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class="vector-toc-numb">1.6</span> <span>Terrestrial Tomography</span> </div> </a> <ul id="toc-Terrestrial_Tomography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Crystallography" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Crystallography"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.7</span> <span>Crystallography</span> </div> </a> <ul id="toc-Crystallography-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geophysics" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geophysics"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.8</span> <span>Geophysics</span> </div> </a> <ul id="toc-Geophysics-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geomorphology" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geomorphology"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.9</span> <span>Geomorphology</span> 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nowraplinks hlist"><tbody><tr><td class="sidebar-pretitle">Part of a series on</td></tr><tr><th class="sidebar-title-with-pretitle"><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a></th></tr><tr><td class="sidebar-above" style="padding-bottom:0.35em;"> <ul><li><a href="/wiki/History_of_mathematics" title="History of mathematics">History</a></li> <li><a href="/wiki/Lists_of_mathematics_topics" title="Lists of mathematics topics">Index</a></li></ul></td></tr><tr><td class="sidebar-content-with-subgroup"> <table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;;color: var(--color-base)"><a href="/wiki/Areas_of_mathematics" class="mw-redirect" title="Areas of mathematics">Areas</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/Number_theory" title="Number theory">Number theory</a></li> <li><a href="/wiki/Geometry" title="Geometry">Geometry</a></li> <li><a href="/wiki/Algebra" title="Algebra">Algebra</a></li> <li><a href="/wiki/Calculus" title="Calculus">Calculus</a> and <a href="/wiki/Mathematical_analysis" title="Mathematical analysis">Analysis</a></li> <li><a href="/wiki/Discrete_mathematics" title="Discrete mathematics">Discrete mathematics</a></li> <li><a href="/wiki/Mathematical_logic" title="Mathematical logic">Logic</a> and <a href="/wiki/Set_theory" title="Set theory">Set theory</a></li> <li><a href="/wiki/Probability" title="Probability">Probability</a></li> <li><a href="/wiki/Statistics" title="Statistics">Statistics</a> and <a href="/wiki/Decision_theory" title="Decision theory">Decision theory</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;;color: 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</tr></tbody></table></td> </tr><tr><th class="sidebar-heading"> <span typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/20px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="20" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/30px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/40px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:Mathematics" title="Portal:Mathematics">Mathematics Portal</a></th></tr><tr><td class="sidebar-navbar"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1239400231">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Math_topics_sidebar" title="Template:Math topics sidebar"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Math_topics_sidebar" title="Template talk:Math topics sidebar"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Math_topics_sidebar" title="Special:EditPage/Template:Math topics sidebar"><abbr title="Edit this template">e</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>Geomathematics</b> (also: <b>mathematical geosciences</b>, <b>mathematical geology</b>, <b>mathematical geophysics</b>) is the application of <a href="/wiki/Mathematical" class="mw-redirect" title="Mathematical">mathematical</a> methods to solve problems in <a href="/wiki/Geosciences" class="mw-redirect" title="Geosciences">geosciences</a>, including <a href="/wiki/Geology" title="Geology">geology</a> and <a href="/wiki/Geophysics" title="Geophysics">geophysics</a>, and particularly <a href="/wiki/Geodynamics" title="Geodynamics">geodynamics</a> and <a href="/wiki/Seismology" title="Seismology">seismology</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Applications">Applications</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=1" title="Edit section: Applications"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Geophysical_fluid_dynamics">Geophysical fluid dynamics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=2" title="Edit section: Geophysical fluid dynamics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Geophysical_fluid_dynamics" title="Geophysical fluid dynamics">Geophysical fluid dynamics</a> develops the theory of <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid dynamics</a> for the atmosphere, ocean and Earth's interior.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Applications include geodynamics and the theory of the <a href="/wiki/Geodynamo" class="mw-redirect" title="Geodynamo">geodynamo</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Geophysical_inverse_theory">Geophysical inverse theory</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=3" title="Edit section: Geophysical inverse theory"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Geophysical <a href="/wiki/Inverse_theory" class="mw-redirect" title="Inverse theory">inverse theory</a> is concerned with analyzing geophysical data to get model parameters.<sup id="cite_ref-Parker_2-0" class="reference"><a href="#cite_note-Parker-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Tarantola_3-0" class="reference"><a href="#cite_note-Tarantola-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> It is concerned with the question: What can be known about the Earth's interior from measurements on the surface? Generally there are limits on what can be known even in the ideal limit of exact data.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>The goal of inverse theory is to determine the spatial distribution of some variable (for example, density or seismic wave velocity). The distribution determines the values of an observable at the surface (for example, gravitational acceleration for density). There must be a <i>forward model</i> predicting the surface observations given the distribution of this variable. </p><p>Applications include <a href="/wiki/Geomagnetism" class="mw-redirect" title="Geomagnetism">geomagnetism</a>, <a href="/wiki/Magnetotellurics" title="Magnetotellurics">magnetotellurics</a> and seismology. </p> <div class="mw-heading mw-heading3"><h3 id="Fractals_and_complexity">Fractals and complexity</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=4" title="Edit section: Fractals and complexity"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many geophysical data sets have spectra that follow a <a href="/wiki/Power_law" title="Power law">power law</a>, meaning that the frequency of an observed magnitude varies as some power of the magnitude. An example is the distribution of <a href="/wiki/Earthquake" title="Earthquake">earthquake</a> magnitudes; small earthquakes are far more common than large earthquakes. This is often an indicator that the data sets have an underlying <a href="/wiki/Fractal" title="Fractal">fractal</a> geometry. Fractal sets have a number of common features, including structure at many scales, irregularity, and <a href="/wiki/Self-similarity" title="Self-similarity">self-similarity</a> (they can be split into parts that look much like the whole). The manner in which these sets can be divided determine the <a href="/wiki/Hausdorff_dimension" title="Hausdorff dimension">Hausdorff dimension</a> of the set, which is generally different from the more familiar <a href="/wiki/Topological_dimension" class="mw-redirect" title="Topological dimension">topological dimension</a>. Fractal phenomena are associated with <a href="/wiki/Chaos_theory" title="Chaos theory">chaos</a>, <a href="/wiki/Self-organized_criticality" title="Self-organized criticality">self-organized criticality</a> and <a href="/wiki/Turbulence" title="Turbulence">turbulence</a>.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Fractal Models in the Earth Sciences by <a href="/wiki/Gabor_Korvin" title="Gabor Korvin">Gabor Korvin</a> was one of the earlier books on the application of <a href="/wiki/Fractals" class="mw-redirect" title="Fractals">Fractals</a> in the <a href="/wiki/Earth_Sciences" class="mw-redirect" title="Earth Sciences">Earth Sciences</a>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Data_assimilation">Data assimilation</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=5" title="Edit section: Data assimilation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Data_assimilation" title="Data assimilation">Data assimilation</a> combines numerical models of geophysical systems with observations that may be irregular in space and time. Many of the applications involve geophysical fluid dynamics. Fluid dynamic models are governed by a set of <a href="/wiki/Partial_differential_equations" class="mw-redirect" title="Partial differential equations">partial differential equations</a>. For these equations to make good predictions, accurate initial conditions are needed. However, often the initial conditions are not very well known. Data assimilation methods allow the models to incorporate later observations to improve the initial conditions. Data assimilation plays an increasingly important role in <a href="/wiki/Weather_forecasting" title="Weather forecasting">weather forecasting</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Geophysical_statistics">Geophysical statistics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=6" title="Edit section: Geophysical statistics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Some statistical problems come under the heading of mathematical geophysics, including <a href="/wiki/Model_validation" class="mw-redirect" title="Model validation">model validation</a> and quantifying uncertainty. </p> <div class="mw-heading mw-heading3"><h3 id="Terrestrial_Tomography">Terrestrial Tomography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=7" title="Edit section: Terrestrial Tomography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>An important research area that utilises inverse methods is <a href="/wiki/Seismic_tomography" title="Seismic tomography">seismic tomography</a>, a technique for imaging the subsurface of the Earth using <a href="/wiki/Seismic_waves" class="mw-redirect" title="Seismic waves">seismic waves</a>. Traditionally seismic waves produced by <a href="/wiki/Earthquakes" class="mw-redirect" title="Earthquakes">earthquakes</a> or anthropogenic seismic sources (e.g., explosives, marine air guns) were used. </p> <div class="mw-heading mw-heading3"><h3 id="Crystallography">Crystallography</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=8" title="Edit section: Crystallography"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Crystallography" title="Crystallography">Crystallography</a> is one of the traditional areas of <a href="/wiki/Geology" title="Geology">geology</a> that use <a href="/wiki/Mathematics" title="Mathematics">mathematics</a>. Crystallographers make use of <a href="/wiki/Linear_algebra" title="Linear algebra">linear algebra</a> by using the <a href="/wiki/Metric_tensor" title="Metric tensor">Metrical Matrix</a>. The <a href="/wiki/Metric_tensor" title="Metric tensor">Metrical Matrix</a> uses the basis vectors of the <a href="/wiki/Crystal_structure" title="Crystal structure">unit cell</a> dimensions to find the volume of a unit cell, d-spacings, the angle between two planes, the angle between atoms, and the bond length.<sup id="cite_ref-:0_8-0" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> Miller's Index is also helpful in the application of the <a href="/wiki/Metric_tensor" title="Metric tensor">Metrical Matrix</a>. <a href="/wiki/Bragg%27s_law" title="Bragg's law">Brag's equation</a> is also useful when using an <a href="/wiki/Electron_microscope" title="Electron microscope">electron microscope</a> to be able to show relationship between light diffraction angles, wavelength, and the d-spacings within a sample.<sup id="cite_ref-:0_8-1" class="reference"><a href="#cite_note-:0-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Geophysics">Geophysics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=9" title="Edit section: Geophysics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Geophysics" title="Geophysics">Geophysics</a> is one of the most <a href="/wiki/Mathematics" title="Mathematics">math</a> heavy disciplines of <a href="/wiki/Earth_Science" class="mw-redirect" title="Earth Science">Earth Science</a>. There are many applications which include <a href="/wiki/Gravity" title="Gravity">gravity</a>, <a href="/wiki/Magnetism" title="Magnetism">magnetic</a>, <a href="/wiki/Seismology" title="Seismology">seismic</a>, <a href="/wiki/Electricity" title="Electricity">electric</a>, <a href="/wiki/Electromagnetism" title="Electromagnetism">electromagnetic</a>, <a href="/wiki/Resistivity_logging" title="Resistivity logging">resistivity</a>, radioactivity, induced polarization, and <a href="/wiki/Well_logging" title="Well logging">well logging</a>.<sup id="cite_ref-:1_9-0" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Gravity and magnetic methods share similar characteristics because they're measuring small changes in the gravitational field based on the density of the rocks in that area.<sup id="cite_ref-:1_9-1" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> While similar <a href="/wiki/Physical_geodesy" title="Physical geodesy">gravity fields</a> tend to be more uniform and smooth compared to <a href="/wiki/Magnetic_field" title="Magnetic field">magnetic fields</a>. Gravity is used often for <a href="/wiki/Hydrocarbon_exploration" title="Hydrocarbon exploration">oil exploration</a> and seismic can also be used, but it is often significantly more expensive.<sup id="cite_ref-:1_9-2" class="reference"><a href="#cite_note-:1-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Seismic is used more than most geophysics techniques because of its ability to penetrate, its resolution, and its accuracy. </p> <div class="mw-heading mw-heading3"><h3 id="Geomorphology">Geomorphology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=10" title="Edit section: Geomorphology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Many applications of <a href="/wiki/Mathematics" title="Mathematics">mathematics</a> in <a href="/wiki/Geomorphology" title="Geomorphology">geomorphology</a> are related to water. In the <a href="/wiki/Soil_mechanics" title="Soil mechanics">soil</a> aspect things like <a href="/wiki/Darcy%27s_law" title="Darcy's law">Darcy's law</a>, <a href="/wiki/Stokes%27_law" title="Stokes' law">Stokes' law</a>, and <a href="/wiki/Pore_space_in_soil" title="Pore space in soil">porosity</a> are used. </p> <ul><li><a href="/wiki/Darcy%27s_law" title="Darcy's law">Darcy's law</a> is used when one has a saturated soil that is uniform to describe how <a href="/wiki/Fluid_dynamics" title="Fluid dynamics">fluid flows</a> through that medium.<sup id="cite_ref-:2_10-0" class="reference"><a href="#cite_note-:2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This type of work would fall under <a href="/wiki/Hydrogeology" title="Hydrogeology">hydrogeology</a>.</li> <li><a href="/wiki/Stokes%27_law" title="Stokes' law">Stokes' law</a> measures how quickly different sized particles will settle out of a fluid.<sup id="cite_ref-:2_10-1" class="reference"><a href="#cite_note-:2-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> This is used when doing <a href="/wiki/Particle-size_distribution" title="Particle-size distribution">pipette analysis</a> of soils to find the percentage sand vs silt vs clay.<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup> A potential error is it assumes perfectly spherical particles which don't exist.</li> <li><a href="/wiki/Stream_power" title="Stream power">Stream power</a> is used to find the ability of a river to <a href="/wiki/River_incision" title="River incision">incise</a> into the <a href="/wiki/Stream_bed" title="Stream bed">river bed</a>. This is applicable to see where a river is likely to fail and change course or when looking at the damage of losing stream sediments on a river system (like downstream of a dam).</li> <li><a href="/wiki/Differential_equation" title="Differential equation">Differential equations</a> can be used in multiple areas of <a href="/wiki/Geomorphology" title="Geomorphology">geomorphology</a> including: The <a href="/wiki/Exponential_growth" title="Exponential growth">exponential growth equation</a>, distribution of sedimentary rocks, <a href="/wiki/Gas_diffusion_in_soil" class="mw-redirect" title="Gas diffusion in soil">diffusion of gas</a> through rocks, and <a href="/wiki/Crenulation" title="Crenulation">crenulation</a> cleavages.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup></li></ul> <div class="mw-heading mw-heading3"><h3 id="Glaciology">Glaciology</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=11" title="Edit section: Glaciology"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Mathematics" title="Mathematics">Mathematics</a> in <a href="/wiki/Glaciology" title="Glaciology">Glaciology</a> consists of theoretical, experimental, and modeling. It usually covers <a href="/wiki/Glacier" title="Glacier">glaciers</a>, <a href="/wiki/Sea_ice" title="Sea ice">sea ice</a>, <a href="/wiki/Environmental_flow" title="Environmental flow">waterflow</a>, and the land under the glacier. </p><p><a href="/wiki/Crystallite" title="Crystallite">Polycrystalline</a> ice deforms slower than single crystalline ice, due to the stress being on the basal planes that are already blocked by other ice crystals.<sup id="cite_ref-:3_13-0" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> It can be <a href="/wiki/Mathematical_model" title="Mathematical model">mathematically modeled</a> with <a href="/wiki/Hooke%27s_law" title="Hooke's law">Hooke's Law</a> to show the elastic characteristics while using <a href="/wiki/Lam%C3%A9_parameters" title="Lamé parameters">Lamé constants</a>.<sup id="cite_ref-:3_13-1" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Generally the ice has its linear <a href="/wiki/Elasticity_(physics)" title="Elasticity (physics)">elasticity</a> constants averaged over one dimension of space to simplify the equations while still maintaining accuracy.<sup id="cite_ref-:3_13-2" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p><a href="/wiki/Viscoelasticity" title="Viscoelasticity">Viscoelastic</a> <a href="/wiki/Crystallite" title="Crystallite">polycrystalline</a> ice is considered to have low amounts of <a href="/wiki/Stress_(mechanics)" title="Stress (mechanics)">stress</a> usually below one <a href="/wiki/Bar_(unit)" title="Bar (unit)">bar</a>.<sup id="cite_ref-:3_13-3" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> This type of ice system is where one would test for <a href="/wiki/Creep_(deformation)" title="Creep (deformation)">creep</a> or <a href="/wiki/Vibration" title="Vibration">vibrations</a> from the <a href="/wiki/Tension_(physics)" title="Tension (physics)">tension</a> on the ice. One of the more important equations to this area of study is called the relaxation function.<sup id="cite_ref-:3_13-4" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> Where it's a <a href="/wiki/Stress-strain_relationship" class="mw-redirect" title="Stress-strain relationship">stress-strain</a> relationship independent of time.<sup id="cite_ref-:3_13-5" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> This area is usually applied to transportation or building onto floating ice.<sup id="cite_ref-:3_13-6" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p><p>Shallow-Ice approximation is useful for <a href="/wiki/Glacier" title="Glacier">glaciers</a> that have variable thickness, with a small amount of stress and variable velocity.<sup id="cite_ref-:3_13-7" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> One of the main goals of the mathematical work is to be able to predict the stress and velocity. Which can be affected by changes in the properties of the ice and temperature. This is an area in which the basal shear-stress formula can be used.<sup id="cite_ref-:3_13-8" class="reference"><a href="#cite_note-:3-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Academic_journals">Academic journals</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=12" title="Edit section: Academic journals"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><i><a href="/w/index.php?title=International_Journal_on_Geomathematics&action=edit&redlink=1" class="new" title="International Journal on Geomathematics (page does not exist)">International Journal on Geomathematics</a></i></li> <li><i><a href="/wiki/Mathematical_Geosciences" title="Mathematical Geosciences">Mathematical Geosciences</a></i></li></ul> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=13" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Geocomputation" title="Geocomputation">Geocomputation</a></li> <li><a href="/wiki/Geoinformatics" title="Geoinformatics">Geoinformatics</a></li> <li><a href="/wiki/International_Association_for_Mathematical_Geosciences" title="International Association for Mathematical Geosciences">International Association for Mathematical Geosciences</a> (IAMG)</li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=14" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><a href="#CITEREFPedlosky2005">Pedlosky 2005</a></span> </li> <li id="cite_note-Parker-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Parker_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFParker1994">Parker 1994</a></span> </li> <li id="cite_note-Tarantola-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-Tarantola_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTarantola1987">Tarantola 1987</a></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><a href="#CITEREFParker1994">Parker 1994</a>, chapter 2</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><a href="#CITEREFTurcotte1997">Turcotte 1997</a></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFKorvin_G.1992" class="citation book cs1">Korvin G. (1992). <i>Fractal Methods in the Earth Science</i>. Amsterdam: Elsevier.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fractal+Methods+in+the+Earth+Science.&rft.place=Amsterdam&rft.pub=Elsevier&rft.date=1992&rft.au=Korvin+G.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><a href="#CITEREFWangZouZhu2000">Wang, Zou & Zhu 2000</a></span> </li> <li id="cite_note-:0-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-:0_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:0_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGibbs" class="citation book cs1">Gibbs, G. V. <i>The Metrical Matrix in Teaching Mineralogy</i>. Virginia Polytechnic Institute and State University. pp. 201–212.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=The+Metrical+Matrix+in+Teaching+Mineralogy&rft.pages=201-212&rft.pub=Virginia+Polytechnic+Institute+and+State+University&rft.aulast=Gibbs&rft.aufirst=G.+V.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> <li id="cite_note-:1-9"><span class="mw-cite-backlink">^ <a href="#cite_ref-:1_9-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:1_9-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:1_9-2"><sup><i><b>c</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTelfordGeldartSheriff1990" class="citation book cs1">Telford, W. M.; Geldart, L. P.; Sheriff, R. E. (1990-10-26). <i>Applied Geophysics</i> (2 ed.). <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780521339384" title="Special:BookSources/9780521339384"><bdi>9780521339384</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Applied+Geophysics&rft.edition=2&rft.pub=Cambridge+University+Press&rft.date=1990-10-26&rft.isbn=9780521339384&rft.aulast=Telford&rft.aufirst=W.+M.&rft.au=Geldart%2C+L.+P.&rft.au=Sheriff%2C+R.+E.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> <li id="cite_note-:2-10"><span class="mw-cite-backlink">^ <a href="#cite_ref-:2_10-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:2_10-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHillel2003" class="citation book cs1">Hillel, Daniel (2003-11-05). <i>Introduction to Environmental Soil Physics</i> (1 ed.). <a href="/wiki/Academic_Press" title="Academic Press">Academic Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780123486554" title="Special:BookSources/9780123486554"><bdi>9780123486554</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Introduction+to+Environmental+Soil+Physics&rft.edition=1&rft.pub=Academic+Press&rft.date=2003-11-05&rft.isbn=9780123486554&rft.aulast=Hillel&rft.aufirst=Daniel&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLiuPh.D2008" class="citation book cs1">Liu, Cheng; Ph.D, Jack Evett (2008-04-16). <i>Soil Properties: Testing, Measurement, and Evaluation</i> (6 ed.). Pearson. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780136141235" title="Special:BookSources/9780136141235"><bdi>9780136141235</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Soil+Properties%3A+Testing%2C+Measurement%2C+and+Evaluation&rft.edition=6&rft.pub=Pearson&rft.date=2008-04-16&rft.isbn=9780136141235&rft.aulast=Liu&rft.aufirst=Cheng&rft.au=Ph.D%2C+Jack+Evett&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFerguson2013" class="citation book cs1">Ferguson, John (2013-12-31). <i>Mathematics in Geology</i> (Softcover reprint of the original 1st ed. 1988 ed.). Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9789401540117" title="Special:BookSources/9789401540117"><bdi>9789401540117</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Mathematics+in+Geology&rft.edition=Softcover+reprint+of+the+original+1st+ed.+1988&rft.pub=Springer&rft.date=2013-12-31&rft.isbn=9789401540117&rft.aulast=Ferguson&rft.aufirst=John&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> <li id="cite_note-:3-13"><span class="mw-cite-backlink">^ <a href="#cite_ref-:3_13-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-:3_13-1"><sup><i><b>b</b></i></sup></a> <a href="#cite_ref-:3_13-2"><sup><i><b>c</b></i></sup></a> <a href="#cite_ref-:3_13-3"><sup><i><b>d</b></i></sup></a> <a href="#cite_ref-:3_13-4"><sup><i><b>e</b></i></sup></a> <a href="#cite_ref-:3_13-5"><sup><i><b>f</b></i></sup></a> <a href="#cite_ref-:3_13-6"><sup><i><b>g</b></i></sup></a> <a href="#cite_ref-:3_13-7"><sup><i><b>h</b></i></sup></a> <a href="#cite_ref-:3_13-8"><sup><i><b>i</b></i></sup></a></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFHutter1983" class="citation book cs1">Hutter, K. (1983-08-31). <i>Theoretical Glaciology: Material Science of Ice and the Mechanics of Glaciers and Ice Sheets</i> (Softcover reprint of the original 1st ed. 1983 ed.). Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9789401511698" title="Special:BookSources/9789401511698"><bdi>9789401511698</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Theoretical+Glaciology%3A+Material+Science+of+Ice+and+the+Mechanics+of+Glaciers+and+Ice+Sheets&rft.edition=Softcover+reprint+of+the+original+1st+ed.+1983&rft.pub=Springer&rft.date=1983-08-31&rft.isbn=9789401511698&rft.aulast=Hutter&rft.aufirst=K.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></span> </li> </ol></div></div> <div class="mw-heading mw-heading3"><h3 id="Works_cited">Works cited</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=15" title="Edit section: Works cited"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFParker1994" class="citation book cs1">Parker, Robert L. (1994). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/geophysicalinver0000park"><i>Geophysical Inverse Theory</i></a></span>. <a href="/wiki/Princeton_University_Press" title="Princeton University Press">Princeton University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-691-03634-9" title="Special:BookSources/0-691-03634-9"><bdi>0-691-03634-9</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geophysical+Inverse+Theory&rft.pub=Princeton+University+Press&rft.date=1994&rft.isbn=0-691-03634-9&rft.aulast=Parker&rft.aufirst=Robert+L.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgeophysicalinver0000park&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFPedlosky2005" class="citation book cs1">Pedlosky, Joseph (2005). <i>Geophysical Fluid Dynamics</i>. <a href="/wiki/Society_for_Industrial_and_Applied_Mathematics" title="Society for Industrial and Applied Mathematics">Society for Industrial and Applied Mathematics</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-89871-572-5" title="Special:BookSources/0-89871-572-5"><bdi>0-89871-572-5</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geophysical+Fluid+Dynamics&rft.pub=Society+for+Industrial+and+Applied+Mathematics&rft.date=2005&rft.isbn=0-89871-572-5&rft.aulast=Pedlosky&rft.aufirst=Joseph&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTarantola1987" class="citation book cs1"><a href="/wiki/Albert_Tarantola" title="Albert Tarantola">Tarantola, Albert</a> (1987). <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/geophysicalfluid00jose"><i>Inverse Problem Theory and Methods for Model Parameter Estimation</i></a></span>. <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-387-96387-1" title="Special:BookSources/0-387-96387-1"><bdi>0-387-96387-1</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Inverse+Problem+Theory+and+Methods+for+Model+Parameter+Estimation&rft.pub=Springer-Verlag&rft.date=1987&rft.isbn=0-387-96387-1&rft.aulast=Tarantola&rft.aufirst=Albert&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fgeophysicalfluid00jose&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFTurcotte1997" class="citation book cs1">Turcotte, Donald L. (1997). <i>Fractals and Chaos in Geology and Geophysics</i>. <a href="/wiki/Cambridge_University_Press" title="Cambridge University Press">Cambridge University Press</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0-521-56164-7" title="Special:BookSources/0-521-56164-7"><bdi>0-521-56164-7</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Fractals+and+Chaos+in+Geology+and+Geophysics&rft.pub=Cambridge+University+Press&rft.date=1997&rft.isbn=0-521-56164-7&rft.aulast=Turcotte&rft.aufirst=Donald+L.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWangZouZhu2000" class="citation journal cs1">Wang, Bin; Zou, Xiaolei; Zhu, Jiang (2000). <a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC34050">"Data assimilation and its applications"</a>. <i><a href="/wiki/Proceedings_of_the_National_Academy_of_Sciences_of_the_United_States_of_America" title="Proceedings of the National Academy of Sciences of the United States of America">Proceedings of the National Academy of Sciences of the United States of America</a></i>. <b>97</b> (21): 11143–11144. <a href="/wiki/Bibcode_(identifier)" class="mw-redirect" title="Bibcode (identifier)">Bibcode</a>:<a rel="nofollow" class="external text" href="https://ui.adsabs.harvard.edu/abs/2000PNAS...9711143W">2000PNAS...9711143W</a>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://doi.org/10.1073%2Fpnas.97.21.11143">10.1073/pnas.97.21.11143</a></span>. <a href="/wiki/PMC_(identifier)" class="mw-redirect" title="PMC (identifier)">PMC</a> <span class="id-lock-free" title="Freely accessible"><a rel="nofollow" class="external text" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC34050">34050</a></span>. <a href="/wiki/PMID_(identifier)" class="mw-redirect" title="PMID (identifier)">PMID</a> <a rel="nofollow" class="external text" href="https://pubmed.ncbi.nlm.nih.gov/11027322">11027322</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Proceedings+of+the+National+Academy+of+Sciences+of+the+United+States+of+America&rft.atitle=Data+assimilation+and+its+applications&rft.volume=97&rft.issue=21&rft.pages=11143-11144&rft.date=2000&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC34050%23id-name%3DPMC&rft_id=info%3Apmid%2F11027322&rft_id=info%3Adoi%2F10.1073%2Fpnas.97.21.11143&rft_id=info%3Abibcode%2F2000PNAS...9711143W&rft.aulast=Wang&rft.aufirst=Bin&rft.au=Zou%2C+Xiaolei&rft.au=Zhu%2C+Jiang&rft_id=https%3A%2F%2Fwww.ncbi.nlm.nih.gov%2Fpmc%2Farticles%2FPMC34050&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Geomathematics&action=edit&section=16" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFAgterberg2014" class="citation book cs1">Agterberg, Frits (2014). <i>Geomathematics : theoretical foundations, applications and future developments</i>. Cham: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-319-06874-9" title="Special:BookSources/978-3-319-06874-9"><bdi>978-3-319-06874-9</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/885024357">885024357</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Geomathematics+%3A+theoretical+foundations%2C+applications+and+future+developments&rft.place=Cham&rft.pub=Springer&rft.date=2014&rft_id=info%3Aoclcnum%2F885024357&rft.isbn=978-3-319-06874-9&rft.aulast=Agterberg&rft.aufirst=Frits&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFMerriam1982" class="citation journal cs1"><a href="/wiki/Daniel_F._Merriam" class="mw-redirect" title="Daniel F. Merriam">Merriam, Daniel F.</a> (February 1982). "Development, significance, and influence of geomathematics: Observations of one geologist". <i>Mathematical Geology</i>. <b>14</b> (1). <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2FBF01037443">10.1007/BF01037443</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Mathematical+Geology&rft.atitle=Development%2C+significance%2C+and+influence+of+geomathematics%3A+Observations+of+one+geologist&rft.volume=14&rft.issue=1&rft.date=1982-02&rft_id=info%3Adoi%2F10.1007%2FBF01037443&rft.aulast=Merriam&rft.aufirst=Daniel+F.&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFFreeden2010" class="citation book cs1">Freeden, W (2010). <a rel="nofollow" class="external text" href="https://www.springer.com/gp/book/9783642015458"><i>Handbook of geomathematics</i></a>. Berlin London: Springer. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-642-01546-5" title="Special:BookSources/978-3-642-01546-5"><bdi>978-3-642-01546-5</bdi></a>. <a href="/wiki/OCLC_(identifier)" class="mw-redirect" title="OCLC (identifier)">OCLC</a> <a rel="nofollow" class="external text" href="https://search.worldcat.org/oclc/676700046">676700046</a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Handbook+of+geomathematics&rft.place=Berlin+London&rft.pub=Springer&rft.date=2010&rft_id=info%3Aoclcnum%2F676700046&rft.isbn=978-3-642-01546-5&rft.aulast=Freeden&rft.aufirst=W&rft_id=https%3A%2F%2Fwww.springer.com%2Fgp%2Fbook%2F9783642015458&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFSpringer_Berlin_Heidelberg2008" class="citation book cs1">Bonham-Carter, Graeme; Cheng, Qiuming, eds. (2008). <i>Progress in Geomathematics</i>. Berlin, Heidelberg: Springer Berlin Heidelberg. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1007%2F978-3-540-69496-0">10.1007/978-3-540-69496-0</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/978-3-540-69495-3" title="Special:BookSources/978-3-540-69495-3"><bdi>978-3-540-69495-3</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Progress+in+Geomathematics&rft.place=Berlin%2C+Heidelberg&rft.pub=Springer+Berlin+Heidelberg&rft.date=2008&rft_id=info%3Adoi%2F10.1007%2F978-3-540-69496-0&rft.isbn=978-3-540-69495-3&rfr_id=info%3Asid%2Fen.wikipedia.org%3AGeomathematics" class="Z3988"></span></li></ul> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1129693374"><style data-mw-deduplicate="TemplateStyles:r1236075235">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output 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