws on continuum mechanics and the asympto...","ai_title_tag":"Seismic Waves in Elastic Anisotropic Nonuniform Continua"},"translated_abstract":"Most sedimentary rocks are anisotropic. Most sedimentary basins are nonuniform. Consequently, exploration seismologists benefit from knowledge of these properties. This knowledge provides us with rock-physics information and also enables us to account for the effects of anisotropy and nonuniformity on seismic imaging. Anisotropy and nonuniformity are conveniently studied in the context of continuum mechanics. Aki and Richards (1980) at the beginning of their classic book, while referring to certain standard conjectures used in seismology, write “[t]hese conjectures, and many others that are generally assumed by seismologists to be true, are properties of infinitesimal motion in classical continuum mechanics for an elastic medium with a linear stress-strain relation”. This tutorial presents aspects of a scientific foundation for the study and interpretation of seismic wave phenomena in linearly elastic, anisotropic, nonuniform continua. It draws on continuum mechanics and the asympto...","internal_url":"https://www.academia.edu/32210959/On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial","translated_internal_url":"","created_at":"2017-04-02T19:02:22.774-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439615,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439615/thumbnails/1.jpg","file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r.pdf","download_url":"https://www.academia.edu/attachments/52439615/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439615/On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r-libre.pdf?1491185623=\u0026response-content-disposition=attachment%3B+filename%3DOn_Seismic_Waves_in_Linearly_Elastic_Ani.pdf\u0026Expires=1733049543\u0026Signature=XvoEr4oTgefM83dwdLgcjpdKKqUQ4pz1qxghepCrf~nl2p69O-S3LeSdLxiDKpCpyJUD3QBq53JPNB9~X5L46hPFGmvNcdKfseWnvaLHeYIMR~SPQAhPklF6rGivNxNTUJQ1cuOEqVylP8D2juImB4LBq3ZmnCbzUtfpLu4Ft1kL8MlSMlicJ8lplD0dvWLooXQ3o81bVXqQNDmIyS~uvrkUqSNEnlinYWgGsDVN9pz9K1tV2TH-crqixzIIyvmJuJ0xXI1gGiUIXVkizJhXcOdxXwPH2LO6nn62VcDF1RC~FJdt1~eE7Rnx5QIRwf6KO9~EUPb0HVu7drFcegtJgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"On_Seismic_Waves_in_Linearly_Elastic_Anisotropic_and_Nonuniform_Continua_Tutorial","translated_slug":"","page_count":8,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[{"id":52439615,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439615/thumbnails/1.jpg","file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r.pdf","download_url":"https://www.academia.edu/attachments/52439615/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"On_Seismic_Waves_in_Linearly_Elastic_Ani.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439615/On_Seismic_Waves_in_Linearly_Elastic_Ani20170402-6042-3c3b7r-libre.pdf?1491185623=\u0026response-content-disposition=attachment%3B+filename%3DOn_Seismic_Waves_in_Linearly_Elastic_Ani.pdf\u0026Expires=1733049543\u0026Signature=XvoEr4oTgefM83dwdLgcjpdKKqUQ4pz1qxghepCrf~nl2p69O-S3LeSdLxiDKpCpyJUD3QBq53JPNB9~X5L46hPFGmvNcdKfseWnvaLHeYIMR~SPQAhPklF6rGivNxNTUJQ1cuOEqVylP8D2juImB4LBq3ZmnCbzUtfpLu4Ft1kL8MlSMlicJ8lplD0dvWLooXQ3o81bVXqQNDmIyS~uvrkUqSNEnlinYWgGsDVN9pz9K1tV2TH-crqixzIIyvmJuJ0xXI1gGiUIXVkizJhXcOdxXwPH2LO6nn62VcDF1RC~FJdt1~eE7Rnx5QIRwf6KO9~EUPb0HVu7drFcegtJgA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210958"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210958/Angle_of_Incidence_as_a_Function_of_Source_receiver_Offset_of_a_Dipping_Refractor_An_Exact_Expression_for_VSP_Apllications"><img alt="Research paper thumbnail of Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications" class="work-thumbnail" src="https://attachments.academia-assets.com/52439613/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210958/Angle_of_Incidence_as_a_Function_of_Source_receiver_Offset_of_a_Dipping_Refractor_An_Exact_Expression_for_VSP_Apllications">Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however,...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Reflection amplitudes are intimately connected to the angle of incidence. In seismology, however, the angle of incidence is often difficult to establish. Partially, because of this difficulty it is more common to consider Amplitude Variations as a function of a lateral source-receiver Offset (AVO) rather than Amplitude Variations as a function of the Angle of incidence (AVA). Computational modelling and theoretical analysis, nevertheless, require the knowledge of angles of incidence in order to relate them directly to various forms of Zoeppritz equations (e.g., Aki and Richards, 1980). Furthermore, although a lateral source-receiver offset is eas-ily established based on field acquisition parameters, the angle of incidence requires a more involved calculation. This Short Note provides explicit and exact expressions which can be used in AVA studies using the Vertical Seismic Profile (VSP). The expressions can be conveniently used in planning an AVAiAVO survey while designing source-r...</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ce0e975575eacb4009209bca1ee2c6b1" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439613,"asset_id":32210958,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439613/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210958"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210958"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210958; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210958]").text(description); $(".js-view-count[data-work-id=32210958]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210958; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210958']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210958, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ce0e975575eacb4009209bca1ee2c6b1" } } $('.js-work-strip[data-work-id=32210958]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210958,"title":"Angle of Incidence as a Function of Source-receiver Offset of a Dipping Refractor; An Exact Expression for VSP Apllications","translated_title":"","metadata":{"abstract":"Reflection amplitudes are intimately connected to the angle of incidence. 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$(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210957"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210957/VSP_Reflection_Points_for_Linear_Inhomogeneity_and_Elliptical_Anisotropy"><img alt="Research paper thumbnail of VSP Reflection Points for Linear Inhomogeneity and Elliptical Anisotropy" class="work-thumbnail" src="https://attachments.academia-assets.com/52439617/thumbnails/1.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210957/VSP_Reflection_Points_for_Linear_Inhomogeneity_and_Elliptical_Anisotropy">VSP Reflection Points for Linear Inhomogeneity and Elliptical Anisotropy</a></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">An exact analytical expression for traveltime in a medium with a constant velocity gradient and e...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">An exact analytical expression for traveltime in a medium with a constant velocity gradient and elliptical velocity dependence is used to calculate possible reflection points for a given source receiver geometry. The set of reflection points are collectively referred to as the illumination zone. Also, we give an expression that can be used to trace rays in a vertically inhomogeneous elliptically anisotropic medi-um. These expressions are applicable for both survey design and data interpretation.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><a id="ee199ca5530151b57ee0bd0856539e19" class="wp-workCard--action" rel="nofollow" data-click-track="profile-work-strip-download" data-download="{"attachment_id":52439617,"asset_id":32210957,"asset_type":"Work","button_location":"profile"}" href="https://www.academia.edu/attachments/52439617/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&s=profile"><span><i class="fa fa-arrow-down"></i></span><span>Download</span></a><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210957"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210957"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210957; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210957]").text(description); $(".js-view-count[data-work-id=32210957]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210957; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210957']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210957, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (true){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "ee199ca5530151b57ee0bd0856539e19" } } $('.js-work-strip[data-work-id=32210957]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210957,"title":"VSP Reflection Points for Linear Inhomogeneity and Elliptical Anisotropy","translated_title":"","metadata":{"abstract":"An exact analytical expression for traveltime in a medium with a constant velocity gradient and elliptical velocity dependence is used to calculate possible reflection points for a given source receiver geometry. 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Inferring material properties of t...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">Geophysics—similarly to astrophysics—relies on remote sensing. Inferring material properties of the Earth’s interior is akin to inferring the composition of a distant star. In both cases, scientists rely on matching theoretical predictions or explanations with observations. Notably, obtaining a sample of a material from the interior of our planet might not be less difficult than obtaining a sample from a distant celestial object. To infer the presence and orientations of subsurface fractures, seismologists might use directional properties of Hookean solids. In other words—using such a solid as a mathematical model— seismologists match its quantitative predictions with observations.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210956"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210956"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210956; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210956]").text(description); $(".js-view-count[data-work-id=32210956]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210956; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210956']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210956, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210956]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210956,"title":"On Hookean Solids in Seismology: Anisotropy and Fractures","translated_title":"","metadata":{"abstract":"Geophysics—similarly to astrophysics—relies on remote sensing. 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Notably, obtaining a sample of a material from the interior of our planet might not be less difficult than obtaining a sample from a distant celestial object. To infer the presence and orientations of subsurface fractures, seismologists might use directional properties of Hookean solids. In other words—using such a solid as a mathematical model— seismologists match its quantitative predictions with observations.","internal_url":"https://www.academia.edu/32210956/On_Hookean_Solids_in_Seismology_Anisotropy_and_Fractures","translated_internal_url":"","created_at":"2017-04-02T19:02:22.451-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[],"slug":"On_Hookean_Solids_in_Seismology_Anisotropy_and_Fractures","translated_slug":"","page_count":null,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[],"research_interests":[],"urls":[]}, dispatcherData: dispatcherData }); 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The resulting effective tensor is the highestlikelihood estimate within the specified symmetry class. Given two material-symmetry classes, with one included in the other, the weighted Frobenius distance from the given tensor to the two effective tensors can be used to decide between the two models-one with higher and one with lower symmetry-by means of the likelihood ratio test.","publication_date":{"day":null,"month":null,"year":2015,"errors":{}},"publication_name":"Journal of Elasticity","grobid_abstract_attachment_id":52439614},"translated_abstract":null,"internal_url":"https://www.academia.edu/32210955/Effective_Elasticity_Tensors_in_Context_of_Random_Errors","translated_internal_url":"","created_at":"2017-04-02T19:02:22.353-07:00","preview_url":null,"current_user_can_edit":null,"current_user_is_owner":null,"owner_id":34310548,"coauthors_can_edit":true,"document_type":"paper","co_author_tags":[],"downloadable_attachments":[{"id":52439614,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439614/thumbnails/1.jpg","file_name":"Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3.pdf","download_url":"https://www.academia.edu/attachments/52439614/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_Elasticity_Tensors_in_Context.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439614/Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3-libre.pdf?1491185629=\u0026response-content-disposition=attachment%3B+filename%3DEffective_Elasticity_Tensors_in_Context.pdf\u0026Expires=1733049543\u0026Signature=Wk2aJ6FdiBGuE7JOs6E2eSXwkkggB1G6OopMv5sNHNjnxYxWeqtNFTgjf4pUOGTHYIu0XEYU97jyCx3z-KhGhNZFj3PiJits32nXe2QZrfoK3vWXa0EQmbZA9zPrpKC-F-5iR9upqZUjaANPu-l2fdX9lxBSA6JP4TG2atQ~10sT7hqX14VxXgzdWWB0lrTcqQCDJWLbXn0Fp5HofiWHkVPANH86G-PvXJrqW4aMF~Fht5ypNH1XsswIm5zdjxrxG1FLrtiVd74WApQYDIpBCZmTxfJDKWe6sV-5Bs1AE8JZhRUaxVfjPWaQoZl5RzkDZtuJCjV6hHSlxlGx--varA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"slug":"Effective_Elasticity_Tensors_in_Context_of_Random_Errors","translated_slug":"","page_count":15,"language":"en","content_type":"Work","owner":{"id":34310548,"first_name":"Michael","middle_initials":null,"last_name":"Slawinski","page_name":"MSlawinski","domain_name":"independent","created_at":"2015-08-27T23:12:03.624-07:00","display_name":"Michael Slawinski","url":"https://independent.academia.edu/MSlawinski"},"attachments":[{"id":52439614,"title":"","file_type":"pdf","scribd_thumbnail_url":"https://attachments.academia-assets.com/52439614/thumbnails/1.jpg","file_name":"Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3.pdf","download_url":"https://www.academia.edu/attachments/52439614/download_file?st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&st=MTczMzA0NTk0Myw4LjIyMi4yMDguMTQ2&","bulk_download_file_name":"Effective_Elasticity_Tensors_in_Context.pdf","bulk_download_url":"https://d1wqtxts1xzle7.cloudfront.net/52439614/Effective_Elasticity_Tensors_in_Context_20170402-6036-1vyufj3-libre.pdf?1491185629=\u0026response-content-disposition=attachment%3B+filename%3DEffective_Elasticity_Tensors_in_Context.pdf\u0026Expires=1733049543\u0026Signature=Wk2aJ6FdiBGuE7JOs6E2eSXwkkggB1G6OopMv5sNHNjnxYxWeqtNFTgjf4pUOGTHYIu0XEYU97jyCx3z-KhGhNZFj3PiJits32nXe2QZrfoK3vWXa0EQmbZA9zPrpKC-F-5iR9upqZUjaANPu-l2fdX9lxBSA6JP4TG2atQ~10sT7hqX14VxXgzdWWB0lrTcqQCDJWLbXn0Fp5HofiWHkVPANH86G-PvXJrqW4aMF~Fht5ypNH1XsswIm5zdjxrxG1FLrtiVd74WApQYDIpBCZmTxfJDKWe6sV-5Bs1AE8JZhRUaxVfjPWaQoZl5RzkDZtuJCjV6hHSlxlGx--varA__\u0026Key-Pair-Id=APKAJLOHF5GGSLRBV4ZA"}],"research_interests":[{"id":56,"name":"Materials Engineering","url":"https://www.academia.edu/Documents/in/Materials_Engineering"},{"id":73,"name":"Civil Engineering","url":"https://www.academia.edu/Documents/in/Civil_Engineering"},{"id":305,"name":"Applied Mathematics","url":"https://www.academia.edu/Documents/in/Applied_Mathematics"},{"id":48904,"name":"Elasticity","url":"https://www.academia.edu/Documents/in/Elasticity"}],"urls":[]}, dispatcherData: dispatcherData }); $(this).data('initialized', true); } }); $a.trackClickSource(".js-work-strip-work-link", "profile_work_strip") }); </script> <div class="js-work-strip profile--work_container" data-work-id="32210954"><div class="profile--work_thumbnail hidden-xs"><a class="js-work-strip-work-link" data-click-track="profile-work-strip-thumbnail" href="https://www.academia.edu/32210954/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications"><img alt="Research paper thumbnail of VSP‐traveltime inversion for linear‐velocity constants based on nonlinear regression with survey‐design applications" class="work-thumbnail" src="https://a.academia-assets.com/images/blank-paper.jpg" /></a></div><div class="wp-workCard wp-workCard_itemContainer"><div class="wp-workCard_item wp-workCard--title"><a class="js-work-strip-work-link text-gray-darker" data-click-track="profile-work-strip-title" href="https://www.academia.edu/32210954/VSP_traveltime_inversion_for_linear_velocity_constants_based_on_nonlinear_regression_with_survey_design_applications">VSP‐traveltime inversion for linear‐velocity constants based on nonlinear regression with survey‐design applications</a></div><div class="wp-workCard_item"><span>SEG Technical Program Expanded Abstracts 2000</span><span>, 2000</span></div><div class="wp-workCard_item"><span class="js-work-more-abstract-truncated">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption...</span><a class="js-work-more-abstract" data-broccoli-component="work_strip.more_abstract" data-click-track="profile-work-strip-more-abstract" href="javascript:;"><span> more </span><span><i class="fa fa-caret-down"></i></span></a><span class="js-work-more-abstract-untruncated hidden">ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.</span></div><div class="wp-workCard_item wp-workCard--actions"><span class="work-strip-bookmark-button-container"></span><span class="wp-workCard--action visible-if-viewed-by-owner inline-block" style="display: none;"><span class="js-profile-work-strip-edit-button-wrapper profile-work-strip-edit-button-wrapper" data-work-id="32210954"><a class="js-profile-work-strip-edit-button" tabindex="0"><span><i class="fa fa-pencil"></i></span><span>Edit</span></a></span></span><span id="work-strip-rankings-button-container"></span></div><div class="wp-workCard_item wp-workCard--stats"><span><span><span class="js-view-count view-count u-mr2x" data-work-id="32210954"><i class="fa fa-spinner fa-spin"></i></span><script>$(function () { var workId = 32210954; window.Academia.workViewCountsFetcher.queue(workId, function (count) { var description = window.$h.commaizeInt(count) + " " + window.$h.pluralize(count, 'View'); $(".js-view-count[data-work-id=32210954]").text(description); $(".js-view-count[data-work-id=32210954]").attr('title', description).tooltip(); }); });</script></span></span><span><span class="percentile-widget hidden"><span class="u-mr2x work-percentile"></span></span><script>$(function () { var workId = 32210954; window.Academia.workPercentilesFetcher.queue(workId, function (percentileText) { var container = $(".js-work-strip[data-work-id='32210954']"); container.find('.work-percentile').text(percentileText.charAt(0).toUpperCase() + percentileText.slice(1)); container.find('.percentile-widget').show(); container.find('.percentile-widget').removeClass('hidden'); }); });</script></span><span><script>$(function() { new Works.PaperRankView({ workId: 32210954, container: "", }); });</script></span></div><div id="work-strip-premium-row-container"></div></div></div><script> require.config({ waitSeconds: 90 })(["https://a.academia-assets.com/assets/wow_profile-f77ea15d77ce96025a6048a514272ad8becbad23c641fc2b3bd6e24ca6ff1932.js","https://a.academia-assets.com/assets/work_edit-ad038b8c047c1a8d4fa01b402d530ff93c45fee2137a149a4a5398bc8ad67560.js"], function() { // from javascript_helper.rb var dispatcherData = {} if (false){ window.WowProfile.dispatcher = window.WowProfile.dispatcher || _.clone(Backbone.Events); dispatcherData = { dispatcher: window.WowProfile.dispatcher, downloadLinkId: "-1" } } $('.js-work-strip[data-work-id=32210954]').each(function() { if (!$(this).data('initialized')) { new WowProfile.WorkStripView({ el: this, workJSON: {"id":32210954,"title":"VSP‐traveltime inversion for linear‐velocity constants based on nonlinear regression with survey‐design applications","translated_title":"","metadata":{"abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. The velocity function is related to the global rather than to the local properties.","publication_date":{"day":null,"month":null,"year":2000,"errors":{}},"publication_name":"SEG Technical Program Expanded Abstracts 2000"},"translated_abstract":"ABSTRACT This paper considers traveltime related to oblique ray trajectories under the assumption of linear velocity as a function of depth. Exact travel time expressions for oblique ray paths are used for a rigorous nonlinear regression analysis of zero and offset Vertical Seismic Profile (VSP) field measurements. The statistical validity of the linear-velocity models obtained from the regression analysis, shows a good fit within an acceptable range of experimental error. Numerous earlier practical investigations, which inspired our study, have been confined to the one-dimensional realm of a wellbore and acoustic log data. By contrast, offset VSP’s provide traveltime information for many source-receiver configurations. The assumption of a simple analytic velocity function is a convenient and practical approach to traveltime estimation and for modelling the prestack surface seismic or VSP data itself. Furthermore, for large source-receiver offsets involved in imaging and AVO studies, a linear-velocity function yields a conveniently simple yet reasonable estimate of ray trajectories and angles of incidence. Even an excellent fit between a linear-velocity function and experimental data, however, does not provide a direct source of lithological information. 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