First break picking

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/></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>may be <a href="/wiki/Wikipedia:Vagueness" title="Wikipedia:Vagueness">confusing or unclear</a> to readers</b>.<span class="hide-when-compact"> Please help <a href="/wiki/Wikipedia:Please_clarify" title="Wikipedia:Please clarify">clarify the article</a>. There might be a discussion about this on <a href="/wiki/Talk:First_break_picking" title="Talk:First break picking">the talk page</a>.</span> <span class="date-container"><i>(<span class="date">June 2010</span>)</i></span><span class="hide-when-compact"><i> (<small><a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this message</a></small>)</i></span></div></td></tr></tbody></table> <p>In <a href="/wiki/Seismology" title="Seismology">seismology</a>, <b>first-break picking</b> is the detecting or picking the onset arrivals of refracted signals from all the signals received by receiver arrays and produced by a particular source signal generation. It is also called first arrival picking or first break detection. First-break picking can be done automatically, manually or as a combination of both. With the development of computer science and the size of seismic surveys, automatic picking is often preferred.<sup id="cite_ref-Yilmaz_1-0" class="reference"><a href="#cite_note-Yilmaz-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Significance">Significance</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=1" title="Edit section: Significance"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><b>First-break picks</b> associated with the <a href="/wiki/Refracted" class="mw-redirect" title="Refracted">refracted</a> arrival times are used in an <a href="/wiki/Inversion_(geology)" title="Inversion (geology)">inversion scheme</a> to study the near-surface low-<a href="/wiki/Velocity" title="Velocity">velocity</a> zone and subsequent determination of static corrections. Static correction is a correction applied to geophysical data, especially seismic data, to compensate for the effect of near-surface irregularities, differences in the elevation of shots and <a href="/wiki/Geophone" title="Geophone">geophones</a>, or any application to correct the positions of source and receivers. </p> <div class="mw-heading mw-heading2"><h2 id="History_of_First_Break_Picking">History of First Break Picking</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=2" title="Edit section: History of First Break Picking"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Gelchinsky and Shtivelman<sup id="cite_ref-Gelchinsky_2-0" class="reference"><a href="#cite_note-Gelchinsky-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>(1983) used <a href="/wiki/Correlation" title="Correlation">correlation</a> properties of signals and applied a statistical criterion for the estimation of first arrivals time. </p><p>Coppens<sup id="cite_ref-Coppens_3-0" class="reference"><a href="#cite_note-Coppens-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>(1985) calculated the ratio of energy of <a href="/wiki/Seismogram" title="Seismogram">seismogram</a> of the two windows and used that to differentiate in signal and noise. </p><p>Michael D. McCormark <i>et al.</i><sup id="cite_ref-Michael_4-0" class="reference"><a href="#cite_note-Michael-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>(1993) introduced a <a href="/wiki/Backpropagation" title="Backpropagation">backpropagation</a> neural network (BNN) method. The <a href="/wiki/Neural_network" title="Neural network">Neural network</a> which edits <a href="/wiki/Seismic" class="mw-redirect" title="Seismic">seismic</a> data or pick first breaks was trained by users, who were just selecting and presenting to the network examples of trace edits or refraction picks. The network then changes internal weights iteratively until it can reproduce the examples accurately provided by the users. </p><p>Fabio Boschetti <i>et al.</i><sup id="cite_ref-Fabio_5-0" class="reference"><a href="#cite_note-Fabio-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>(1996) introduce a <a href="/wiki/Fractal" title="Fractal">fractal</a>-based <a href="/wiki/Algorithm" title="Algorithm">algorithm</a>, which detects the presence of a signal by analyzing the variation in fractal dimension along the trace. This method works when signal-to-noise ratio is small, but it is considerably slow. </p><p>A direct correlation method was introduced by Joseph <i>et al.</i><sup id="cite_ref-Joseph_6-0" class="reference"><a href="#cite_note-Joseph-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>(1999) which was developed for use in highly time-resolved, low-noise signals acquired in the laboratory. In this method, the greatest value of Pearson's correlation coefficient between segments of observed <a href="/wiki/Waveform" title="Waveform">waveforms</a> near the <a href="/w/index.php?title=Pulse_onset&action=edit&redlink=1" class="new" title="Pulse onset (page does not exist)">pulse onset</a> and at an appropriate reference serves as the time determination criterion. </p><p>Zuolin Chen, <i>et al.</i><sup id="cite_ref-Zuolin_7-0" class="reference"><a href="#cite_note-Zuolin-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>(2005) introduced a multi-window algorithm to detect the first break. In this method, three moving windows were used and the averages of absolute amplitudes in each window need to be calculated, then ratios based on the averages of the windows provide standards to differentiate signals from unwanted noise. </p><p>Wong <i>et al.</i><sup id="cite_ref-Wong_8-0" class="reference"><a href="#cite_note-Wong-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>(2009) introduced STA/LTA ratio method. This method is similar as Coppens'<sup id="cite_ref-Coppens_3-1" class="reference"><a href="#cite_note-Coppens-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> algorithm. The difference is to do the ratio of two averages of energy between a short-term window and a long-term window, which is denoted as STA/LTA (short-term average/long-term average), instead of calculating the ratio of energy of seismogram of the two windows in Coppens' algorithm. </p> <div class="mw-heading mw-heading2"><h2 id="Methods_of_Automatic_First_Break_Picking">Methods of Automatic First Break Picking</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=3" title="Edit section: Methods of Automatic First Break Picking"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="STA/LTA_ratio_Method"><span id="STA.2FLTA_ratio_Method"></span>STA/LTA ratio Method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=4" title="Edit section: STA/LTA ratio Method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Source:<sup id="cite_ref-Wong_8-1" class="reference"><a href="#cite_note-Wong-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup> </p><p>This method is similar as Coppens' (1985) algorithm. The difference is to do the ratio of two averages of energy between a short-term window and a long-term window, which is denoted as STA/LTA (short-term average/long-term average), instead of calculating the ratio of energy of seismogram of the two windows in Coppens' algorithm. The numerical <a href="/wiki/Derivative" title="Derivative">derivative</a> of the ratio can be defined as, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&d_{i}=r_{i+1}-r_{i},i=1,2,...(n-1)\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <msub> <mi>d</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&d_{i}=r_{i+1}-r_{i},i=1,2,...(n-1)\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe283796610cb7103e0e713431b2a4a4e2aa061a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.132ex; height:2.843ex;" alt="{\displaystyle {\begin{aligned}&d_{i}=r_{i+1}-r_{i},i=1,2,...(n-1)\\\end{aligned}}}"></span></dd></dl> <p>where <i>r<sub>i+1</sub></i> is the STA/LTA ratio at time index <i>i+1</i>, and <i>r<sub>i</sub></i> is the STA/LTA ratio at time index <i>i</i>. For noise-free seismograms, the maximum value of the numerical derivative of the STA/LTA ratio is close to the time of the first arrival. </p><p>Wong et al. (2009) modified the algorithm of the energy ratio method, where they named the method as modified energy ratio. In this method, they define the energy ratio as, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&er_{i}=\sum _{j=i}^{i+ne}x_{j}^{2}/\sum _{j=i-ne}^{i}x_{j}^{2}\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mi>e</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>+</mo> <mi>n</mi> <mi>e</mi> </mrow> </munderover> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mi>i</mi> <mo>−</mo> <mi>n</mi> <mi>e</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munderover> <msubsup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&er_{i}=\sum _{j=i}^{i+ne}x_{j}^{2}/\sum _{j=i-ne}^{i}x_{j}^{2}\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab0d38cdb50e4020ff24fde7477d955296597649" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:23.026ex; height:7.509ex;" alt="{\displaystyle {\begin{aligned}&er_{i}=\sum _{j=i}^{i+ne}x_{j}^{2}/\sum _{j=i-ne}^{i}x_{j}^{2}\\\end{aligned}}}"></span></dd></dl> <p>where <i>x<sub>i</sub></i> is the times series representing a seismogram with the time index <i>i=1, 2 ... N.</i> and the number of points in an energy window is <i>ne</i>. Then, the modified energy ratio is defined as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&er3_{i}=(abs(x_{i})^{*}er_{i})^{3}\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mi>e</mi> <mi>r</mi> <msub> <mn>3</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mi>b</mi> <mi>s</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo>∗</mo> </mrow> </msup> <mi>e</mi> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&er3_{i}=(abs(x_{i})^{*}er_{i})^{3}\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4e96580569773a85c36c7f74bac3cf7e5481beee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:22.05ex; height:3.176ex;" alt="{\displaystyle {\begin{aligned}&er3_{i}=(abs(x_{i})^{*}er_{i})^{3}\\\end{aligned}}}"></span></dd></dl> <p>The peak of the modified energy ratio <i>er3i</i> is very closed to the time of first arrivals on noise-free seismograms. </p> <div class="mw-heading mw-heading3"><h3 id="Multi-Window_Method">Multi-Window Method</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=5" title="Edit section: Multi-Window Method"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Source:<sup id="cite_ref-Zuolin_7-1" class="reference"><a href="#cite_note-Zuolin-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>This method needs to calculate the averages of absolute <a href="/wiki/Amplitude" title="Amplitude">amplitudes</a> from a seismic trace by using three moving time windows before and after each time point (sample). </p><p>When the instantaneous absolute amplitude exceeds an automatically adjusted threshold, ratios based on the averages of the windows over previous time samples provide standards to differentiate signals from unwanted noise. </p><p>The multi-window automatic P phase picker operates in the time-domain. It includes procedures to define: time windows, standards, corresponding thresholds and <a href="/wiki/Waveform" title="Waveform">waveform</a> correction. </p><p>1. The averages of absolute amplitudes within BTA (Before Term Average), ATA (After Term Average) and DTA (Delayed Term Average) windows are respectively defined as follows: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&{\overline {BTA(t)}}=\sum _{i=1}^{m}{\frac {|u(t-i)|}{m}}\\&{\overline {ATA(t)}}=\sum _{i=1}^{n}{\frac {|u(t+j)|}{n}}\\&{\overline {DTA(t)}}=\sum _{j=1}^{q}{\frac {|u(t+j+d)|}{q}}\\&R_{2}(t)={\frac {\overline {ATA(t)}}{\overline {BTA(t)}}}\\&R_{3}(t)={\frac {\overline {DTA(t)}}{\overline {BTA(t)}}}\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>B</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mi>m</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>A</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mi>j</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mi>n</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mrow class="MJX-TeXAtom-ORD"> <mover> <mrow> <mi>D</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>q</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>u</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>+</mo> <mi>j</mi> <mo>+</mo> <mi>d</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> </mrow> <mi>q</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mover> <mrow> <mi>A</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> <mover> <mrow> <mi>B</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <msub> <mi>R</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mover> <mrow> <mi>D</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> <mover> <mrow> <mi>B</mi> <mi>T</mi> <mi>A</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo accent="false">¯</mo> </mover> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&{\overline {BTA(t)}}=\sum _{i=1}^{m}{\frac {|u(t-i)|}{m}}\\&{\overline {ATA(t)}}=\sum _{i=1}^{n}{\frac {|u(t+j)|}{n}}\\&{\overline {DTA(t)}}=\sum _{j=1}^{q}{\frac {|u(t+j+d)|}{q}}\\&R_{2}(t)={\frac {\overline {ATA(t)}}{\overline {BTA(t)}}}\\&R_{3}(t)={\frac {\overline {DTA(t)}}{\overline {BTA(t)}}}\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0bb3bba34c4916aa173be980e9bb3c1d066720bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -18.11ex; margin-bottom: -0.228ex; width:29.623ex; height:37.843ex;" alt="{\displaystyle {\begin{aligned}&{\overline {BTA(t)}}=\sum _{i=1}^{m}{\frac {|u(t-i)|}{m}}\\&{\overline {ATA(t)}}=\sum _{i=1}^{n}{\frac {|u(t+j)|}{n}}\\&{\overline {DTA(t)}}=\sum _{j=1}^{q}{\frac {|u(t+j+d)|}{q}}\\&R_{2}(t)={\frac {\overline {ATA(t)}}{\overline {BTA(t)}}}\\&R_{3}(t)={\frac {\overline {DTA(t)}}{\overline {BTA(t)}}}\\\end{aligned}}}"></span></dd></dl> <p>Standards <i>R<sub>2</sub>(t)</i> and <i>R<sub>3</sub>(t)</i> are used for the discrimination of high-amplitude short-duration and long-duration noise. </p><p>2.Thresholds is defined as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}&H_{1}(t)=E_{m}(t-p)+\alpha E_{sd}(t-p)\\\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd /> <mtd> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>α</mi> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mi>d</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>t</mi> <mo>−</mo> <mi>p</mi> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}&H_{1}(t)=E_{m}(t-p)+\alpha E_{sd}(t-p)\\\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/38764b116017ae97c890d088c630a18007609a46" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.098ex; height:2.843ex;" alt="{\displaystyle {\begin{aligned}&H_{1}(t)=E_{m}(t-p)+\alpha E_{sd}(t-p)\\\end{aligned}}}"></span></dd></dl> <p>where <i>E<sub>m</sub></i> is mean and <i>E<sub>sd</sub></i> is <a href="/wiki/Standard_deviation" title="Standard deviation">standard deviation</a>; <i>p</i> is the number of shifted samples; <i>α</i> is the coefficient to adjust the height of the first threshold and is taken to be 3. From this equation it is obvious that <i>H<sub>1</sub>(t)</i> is automatically adjusted with the variance of the background noise. </p><p>3. <i>H<sub>1</sub>(t)</i> is defined larger than most pre-existing noise levels, and the instantaneous absolute amplitude at the trigger time point is higher than <i>H<sub>1</sub>(t)</i>, according to the configuration of the first arrival of an event the real onset time must be earlier than the trigger time point. A waveform correction should be used to compensate this belated onset time. For an impulsive first arrival, the height of the absolute amplitude and the representative <a href="/wiki/Gradient" title="Gradient">gradient</a> at the trigger point can be used to accomplish the correction. </p> <div class="mw-heading mw-heading2"><h2 id="Available_Code">Available Code</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=6" title="Edit section: Available Code"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Potash SU is a package including <a href="/wiki/Seismic_Unix" title="Seismic Unix">Seismic Unix</a> style codes developed by Balazs Nemeth, it provides a <a href="/wiki/Subroutine" class="mw-redirect" title="Subroutine">subroutine</a> called simple window-based first break picker, the figure shows the seismic images before and after the application of subroutine. </p> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Wagc%3D1.PNG" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Wagc%3D1.PNG/220px-Wagc%3D1.PNG" decoding="async" width="220" height="143" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Wagc%3D1.PNG/330px-Wagc%3D1.PNG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Wagc%3D1.PNG/440px-Wagc%3D1.PNG 2x" data-file-width="1105" data-file-height="717" /></a><figcaption>Right one is before first break picking, left one is after first break picking</figcaption></figure> <div class="mw-heading mw-heading2"><h2 id="Future_Trend_of_the_Topic">Future Trend of the Topic</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=7" title="Edit section: Future Trend of the Topic"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Methods of Picking: automatic first-break picking has played an important role in seismic data processing, and directly influences the quality of seismic sections. Because of the increase of <a href="/wiki/Seismic_survey" class="mw-redirect" title="Seismic survey">seismic survey</a> size, more efficient and fast first break picking methods are needed, with parallel methods being preferred. </p><p>Application of First Break detection: Traditionally the <a href="/wiki/Geophysicist" class="mw-redirect" title="Geophysicist">geophysicist</a> uses first breaks for static correction. First break signal can also be used as observation data for history matching. </p> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=First_break_picking&action=edit&section=8" title="Edit section: Notes"><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"><ol class="references"> <li id="cite_note-Yilmaz-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Yilmaz_1-0">^</a></b></span> <span class="reference-text">ÖZ, YILMAZ, (2000). <i>Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data.</i> Volume I: Society of Exploration Geophysicists.</span> </li> <li id="cite_note-Gelchinsky-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-Gelchinsky_2-0">^</a></b></span> <span class="reference-text">Gelchinsky B. and Shtivelman V., (1983). <i>Automatic picking of first arrivals and parameterization of traveltime curves.</i> Geophysical Prospecting, 31, 915-928.</span> </li> <li id="cite_note-Coppens-3"><span class="mw-cite-backlink">^ <a href="#cite_ref-Coppens_3-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Coppens_3-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Coppens F., (1985). <i>First arrival picking on common-offset trace collections for automatic estimation of static corrections.</i> Geophysical Prospecting, 33, 1212-1231.</span> </li> <li id="cite_note-Michael-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-Michael_4-0">^</a></b></span> <span class="reference-text">Michael D. McCormack et al., (1993). <i>First-break refraction event picking and seismic data trace editing using neural networks.</i> Geophysics, Vol.58, No.1, P. 67-78.</span> </li> <li id="cite_note-Fabio-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-Fabio_5-0">^</a></b></span> <span class="reference-text">Fabio Boschetti, Mike D. Dentith, and Ron D. List, (1996). <i>A fractal-based algorithm for detecting first arrivals on seismic traces.</i> Geophysics, Vol.61, No.4, P. 1095-1102.</span> </li> <li id="cite_note-Joseph-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-Joseph_6-0">^</a></b></span> <span class="reference-text">Joseph B. Molyneux and Douglas R. Schmitt, (1999). <i>First-break timing: Arrival onset times by direct correlation.</i> Geophysics, Vol.64, No.5, P. 1492-1501.</span> </li> <li id="cite_note-Zuolin-7"><span class="mw-cite-backlink">^ <a href="#cite_ref-Zuolin_7-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Zuolin_7-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Zuolin Chen and Robert Stewart, (2005). <i>Multi-window algorithm for detecting seismic first arrivals.<a rel="nofollow" class="external autonumber" href="http://www.crewes.org/ForOurSponsors/ConferenceAbstracts/2005/CSEG/Chen_CSEG_2005-1.pdf">[1]</a></i></span> </li> <li id="cite_note-Wong-8"><span class="mw-cite-backlink">^ <a href="#cite_ref-Wong_8-0"><sup><i><b>a</b></i></sup></a> <a href="#cite_ref-Wong_8-1"><sup><i><b>b</b></i></sup></a></span> <span class="reference-text">Wong J., Han L., Bancroft J.C., Stewart R.R., (2009). <i>Automatic time-picking of first arrivals on noisy microseismic data.<a rel="nofollow" class="external autonumber" href="http://www.crewes.org/ForOurSponsors/ConferenceAbstracts/2009/CSEG/Wong_CSEG_2009.pdf">[2]</a></i></span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=First_break_picking&oldid=1190295985">https://en.wikipedia.org/w/index.php?title=First_break_picking&oldid=1190295985</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Acoustics" title="Category:Acoustics">Acoustics</a></li><li><a href="/wiki/Category:Seismology" title="Category:Seismology">Seismology</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Wikipedia_articles_needing_clarification_from_June_2010" title="Category:Wikipedia articles needing clarification from June 2010">Wikipedia articles needing clarification from June 2010</a></li><li><a href="/wiki/Category:All_Wikipedia_articles_needing_clarification" title="Category:All Wikipedia articles needing clarification">All Wikipedia articles needing clarification</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 17 December 2023, at 02:37<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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First break picking - Wikipedia