AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS
Identifieur interne : 000482 ( Istex/Corpus ); précédent : 000481; suivant : 000483AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS
Auteurs : M. S. Sambridge ; A. Tarantola ; B. L. N. KennettSource :
- Geophysical Prospecting [ 0016-8025 ] ; 1991-08.
English descriptors
- KwdEn :
- Algorithm, Alternative strategy, Conjugate gradient method, Conjugate gradient methods, Covariance, Covariance operator, Covariance operators, Descent direction, Descent directions, Different dimension, Different parameter types, Duality product, Duality products, Earth model, Earth sciences, Elastic wave equation, Full hessian, Functional space, Geophysical journal, Geophysical prospecting, Gradient methods, Gradient vector, Greatest reduction, Impedance, Inverse problem, Inverse problems, Inversion, Inversion algorithms, Iteration, Kennett, Local linearization, Matrix, Matrix inversion, Misfit, Misfit function, Model parameter type, Model parametrization, Model space, Model vector, Numerical solution, Objective function, Optimization, Optimization problem, Other hand, Overall descent direction, Parameter, Parameter type, Parameter types, Previous descent directions, Receiver positions, Reflection data, Reflection problem, Reflection seismology, Sambridge, Second term, Seismic, Seismic reflection data, Seismic reflection waveforms, Seismic waveforms, Single gradient method, Source function, Steepest, Steepest descent algorithm, Steepest descent direction, Steepest descent vector, Step lengths, Subspace, Subspace approach, Subspace directions, Subspace method, Subspace methods, Subspace scheme, Subspace technique, Surface displacements, Tarantola, Theoretical physics, Tomographic inversion, Waveform, Waveform inversion, Weighted residuals, Weighting functions, Williamson.
- Teeft :
- Algorithm, Alternative strategy, Conjugate gradient method, Conjugate gradient methods, Covariance, Covariance operator, Covariance operators, Descent direction, Descent directions, Different dimension, Different parameter types, Duality product, Duality products, Earth model, Earth sciences, Elastic wave equation, Full hessian, Functional space, Geophysical journal, Geophysical prospecting, Gradient methods, Gradient vector, Greatest reduction, Impedance, Inverse problem, Inverse problems, Inversion, Inversion algorithms, Iteration, Kennett, Local linearization, Matrix, Matrix inversion, Misfit, Misfit function, Model parameter type, Model parametrization, Model space, Model vector, Numerical solution, Objective function, Optimization, Optimization problem, Other hand, Overall descent direction, Parameter, Parameter type, Parameter types, Previous descent directions, Receiver positions, Reflection data, Reflection problem, Reflection seismology, Sambridge, Second term, Seismic, Seismic reflection data, Seismic reflection waveforms, Seismic waveforms, Single gradient method, Source function, Steepest, Steepest descent algorithm, Steepest descent direction, Steepest descent vector, Step lengths, Subspace, Subspace approach, Subspace directions, Subspace method, Subspace methods, Subspace scheme, Subspace technique, Surface displacements, Tarantola, Theoretical physics, Tomographic inversion, Waveform, Waveform inversion, Weighted residuals, Weighting functions, Williamson.
Abstract
A common example of a large‐scale non‐linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large‐scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions. A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process. We propose a new strategy for the non‐linear inversion of multi‐offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large‐scale matrix inversion but pays particular attention to different parameter types in the inversion. We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub‐space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well‐conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.
Url:
DOI: 10.1111/j.1365-2478.1991.tb00341.x
Links to Exploration step
ISTEX:193702978CF9062D5962240E89CC03DF864E89D5Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS</title>
<author><name sortKey="Sambridge, M S" sort="Sambridge, M S" uniqKey="Sambridge M" first="M. S." last="Sambridge">M. S. Sambridge</name>
<affiliation><mods:affiliation>Institute of Theoretical Geophysics, Departments of Earth Sciences and Applied Mathematics and Theoretical Physics, Downing Street, Cambridge CB2 3EO, U.K.</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Tarantola, A" sort="Tarantola, A" uniqKey="Tarantola A" first="A." last="Tarantola">A. Tarantola</name>
<affiliation><mods:affiliation>Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cédex 05, France.</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Kennett, B L N" sort="Kennett, B L N" uniqKey="Kennett B" first="B. L. N." last="Kennett">B. L. N. Kennett</name>
<affiliation><mods:affiliation>Research School of Earth Sciences, A.N.U., P.O. Box 4, Canberra, ACT 2601, Australia.</mods:affiliation>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">ISTEX</idno>
<idno type="RBID">ISTEX:193702978CF9062D5962240E89CC03DF864E89D5</idno>
<date when="1991" year="1991">1991</date>
<idno type="doi">10.1111/j.1365-2478.1991.tb00341.x</idno>
<idno type="url">https://api.istex.fr/document/193702978CF9062D5962240E89CC03DF864E89D5/fulltext/pdf</idno>
<idno type="wicri:Area/Istex/Corpus">000482</idno>
<idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">000482</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title level="a" type="main">AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS<ref type="note" target="#fn1"><hi rend="superscript">1</hi>
</ref>
</title>
<author><name sortKey="Sambridge, M S" sort="Sambridge, M S" uniqKey="Sambridge M" first="M. S." last="Sambridge">M. S. Sambridge</name>
<affiliation><mods:affiliation>Institute of Theoretical Geophysics, Departments of Earth Sciences and Applied Mathematics and Theoretical Physics, Downing Street, Cambridge CB2 3EO, U.K.</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Tarantola, A" sort="Tarantola, A" uniqKey="Tarantola A" first="A." last="Tarantola">A. Tarantola</name>
<affiliation><mods:affiliation>Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cédex 05, France.</mods:affiliation>
</affiliation>
</author>
<author><name sortKey="Kennett, B L N" sort="Kennett, B L N" uniqKey="Kennett B" first="B. L. N." last="Kennett">B. L. N. Kennett</name>
<affiliation><mods:affiliation>Research School of Earth Sciences, A.N.U., P.O. Box 4, Canberra, ACT 2601, Australia.</mods:affiliation>
</affiliation>
</author>
</analytic>
<monogr></monogr>
<series><title level="j" type="main">Geophysical Prospecting</title>
<title level="j" type="alt">GEOPHYSICAL PROSPECTING</title>
<idno type="ISSN">0016-8025</idno>
<idno type="eISSN">1365-2478</idno>
<imprint><biblScope unit="vol">39</biblScope>
<biblScope unit="issue">6</biblScope>
<biblScope unit="page" from="723">723</biblScope>
<biblScope unit="page" to="736">736</biblScope>
<biblScope unit="page-count">14</biblScope>
<publisher>Blackwell Publishing Ltd</publisher>
<pubPlace>Oxford, UK</pubPlace>
<date type="published" when="1991-08">1991-08</date>
</imprint>
<idno type="ISSN">0016-8025</idno>
</series>
</biblStruct>
</sourceDesc>
<seriesStmt><idno type="ISSN">0016-8025</idno>
</seriesStmt>
</fileDesc>
<profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Algorithm</term>
<term>Alternative strategy</term>
<term>Conjugate gradient method</term>
<term>Conjugate gradient methods</term>
<term>Covariance</term>
<term>Covariance operator</term>
<term>Covariance operators</term>
<term>Descent direction</term>
<term>Descent directions</term>
<term>Different dimension</term>
<term>Different parameter types</term>
<term>Duality product</term>
<term>Duality products</term>
<term>Earth model</term>
<term>Earth sciences</term>
<term>Elastic wave equation</term>
<term>Full hessian</term>
<term>Functional space</term>
<term>Geophysical journal</term>
<term>Geophysical prospecting</term>
<term>Gradient methods</term>
<term>Gradient vector</term>
<term>Greatest reduction</term>
<term>Impedance</term>
<term>Inverse problem</term>
<term>Inverse problems</term>
<term>Inversion</term>
<term>Inversion algorithms</term>
<term>Iteration</term>
<term>Kennett</term>
<term>Local linearization</term>
<term>Matrix</term>
<term>Matrix inversion</term>
<term>Misfit</term>
<term>Misfit function</term>
<term>Model parameter type</term>
<term>Model parametrization</term>
<term>Model space</term>
<term>Model vector</term>
<term>Numerical solution</term>
<term>Objective function</term>
<term>Optimization</term>
<term>Optimization problem</term>
<term>Other hand</term>
<term>Overall descent direction</term>
<term>Parameter</term>
<term>Parameter type</term>
<term>Parameter types</term>
<term>Previous descent directions</term>
<term>Receiver positions</term>
<term>Reflection data</term>
<term>Reflection problem</term>
<term>Reflection seismology</term>
<term>Sambridge</term>
<term>Second term</term>
<term>Seismic</term>
<term>Seismic reflection data</term>
<term>Seismic reflection waveforms</term>
<term>Seismic waveforms</term>
<term>Single gradient method</term>
<term>Source function</term>
<term>Steepest</term>
<term>Steepest descent algorithm</term>
<term>Steepest descent direction</term>
<term>Steepest descent vector</term>
<term>Step lengths</term>
<term>Subspace</term>
<term>Subspace approach</term>
<term>Subspace directions</term>
<term>Subspace method</term>
<term>Subspace methods</term>
<term>Subspace scheme</term>
<term>Subspace technique</term>
<term>Surface displacements</term>
<term>Tarantola</term>
<term>Theoretical physics</term>
<term>Tomographic inversion</term>
<term>Waveform</term>
<term>Waveform inversion</term>
<term>Weighted residuals</term>
<term>Weighting functions</term>
<term>Williamson</term>
</keywords>
<keywords scheme="Teeft" xml:lang="en"><term>Algorithm</term>
<term>Alternative strategy</term>
<term>Conjugate gradient method</term>
<term>Conjugate gradient methods</term>
<term>Covariance</term>
<term>Covariance operator</term>
<term>Covariance operators</term>
<term>Descent direction</term>
<term>Descent directions</term>
<term>Different dimension</term>
<term>Different parameter types</term>
<term>Duality product</term>
<term>Duality products</term>
<term>Earth model</term>
<term>Earth sciences</term>
<term>Elastic wave equation</term>
<term>Full hessian</term>
<term>Functional space</term>
<term>Geophysical journal</term>
<term>Geophysical prospecting</term>
<term>Gradient methods</term>
<term>Gradient vector</term>
<term>Greatest reduction</term>
<term>Impedance</term>
<term>Inverse problem</term>
<term>Inverse problems</term>
<term>Inversion</term>
<term>Inversion algorithms</term>
<term>Iteration</term>
<term>Kennett</term>
<term>Local linearization</term>
<term>Matrix</term>
<term>Matrix inversion</term>
<term>Misfit</term>
<term>Misfit function</term>
<term>Model parameter type</term>
<term>Model parametrization</term>
<term>Model space</term>
<term>Model vector</term>
<term>Numerical solution</term>
<term>Objective function</term>
<term>Optimization</term>
<term>Optimization problem</term>
<term>Other hand</term>
<term>Overall descent direction</term>
<term>Parameter</term>
<term>Parameter type</term>
<term>Parameter types</term>
<term>Previous descent directions</term>
<term>Receiver positions</term>
<term>Reflection data</term>
<term>Reflection problem</term>
<term>Reflection seismology</term>
<term>Sambridge</term>
<term>Second term</term>
<term>Seismic</term>
<term>Seismic reflection data</term>
<term>Seismic reflection waveforms</term>
<term>Seismic waveforms</term>
<term>Single gradient method</term>
<term>Source function</term>
<term>Steepest</term>
<term>Steepest descent algorithm</term>
<term>Steepest descent direction</term>
<term>Steepest descent vector</term>
<term>Step lengths</term>
<term>Subspace</term>
<term>Subspace approach</term>
<term>Subspace directions</term>
<term>Subspace method</term>
<term>Subspace methods</term>
<term>Subspace scheme</term>
<term>Subspace technique</term>
<term>Surface displacements</term>
<term>Tarantola</term>
<term>Theoretical physics</term>
<term>Tomographic inversion</term>
<term>Waveform</term>
<term>Waveform inversion</term>
<term>Weighted residuals</term>
<term>Weighting functions</term>
<term>Williamson</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">A common example of a large‐scale non‐linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large‐scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions. A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process. We propose a new strategy for the non‐linear inversion of multi‐offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large‐scale matrix inversion but pays particular attention to different parameter types in the inversion. We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub‐space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well‐conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.</div>
</front>
</TEI>
<istex><corpusName>wiley</corpusName>
<keywords><teeft><json:string>tarantola</json:string>
<json:string>waveform</json:string>
<json:string>parameter type</json:string>
<json:string>misfit</json:string>
<json:string>iteration</json:string>
<json:string>inversion</json:string>
<json:string>algorithm</json:string>
<json:string>sambridge</json:string>
<json:string>parameter types</json:string>
<json:string>misfit function</json:string>
<json:string>waveform inversion</json:string>
<json:string>covariance</json:string>
<json:string>impedance</json:string>
<json:string>seismic</json:string>
<json:string>inverse problem</json:string>
<json:string>subspace scheme</json:string>
<json:string>steepest</json:string>
<json:string>descent direction</json:string>
<json:string>earth model</json:string>
<json:string>steepest descent algorithm</json:string>
<json:string>seismic waveforms</json:string>
<json:string>optimization</json:string>
<json:string>williamson</json:string>
<json:string>kennett</json:string>
<json:string>previous descent directions</json:string>
<json:string>different parameter types</json:string>
<json:string>seismic reflection data</json:string>
<json:string>geophysical journal</json:string>
<json:string>alternative strategy</json:string>
<json:string>objective function</json:string>
<json:string>model space</json:string>
<json:string>source function</json:string>
<json:string>parameter</json:string>
<json:string>matrix</json:string>
<json:string>weighted residuals</json:string>
<json:string>covariance operator</json:string>
<json:string>duality product</json:string>
<json:string>surface displacements</json:string>
<json:string>seismic reflection waveforms</json:string>
<json:string>optimization problem</json:string>
<json:string>conjugate gradient methods</json:string>
<json:string>elastic wave equation</json:string>
<json:string>subspace approach</json:string>
<json:string>other hand</json:string>
<json:string>subspace technique</json:string>
<json:string>subspace methods</json:string>
<json:string>numerical solution</json:string>
<json:string>subspace</json:string>
<json:string>subspace method</json:string>
<json:string>reflection data</json:string>
<json:string>geophysical prospecting</json:string>
<json:string>different dimension</json:string>
<json:string>matrix inversion</json:string>
<json:string>inversion algorithms</json:string>
<json:string>model vector</json:string>
<json:string>duality products</json:string>
<json:string>weighting functions</json:string>
<json:string>covariance operators</json:string>
<json:string>gradient vector</json:string>
<json:string>earth sciences</json:string>
<json:string>functional space</json:string>
<json:string>reflection problem</json:string>
<json:string>receiver positions</json:string>
<json:string>inverse problems</json:string>
<json:string>theoretical physics</json:string>
<json:string>steepest descent direction</json:string>
<json:string>descent directions</json:string>
<json:string>model parameter type</json:string>
<json:string>overall descent direction</json:string>
<json:string>gradient methods</json:string>
<json:string>greatest reduction</json:string>
<json:string>subspace directions</json:string>
<json:string>steepest descent vector</json:string>
<json:string>local linearization</json:string>
<json:string>single gradient method</json:string>
<json:string>conjugate gradient method</json:string>
<json:string>second term</json:string>
<json:string>step lengths</json:string>
<json:string>model parametrization</json:string>
<json:string>full hessian</json:string>
<json:string>tomographic inversion</json:string>
<json:string>reflection seismology</json:string>
</teeft>
</keywords>
<author><json:item><name>M. S. SAMBRIDGE</name>
<affiliations><json:string>Institute of Theoretical Geophysics, Departments of Earth Sciences and Applied Mathematics and Theoretical Physics, Downing Street, Cambridge CB2 3EO, U.K.</json:string>
</affiliations>
</json:item>
<json:item><name>A. TARANTOLA</name>
<affiliations><json:string>Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cédex 05, France.</json:string>
</affiliations>
</json:item>
<json:item><name>B. L. N. KENNETT</name>
<affiliations><json:string>Research School of Earth Sciences, A.N.U., P.O. Box 4, Canberra, ACT 2601, Australia.</json:string>
</affiliations>
</json:item>
</author>
<articleId><json:string>GPR723</json:string>
</articleId>
<arkIstex>ark:/67375/WNG-JW1Q44P5-8</arkIstex>
<language><json:string>eng</json:string>
</language>
<originalGenre><json:string>article</json:string>
</originalGenre>
<abstract>A common example of a large‐scale non‐linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large‐scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions. A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process. We propose a new strategy for the non‐linear inversion of multi‐offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large‐scale matrix inversion but pays particular attention to different parameter types in the inversion. We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub‐space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well‐conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.</abstract>
<qualityIndicators><score>10</score>
<pdfWordCount>5269</pdfWordCount>
<pdfCharCount>28617</pdfCharCount>
<pdfVersion>1.4</pdfVersion>
<pdfPageCount>14</pdfPageCount>
<pdfPageSize>439.679 x 641.76 pts</pdfPageSize>
<refBibsNative>true</refBibsNative>
<abstractWordCount>456</abstractWordCount>
<abstractCharCount>2954</abstractCharCount>
<keywordCount>0</keywordCount>
</qualityIndicators>
<title>AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS</title>
<genre><json:string>article</json:string>
</genre>
<host><title>Geophysical Prospecting</title>
<language><json:string>unknown</json:string>
</language>
<doi><json:string>10.1111/(ISSN)1365-2478</json:string>
</doi>
<issn><json:string>0016-8025</json:string>
</issn>
<eissn><json:string>1365-2478</json:string>
</eissn>
<publisherId><json:string>GPR</json:string>
</publisherId>
<volume>39</volume>
<issue>6</issue>
<pages><first>723</first>
<last>736</last>
<total>14</total>
</pages>
<genre><json:string>journal</json:string>
</genre>
</host>
<namedEntities><unitex><date><json:string>1990</json:string>
<json:string>1991</json:string>
</date>
<geogName></geogName>
<orgName><json:string>Majorana International School</json:string>
<json:string>Research School of Earth Sciences</json:string>
</orgName>
<orgName_funder></orgName_funder>
<orgName_provider></orgName_provider>
<persName><json:string>P.O. Box</json:string>
<json:string>Paris Cbdex</json:string>
<json:string>The</json:string>
<json:string>To</json:string>
</persName>
<placeName><json:string>Australia</json:string>
<json:string>Canberra</json:string>
<json:string>France</json:string>
</placeName>
<ref_url></ref_url>
<ref_bibl><json:string>Kennett and Williamson 1987; Sambridge 1988, 1990</json:string>
<json:string>Tarantola 1986</json:string>
<json:string>Sambridge and Kennett 1986</json:string>
<json:string>Morse and Feshbach 1953</json:string>
<json:string>Sambridge and Williamson (1988)</json:string>
<json:string>Kennett et al. (1988)</json:string>
<json:string>Williamson 1986</json:string>
<json:string>Mora 1987</json:string>
<json:string>1986, 1990</json:string>
<json:string>Vireux 1986</json:string>
<json:string>Tarantola (1986)</json:string>
</ref_bibl>
<bibl></bibl>
</unitex>
</namedEntities>
<ark><json:string>ark:/67375/WNG-JW1Q44P5-8</json:string>
</ark>
<categories><wos><json:string>1 - science</json:string>
<json:string>2 - geochemistry & geophysics</json:string>
</wos>
<scienceMetrix><json:string>1 - natural sciences</json:string>
<json:string>2 - earth & environmental sciences</json:string>
<json:string>3 - geochemistry & geophysics</json:string>
</scienceMetrix>
<scopus><json:string>1 - Physical Sciences</json:string>
<json:string>2 - Earth and Planetary Sciences</json:string>
<json:string>3 - Geochemistry and Petrology</json:string>
<json:string>1 - Physical Sciences</json:string>
<json:string>2 - Earth and Planetary Sciences</json:string>
<json:string>3 - Geophysics</json:string>
</scopus>
<inist><json:string>1 - sciences appliquees, technologies et medecines</json:string>
<json:string>2 - sciences exactes et technologie</json:string>
<json:string>3 - terre, ocean, espace</json:string>
<json:string>4 - geophysique externe</json:string>
</inist>
</categories>
<publicationDate>1991</publicationDate>
<copyrightDate>1991</copyrightDate>
<doi><json:string>10.1111/j.1365-2478.1991.tb00341.x</json:string>
</doi>
<id>193702978CF9062D5962240E89CC03DF864E89D5</id>
<score>1</score>
<fulltext><json:item><extension>pdf</extension>
<original>true</original>
<mimetype>application/pdf</mimetype>
<uri>https://api.istex.fr/document/193702978CF9062D5962240E89CC03DF864E89D5/fulltext/pdf</uri>
</json:item>
<json:item><extension>zip</extension>
<original>false</original>
<mimetype>application/zip</mimetype>
<uri>https://api.istex.fr/document/193702978CF9062D5962240E89CC03DF864E89D5/fulltext/zip</uri>
</json:item>
<istex:fulltextTEI uri="https://api.istex.fr/document/193702978CF9062D5962240E89CC03DF864E89D5/fulltext/tei"><teiHeader><fileDesc><titleStmt><title level="a" type="main">AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS<ref type="note" target="#fn1"><hi rend="superscript">1</hi>
</ref>
</title>
</titleStmt>
<publicationStmt><authority>ISTEX</authority>
<publisher>Blackwell Publishing Ltd</publisher>
<pubPlace>Oxford, UK</pubPlace>
<date type="published" when="1991-08"></date>
</publicationStmt>
<notesStmt><note type="content-type" subtype="article" source="article" scheme="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</note>
<note type="publication-type" subtype="journal" scheme="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</note>
</notesStmt>
<sourceDesc><biblStruct type="article"><analytic><title level="a" type="main">AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS<ref type="note" target="#fn1"><hi rend="superscript">1</hi>
</ref>
</title>
<author xml:id="author-0000"><persName><forename type="first">M. S.</forename>
<surname>SAMBRIDGE</surname>
</persName>
<affiliation>Institute of Theoretical Geophysics, Departments of Earth Sciences and Applied Mathematics and Theoretical Physics, Downing Street, Cambridge CB2 3EO, U.K.</affiliation>
</author>
<author xml:id="author-0001"><persName><forename type="first">A.</forename>
<surname>TARANTOLA</surname>
</persName>
<affiliation>Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cédex 05, France.<address><country key="FR"></country>
</address>
</affiliation>
</author>
<author xml:id="author-0002"><persName><forename type="first">B. L. N.</forename>
<surname>KENNETT</surname>
</persName>
<affiliation>Research School of Earth Sciences, A.N.U., P.O. Box 4, Canberra, ACT 2601, Australia.<address><country key="AU"></country>
</address>
</affiliation>
</author>
<idno type="istex">193702978CF9062D5962240E89CC03DF864E89D5</idno>
<idno type="ark">ark:/67375/WNG-JW1Q44P5-8</idno>
<idno type="DOI">10.1111/j.1365-2478.1991.tb00341.x</idno>
<idno type="unit">GPR723</idno>
<idno type="toTypesetVersion">file:GPR.GPR723.pdf</idno>
</analytic>
<monogr><title level="j" type="main">Geophysical Prospecting</title>
<title level="j" type="alt">GEOPHYSICAL PROSPECTING</title>
<idno type="pISSN">0016-8025</idno>
<idno type="eISSN">1365-2478</idno>
<idno type="book-DOI">10.1111/(ISSN)1365-2478</idno>
<idno type="book-part-DOI">10.1111/gpr.1991.39.issue-6</idno>
<idno type="product">GPR</idno>
<idno type="publisherDivision">ST</idno>
<imprint><biblScope unit="vol">39</biblScope>
<biblScope unit="issue">6</biblScope>
<biblScope unit="page" from="723">723</biblScope>
<biblScope unit="page" to="736">736</biblScope>
<biblScope unit="page-count">14</biblScope>
<publisher>Blackwell Publishing Ltd</publisher>
<pubPlace>Oxford, UK</pubPlace>
<date type="published" when="1991-08"></date>
</imprint>
</monogr>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><abstract xml:lang="en" style="main"><head>A<hi rend="smallCaps">bstract</hi>
</head>
<p>A common example of a large‐scale non‐linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large‐scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions.</p>
<p>A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process.</p>
<p>We propose a new strategy for the non‐linear inversion of multi‐offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large‐scale matrix inversion but pays particular attention to different parameter types in the inversion.</p>
<p>We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub‐space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well‐conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.</p>
</abstract>
<langUsage><language ident="en"></language>
</langUsage>
</profileDesc>
</teiHeader>
</istex:fulltextTEI>
<json:item><extension>txt</extension>
<original>false</original>
<mimetype>text/plain</mimetype>
<uri>https://api.istex.fr/document/193702978CF9062D5962240E89CC03DF864E89D5/fulltext/txt</uri>
</json:item>
</fulltext>
<metadata><istex:metadataXml wicri:clean="Wiley, elements deleted: body"><istex:xmlDeclaration>version="1.0" encoding="UTF-8" standalone="yes"</istex:xmlDeclaration>
<istex:document><component version="2.0" type="serialArticle" xml:lang="en"><header><publicationMeta level="product"><publisherInfo><publisherName>Blackwell Publishing Ltd</publisherName>
<publisherLoc>Oxford, UK</publisherLoc>
</publisherInfo>
<doi origin="wiley" registered="yes">10.1111/(ISSN)1365-2478</doi>
<issn type="print">0016-8025</issn>
<issn type="electronic">1365-2478</issn>
<idGroup><id type="product" value="GPR"></id>
<id type="publisherDivision" value="ST"></id>
</idGroup>
<titleGroup><title type="main" sort="GEOPHYSICAL PROSPECTING">Geophysical Prospecting</title>
</titleGroup>
</publicationMeta>
<publicationMeta level="part" position="08006"><doi origin="wiley">10.1111/gpr.1991.39.issue-6</doi>
<numberingGroup><numbering type="journalVolume" number="39">39</numbering>
<numbering type="journalIssue" number="6">6</numbering>
</numberingGroup>
<coverDate startDate="1991-08">August 1991</coverDate>
</publicationMeta>
<publicationMeta level="unit" type="article" position="0072300" status="forIssue"><doi origin="wiley">10.1111/j.1365-2478.1991.tb00341.x</doi>
<idGroup><id type="unit" value="GPR723"></id>
</idGroup>
<countGroup><count type="pageTotal" number="14"></count>
</countGroup>
<eventGroup><event type="firstOnline" date="2006-04-27"></event>
<event type="publishedOnlineFinalForm" date="2006-04-27"></event>
<event type="xmlConverted" agent="Converter:BPG_TO_WML3G version:2.3.2 mode:FullText source:HeaderRef result:HeaderRef" date="2010-02-27"></event>
<event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-01-26"></event>
<event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.1.7 mode:FullText,remove_FC" date="2014-10-16"></event>
</eventGroup>
<numberingGroup><numbering type="pageFirst" number="723">723</numbering>
<numbering type="pageLast" number="736">736</numbering>
</numberingGroup>
<linkGroup><link type="toTypesetVersion" href="file:GPR.GPR723.pdf"></link>
</linkGroup>
</publicationMeta>
<contentMeta><countGroup><count type="referenceTotal" number="12"></count>
<count type="linksCrossRef" number="4"></count>
</countGroup>
<titleGroup><title type="main">AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS<link href="#fn1"><sup>1</sup>
</link>
</title>
</titleGroup>
<creators><creator creatorRole="author" xml:id="cr1" affiliationRef="#a1"><personName><givenNames>M. S.</givenNames>
<familyName>SAMBRIDGE</familyName>
</personName>
</creator>
<creator creatorRole="author" xml:id="cr2" affiliationRef="#a2"><personName><givenNames>A.</givenNames>
<familyName>TARANTOLA</familyName>
</personName>
</creator>
<creator creatorRole="author" xml:id="cr3" affiliationRef="#a3"><personName><givenNames>B. L. N.</givenNames>
<familyName>KENNETT</familyName>
</personName>
</creator>
</creators>
<affiliationGroup><affiliation xml:id="a1"><unparsedAffiliation>Institute of Theoretical Geophysics, Departments of Earth Sciences and Applied Mathematics and Theoretical Physics, Downing Street, Cambridge CB2 3EO, U.K.</unparsedAffiliation>
</affiliation>
<affiliation xml:id="a2" countryCode="FR"><unparsedAffiliation>Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cédex 05, France.</unparsedAffiliation>
</affiliation>
<affiliation xml:id="a3" countryCode="AU"><unparsedAffiliation>Research School of Earth Sciences, A.N.U., P.O. Box 4, Canberra, ACT 2601, Australia.</unparsedAffiliation>
</affiliation>
</affiliationGroup>
<abstractGroup><abstract type="main" xml:lang="en"><title type="main">A<sc>bstract</sc>
</title>
<p>A common example of a large‐scale non‐linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large‐scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions.</p>
<p>A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process.</p>
<p>We propose a new strategy for the non‐linear inversion of multi‐offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large‐scale matrix inversion but pays particular attention to different parameter types in the inversion.</p>
<p>We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub‐space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well‐conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.</p>
</abstract>
</abstractGroup>
</contentMeta>
<noteGroup><note xml:id="fn1"><label>1</label>
<p>Received January 1990, revision accepted February 1991.</p>
</note>
</noteGroup>
</header>
</component>
</istex:document>
</istex:metadataXml>
<mods version="3.6"><titleInfo lang="en"><title>AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS</title>
</titleInfo>
<titleInfo type="alternative" contentType="CDATA" lang="en"><title>AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS1</title>
</titleInfo>
<name type="personal"><namePart type="given">M. S.</namePart>
<namePart type="family">SAMBRIDGE</namePart>
<affiliation>Institute of Theoretical Geophysics, Departments of Earth Sciences and Applied Mathematics and Theoretical Physics, Downing Street, Cambridge CB2 3EO, U.K.</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">A.</namePart>
<namePart type="family">TARANTOLA</namePart>
<affiliation>Institut de Physique du Globe, 4 place Jussieu, 75252 Paris Cédex 05, France.</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<name type="personal"><namePart type="given">B. L. N.</namePart>
<namePart type="family">KENNETT</namePart>
<affiliation>Research School of Earth Sciences, A.N.U., P.O. Box 4, Canberra, ACT 2601, Australia.</affiliation>
<role><roleTerm type="text">author</roleTerm>
</role>
</name>
<typeOfResource>text</typeOfResource>
<genre type="article" displayLabel="article" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-6N5SZHKN-D">article</genre>
<originInfo><publisher>Blackwell Publishing Ltd</publisher>
<place><placeTerm type="text">Oxford, UK</placeTerm>
</place>
<dateIssued encoding="w3cdtf">1991-08</dateIssued>
<copyrightDate encoding="w3cdtf">1991</copyrightDate>
</originInfo>
<language><languageTerm type="code" authority="rfc3066">en</languageTerm>
<languageTerm type="code" authority="iso639-2b">eng</languageTerm>
</language>
<physicalDescription><extent unit="references">12</extent>
<extent unit="linksCrossRef">4</extent>
</physicalDescription>
<abstract lang="en">A common example of a large‐scale non‐linear inverse problem is the inversion of seismic waveforms. Techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions. As the size of the problem increases, techniques requiring the inversion of large matrices become very cumbersome. Considerable storage and computational effort are required to perform the inversion and to avoid stability problems. Consequently methods which do not require any large‐scale matrix inversion have proved to be very popular. Currently, descent type algorithms are in widespread use. Usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this, and perhaps previous descent directions. A common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion, i.e. unknowns of different dimension and character. However, this fundamental difference in parameter types is not reflected in the inversion algorithms used. Usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process. We propose a new strategy for the non‐linear inversion of multi‐offset reflection data. The paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3D structure, may be used in the waveform case. Specifically we show how to extend the algorithm presented by Tarantola to incorporate the subspace scheme. The proposed strategy involves no large‐scale matrix inversion but pays particular attention to different parameter types in the inversion. We use the formulae of Tarantola to state the problem as one of optimization and derive the same descent vectors. The new technique splits the descent vector so that each part depends on a different parameter type, and proceeds to minimize the misfit function within the sub‐space defined by these individual descent vectors. In this way, optimal use is made of the descent vector components, i.e. one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace. This is not the case with other gradient methods. By solving a linearized problem in the chosen subspace, at each iteration one need only invert a small well‐conditioned matrix (the projection of the full Hessian on to the subspace). The method is a hybrid between gradient and matrix inversion methods. The proposed algorithm requires the same gradient vectors to be determined as in the algorithm of Tarantola, although its primary aim is to make better use of those calculations in minimizing the objective function.</abstract>
<note type="content">*Received January 1990, revision accepted February 1991.</note>
<relatedItem type="host"><titleInfo><title>Geophysical Prospecting</title>
</titleInfo>
<genre type="journal" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0GLKJH51-B">journal</genre>
<identifier type="ISSN">0016-8025</identifier>
<identifier type="eISSN">1365-2478</identifier>
<identifier type="DOI">10.1111/(ISSN)1365-2478</identifier>
<identifier type="PublisherID">GPR</identifier>
<part><date>1991</date>
<detail type="volume"><caption>vol.</caption>
<number>39</number>
</detail>
<detail type="issue"><caption>no.</caption>
<number>6</number>
</detail>
<extent unit="pages"><start>723</start>
<end>736</end>
<total>14</total>
</extent>
</part>
</relatedItem>
<identifier type="istex">193702978CF9062D5962240E89CC03DF864E89D5</identifier>
<identifier type="ark">ark:/67375/WNG-JW1Q44P5-8</identifier>
<identifier type="DOI">10.1111/j.1365-2478.1991.tb00341.x</identifier>
<identifier type="ArticleID">GPR723</identifier>
<recordInfo><recordContentSource authority="ISTEX" authorityURI="https://loaded-corpus.data.istex.fr" valueURI="https://loaded-corpus.data.istex.fr/ark:/67375/XBH-L0C46X92-X">wiley</recordContentSource>
<recordOrigin>Blackwell Publishing Ltd</recordOrigin>
</recordInfo>
</mods>
<json:item><extension>json</extension>
<original>false</original>
<mimetype>application/json</mimetype>
<uri>https://api.istex.fr/document/193702978CF9062D5962240E89CC03DF864E89D5/metadata/json</uri>
</json:item>
</metadata>
<serie></serie>
</istex>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Asie/explor/AustralieFrV1/Data/Istex/Corpus
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000482 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Istex/Corpus/biblio.hfd -nk 000482 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Asie |area= AustralieFrV1 |flux= Istex |étape= Corpus |type= RBID |clé= ISTEX:193702978CF9062D5962240E89CC03DF864E89D5 |texte= AN ALTERNATIVE STRATEGY FOR NON‐LINEAR INVERSION OF SEISMIC WAVEFORMS }}
![]() | This area was generated with Dilib version V0.6.33. | ![]() |