Transdimensional inversion of receiver functions and surface wave dispersion
Identifieur interne : 000948 ( Istex/Corpus ); précédent : 000947; suivant : 000949Transdimensional inversion of receiver functions and surface wave dispersion
Auteurs : T. Bodin ; M. Sambridge ; H. Tkal I ; P. Arroucau ; K. Gallagher ; N. RawlinsonSource :
- Journal of Geophysical Research: Solid Earth [ 0148-0227 ] ; 2012-02.
English descriptors
- KwdEn :
- Acceptance probability, Acceptance term, Agostinetti, Algorithm, Ambient, Ammon, Average solution, Average solution model, Bayes, Bayesian, Bayesian approach, Bayesian formulation, Bayesian framework, Bayesian inference, Birth step, Blue line, Bodin, Carlo, Computational, Constraint, Correlation function, Covariance, Covariance matrix, Crust, Crustal, Crustal structure, Current model, Data errors, Data noise, Data noise covariance matrix, Data sets, Data type, Data uncertainty, Data vector, Data vectors, Deconvolution, Determinant, Dettmer, Different data types, Different values, Discontinuity, Dispersion, Dispersion data, Dobs, Earth models, Earth planet, Earth sciences, Electromagnetic data, Ensemble, Ensemble solution, Exponential, Exponential correlation, First type, Frequency domain deconvolution, Gallagher, Gaussian, Gaussian correlation, Gaussian filter, Geoacoustic inversion, Geophys, Geophysical, Geophysical inversion, Geophysics, Hierarchical, Hierarchical bayes, Hierarchical bayes inversion, Hierarchical bayes procedure, Histogram, Interface, Inverse problem, Inversion, Inverted, Jacobian, Jacobian term, Jcej, Joint inversion, Joint inversions, Kennett, Large number, Layer, Lett, Lithospheric structure, Malinverno, Marginal distribution, Markov, Markov chain monte carlo, Matrix, Maximum solution, Maximum solution model, Misfit, Misfit function, Model parameter, Model parameters, Model space, Modelling, Moho, Neighborhood algorithm, Noise, Noise correlation, Noise covariance, Noise estimates, Noise parameterization, Noise parameters, Objective function, Optimization, Parameter, Parameterization, Parameterized, Partial derivatives, Perturbed, Piana, Piana agostinetti, Posterior, Posterior distribution, Posterior distributions, Posterior inference, Posterior probability, Posterior probability distribution, Probability density, Probability distribution, Proposal distribution, Proposal distributions, Proposal ratio, Rawlinson, Receiver function, Receiver function analysis, Receiver functions, Residual, Reversible jump algorithm, Sambridge, Second type, Seismic, Seismic structure, Seismic tomography, Seismol, Shear wave velocity, Station pairs, Surface wave dispersion, Surface wave dispersion data, Surface wave dispersion measurements, Surface waves, Synthetic data, Synthetic experiments, Synthetic noise, Teleseismic, Teleseismic receiver functions, Theory errors, Time series, Tomography, Transdimensional, Transdimensional inversion, True model, Uniform distribution, Upper mantle, Variable number, Variance, Velocity model, Velocity value, Velocity values, Vertical component, Visual inspection, Voronoi, Voronoi nuclei, Waveform, Wide range.
- Teeft :
- Acceptance probability, Acceptance term, Agostinetti, Algorithm, Ambient, Ammon, Average solution, Average solution model, Bayes, Bayesian, Bayesian approach, Bayesian formulation, Bayesian framework, Bayesian inference, Birth step, Blue line, Bodin, Carlo, Computational, Constraint, Correlation function, Covariance, Covariance matrix, Crust, Crustal, Crustal structure, Current model, Data errors, Data noise, Data noise covariance matrix, Data sets, Data type, Data uncertainty, Data vector, Data vectors, Deconvolution, Determinant, Dettmer, Different data types, Different values, Discontinuity, Dispersion, Dispersion data, Dobs, Earth models, Earth planet, Earth sciences, Electromagnetic data, Ensemble, Ensemble solution, Exponential, Exponential correlation, First type, Frequency domain deconvolution, Gallagher, Gaussian, Gaussian correlation, Gaussian filter, Geoacoustic inversion, Geophys, Geophysical, Geophysical inversion, Geophysics, Hierarchical, Hierarchical bayes, Hierarchical bayes inversion, Hierarchical bayes procedure, Histogram, Interface, Inverse problem, Inversion, Inverted, Jacobian, Jacobian term, Jcej, Joint inversion, Joint inversions, Kennett, Large number, Layer, Lett, Lithospheric structure, Malinverno, Marginal distribution, Markov, Markov chain monte carlo, Matrix, Maximum solution, Maximum solution model, Misfit, Misfit function, Model parameter, Model parameters, Model space, Modelling, Moho, Neighborhood algorithm, Noise, Noise correlation, Noise covariance, Noise estimates, Noise parameterization, Noise parameters, Objective function, Optimization, Parameter, Parameterization, Parameterized, Partial derivatives, Perturbed, Piana, Piana agostinetti, Posterior, Posterior distribution, Posterior distributions, Posterior inference, Posterior probability, Posterior probability distribution, Probability density, Probability distribution, Proposal distribution, Proposal distributions, Proposal ratio, Rawlinson, Receiver function, Receiver function analysis, Receiver functions, Residual, Reversible jump algorithm, Sambridge, Second type, Seismic, Seismic structure, Seismic tomography, Seismol, Shear wave velocity, Station pairs, Surface wave dispersion, Surface wave dispersion data, Surface wave dispersion measurements, Surface waves, Synthetic data, Synthetic experiments, Synthetic noise, Teleseismic, Teleseismic receiver functions, Theory errors, Time series, Tomography, Transdimensional, Transdimensional inversion, True model, Uniform distribution, Upper mantle, Variable number, Variance, Velocity model, Velocity value, Velocity values, Vertical component, Visual inspection, Voronoi, Voronoi nuclei, Waveform, Wide range.
Abstract
We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.
Url:
DOI: 10.1029/2011JB008560
Links to Exploration step
ISTEX:31ED01A1129DBF445173C8C77E9ACB291D43297BLe document en format XML
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Sambridge</name><affiliation><mods:affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</mods:affiliation></affiliation></author><author wicri:is="90%"><name sortKey="Tkal I, H" sort="Tkal I, H" uniqKey="Tkal I H" first="H." last="Tkal I">H. Tkal I</name><affiliation><mods:affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</mods:affiliation></affiliation></author><author wicri:is="90%"><name sortKey="Arroucau, P" sort="Arroucau, P" uniqKey="Arroucau P" first="P." last="Arroucau">P. Arroucau</name><affiliation><mods:affiliation>Environmental, Earth and Geospatial Sciences, North Carolina Central University, Durham, North Carolina, USA</mods:affiliation></affiliation></author><author><name sortKey="Gallagher, K" sort="Gallagher, K" uniqKey="Gallagher K" first="K." last="Gallagher">K. Gallagher</name><affiliation><mods:affiliation>Géosciences Rennes, Université de Rennes 1, Rennes, France</mods:affiliation></affiliation></author><author><name sortKey="Rawlinson, N" sort="Rawlinson, N" uniqKey="Rawlinson N" first="N." last="Rawlinson">N. 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Bodin</name><affiliation><mods:affiliation>E-mail: thomas.bodin@anu.edu.au</mods:affiliation></affiliation><affiliation><mods:affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</mods:affiliation></affiliation><affiliation><mods:affiliation>E-mail: thomas.bodin@anu.edu.au</mods:affiliation></affiliation></author><author><name sortKey="Sambridge, M" sort="Sambridge, M" uniqKey="Sambridge M" first="M." last="Sambridge">M. Sambridge</name><affiliation><mods:affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</mods:affiliation></affiliation></author><author wicri:is="90%"><name sortKey="Tkal I, H" sort="Tkal I, H" uniqKey="Tkal I H" first="H." last="Tkal I">H. Tkal I</name><affiliation><mods:affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</mods:affiliation></affiliation></author><author wicri:is="90%"><name sortKey="Arroucau, P" sort="Arroucau, P" uniqKey="Arroucau P" first="P." last="Arroucau">P. Arroucau</name><affiliation><mods:affiliation>Environmental, Earth and Geospatial Sciences, North Carolina Central University, Durham, North Carolina, USA</mods:affiliation></affiliation></author><author><name sortKey="Gallagher, K" sort="Gallagher, K" uniqKey="Gallagher K" first="K." last="Gallagher">K. Gallagher</name><affiliation><mods:affiliation>Géosciences Rennes, Université de Rennes 1, Rennes, France</mods:affiliation></affiliation></author><author><name sortKey="Rawlinson, N" sort="Rawlinson, N" uniqKey="Rawlinson N" first="N." last="Rawlinson">N. Rawlinson</name><affiliation><mods:affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</mods:affiliation></affiliation></author></analytic><monogr></monogr><series><title level="j" type="main">Journal of Geophysical Research: Solid Earth</title><title level="j" type="alt">JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH</title><idno type="ISSN">0148-0227</idno><idno type="eISSN">2156-2202</idno><imprint><biblScope unit="vol">117</biblScope><biblScope unit="issue">B2</biblScope><biblScope unit="page-count">24</biblScope><date type="published" when="2012-02">2012-02</date></imprint><idno type="ISSN">0148-0227</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0148-0227</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Acceptance probability</term><term>Acceptance term</term><term>Agostinetti</term><term>Algorithm</term><term>Ambient</term><term>Ammon</term><term>Average solution</term><term>Average solution model</term><term>Bayes</term><term>Bayesian</term><term>Bayesian approach</term><term>Bayesian formulation</term><term>Bayesian framework</term><term>Bayesian inference</term><term>Birth step</term><term>Blue line</term><term>Bodin</term><term>Carlo</term><term>Computational</term><term>Constraint</term><term>Correlation function</term><term>Covariance</term><term>Covariance matrix</term><term>Crust</term><term>Crustal</term><term>Crustal structure</term><term>Current model</term><term>Data errors</term><term>Data noise</term><term>Data noise covariance matrix</term><term>Data sets</term><term>Data type</term><term>Data uncertainty</term><term>Data vector</term><term>Data vectors</term><term>Deconvolution</term><term>Determinant</term><term>Dettmer</term><term>Different data types</term><term>Different values</term><term>Discontinuity</term><term>Dispersion</term><term>Dispersion data</term><term>Dobs</term><term>Earth models</term><term>Earth planet</term><term>Earth sciences</term><term>Electromagnetic data</term><term>Ensemble</term><term>Ensemble solution</term><term>Exponential</term><term>Exponential correlation</term><term>First type</term><term>Frequency domain deconvolution</term><term>Gallagher</term><term>Gaussian</term><term>Gaussian correlation</term><term>Gaussian filter</term><term>Geoacoustic inversion</term><term>Geophys</term><term>Geophysical</term><term>Geophysical inversion</term><term>Geophysics</term><term>Hierarchical</term><term>Hierarchical bayes</term><term>Hierarchical bayes inversion</term><term>Hierarchical bayes procedure</term><term>Histogram</term><term>Interface</term><term>Inverse problem</term><term>Inversion</term><term>Inverted</term><term>Jacobian</term><term>Jacobian term</term><term>Jcej</term><term>Joint inversion</term><term>Joint inversions</term><term>Kennett</term><term>Large number</term><term>Layer</term><term>Lett</term><term>Lithospheric structure</term><term>Malinverno</term><term>Marginal distribution</term><term>Markov</term><term>Markov chain monte carlo</term><term>Matrix</term><term>Maximum solution</term><term>Maximum solution model</term><term>Misfit</term><term>Misfit function</term><term>Model parameter</term><term>Model parameters</term><term>Model space</term><term>Modelling</term><term>Moho</term><term>Neighborhood algorithm</term><term>Noise</term><term>Noise correlation</term><term>Noise covariance</term><term>Noise estimates</term><term>Noise parameterization</term><term>Noise parameters</term><term>Objective function</term><term>Optimization</term><term>Parameter</term><term>Parameterization</term><term>Parameterized</term><term>Partial derivatives</term><term>Perturbed</term><term>Piana</term><term>Piana agostinetti</term><term>Posterior</term><term>Posterior distribution</term><term>Posterior distributions</term><term>Posterior inference</term><term>Posterior probability</term><term>Posterior probability distribution</term><term>Probability density</term><term>Probability distribution</term><term>Proposal distribution</term><term>Proposal distributions</term><term>Proposal ratio</term><term>Rawlinson</term><term>Receiver function</term><term>Receiver function analysis</term><term>Receiver functions</term><term>Residual</term><term>Reversible jump algorithm</term><term>Sambridge</term><term>Second type</term><term>Seismic</term><term>Seismic structure</term><term>Seismic tomography</term><term>Seismol</term><term>Shear wave velocity</term><term>Station pairs</term><term>Surface wave dispersion</term><term>Surface wave dispersion data</term><term>Surface wave dispersion measurements</term><term>Surface waves</term><term>Synthetic data</term><term>Synthetic experiments</term><term>Synthetic noise</term><term>Teleseismic</term><term>Teleseismic receiver functions</term><term>Theory errors</term><term>Time 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line</term><term>Bodin</term><term>Carlo</term><term>Computational</term><term>Constraint</term><term>Correlation function</term><term>Covariance</term><term>Covariance matrix</term><term>Crust</term><term>Crustal</term><term>Crustal structure</term><term>Current model</term><term>Data errors</term><term>Data noise</term><term>Data noise covariance matrix</term><term>Data sets</term><term>Data type</term><term>Data uncertainty</term><term>Data vector</term><term>Data vectors</term><term>Deconvolution</term><term>Determinant</term><term>Dettmer</term><term>Different data types</term><term>Different values</term><term>Discontinuity</term><term>Dispersion</term><term>Dispersion data</term><term>Dobs</term><term>Earth models</term><term>Earth planet</term><term>Earth sciences</term><term>Electromagnetic data</term><term>Ensemble</term><term>Ensemble solution</term><term>Exponential</term><term>Exponential correlation</term><term>First type</term><term>Frequency domain deconvolution</term><term>Gallagher</term><term>Gaussian</term><term>Gaussian correlation</term><term>Gaussian filter</term><term>Geoacoustic inversion</term><term>Geophys</term><term>Geophysical</term><term>Geophysical inversion</term><term>Geophysics</term><term>Hierarchical</term><term>Hierarchical bayes</term><term>Hierarchical bayes inversion</term><term>Hierarchical bayes procedure</term><term>Histogram</term><term>Interface</term><term>Inverse problem</term><term>Inversion</term><term>Inverted</term><term>Jacobian</term><term>Jacobian term</term><term>Jcej</term><term>Joint inversion</term><term>Joint inversions</term><term>Kennett</term><term>Large number</term><term>Layer</term><term>Lett</term><term>Lithospheric structure</term><term>Malinverno</term><term>Marginal distribution</term><term>Markov</term><term>Markov chain monte carlo</term><term>Matrix</term><term>Maximum solution</term><term>Maximum solution model</term><term>Misfit</term><term>Misfit function</term><term>Model parameter</term><term>Model parameters</term><term>Model space</term><term>Modelling</term><term>Moho</term><term>Neighborhood algorithm</term><term>Noise</term><term>Noise correlation</term><term>Noise covariance</term><term>Noise estimates</term><term>Noise parameterization</term><term>Noise parameters</term><term>Objective function</term><term>Optimization</term><term>Parameter</term><term>Parameterization</term><term>Parameterized</term><term>Partial derivatives</term><term>Perturbed</term><term>Piana</term><term>Piana agostinetti</term><term>Posterior</term><term>Posterior distribution</term><term>Posterior distributions</term><term>Posterior inference</term><term>Posterior probability</term><term>Posterior probability distribution</term><term>Probability density</term><term>Probability distribution</term><term>Proposal distribution</term><term>Proposal distributions</term><term>Proposal ratio</term><term>Rawlinson</term><term>Receiver function</term><term>Receiver function analysis</term><term>Receiver functions</term><term>Residual</term><term>Reversible jump algorithm</term><term>Sambridge</term><term>Second type</term><term>Seismic</term><term>Seismic structure</term><term>Seismic tomography</term><term>Seismol</term><term>Shear wave velocity</term><term>Station pairs</term><term>Surface wave dispersion</term><term>Surface wave dispersion data</term><term>Surface wave dispersion measurements</term><term>Surface waves</term><term>Synthetic data</term><term>Synthetic experiments</term><term>Synthetic noise</term><term>Teleseismic</term><term>Teleseismic receiver functions</term><term>Theory errors</term><term>Time series</term><term>Tomography</term><term>Transdimensional</term><term>Transdimensional inversion</term><term>True model</term><term>Uniform distribution</term><term>Upper mantle</term><term>Variable number</term><term>Variance</term><term>Velocity model</term><term>Velocity value</term><term>Velocity values</term><term>Vertical component</term><term>Visual inspection</term><term>Voronoi</term><term>Voronoi nuclei</term><term>Waveform</term><term>Wide range</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract">We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.</div></front></TEI><istex><corpusName>wiley</corpusName><keywords><teeft><json:string>transdimensional</json:string><json:string>geophys</json:string><json:string>bayesian</json:string><json:string>data noise</json:string><json:string>covariance</json:string><json:string>inversion</json:string><json:string>algorithm</json:string><json:string>transdimensional inversion</json:string><json:string>ensemble solution</json:string><json:string>joint inversion</json:string><json:string>sambridge</json:string><json:string>bayes</json:string><json:string>hierarchical</json:string><json:string>matrix</json:string><json:string>receiver 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Bodin</name><affiliations><json:string>E-mail: thomas.bodin@anu.edu.au</json:string><json:string>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</json:string><json:string>E-mail: thomas.bodin@anu.edu.au</json:string></affiliations></json:item><json:item><name>M. Sambridge</name><affiliations><json:string>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</json:string></affiliations></json:item><json:item><name>H. Tkalčić</name><affiliations><json:string>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</json:string></affiliations></json:item><json:item><name>P. Arroucau</name><affiliations><json:string>Environmental, Earth and Geospatial Sciences, North Carolina Central University, Durham, North Carolina, USA</json:string></affiliations></json:item><json:item><name>K. Gallagher</name><affiliations><json:string>Géosciences Rennes, Université de Rennes 1, Rennes, France</json:string></affiliations></json:item><json:item><name>N. Rawlinson</name><affiliations><json:string>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</json:string></affiliations></json:item></author><subject><json:item><lang><json:string>eng</json:string></lang><value>Bayesian inference</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>Monte Carlo methods</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>inverse theory</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>receiver function</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>surface waves</value></json:item><json:item><lang><json:string>eng</json:string></lang><value>time series analysis</value></json:item></subject><articleId><json:string>2011JB008560</json:string></articleId><arkIstex>ark:/67375/WNG-9MH9K420-W</arkIstex><language><json:string>eng</json:string></language><originalGenre><json:string>article</json:string></originalGenre><abstract>We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.</abstract><qualityIndicators><score>10</score><pdfWordCount>17371</pdfWordCount><pdfCharCount>101028</pdfCharCount><pdfVersion>1.6</pdfVersion><pdfPageCount>24</pdfPageCount><pdfPageSize>612 x 792 pts (letter)</pdfPageSize><refBibsNative>true</refBibsNative><abstractWordCount>301</abstractWordCount><abstractCharCount>1931</abstractCharCount><keywordCount>6</keywordCount></qualityIndicators><title>Transdimensional inversion of receiver functions and surface wave dispersion</title><genre><json:string>article</json:string></genre><host><title>Journal of Geophysical Research: Solid Earth</title><language><json:string>unknown</json:string></language><doi><json:string>10.1002/(ISSN)2156-2202b</json:string></doi><issn><json:string>0148-0227</json:string></issn><eissn><json:string>2156-2202</json:string></eissn><publisherId><json:string>JGRB</json:string></publisherId><volume>117</volume><issue>B2</issue><pages><first>n/a</first><last>n/a</last><total>24</total></pages><genre><json:string>journal</json:string></genre><subject><json:item><value>Seismology</value></json:item><json:item><value>COMPUTATIONAL GEOPHYSICS</value></json:item><json:item><value>Data analysis: algorithms and implementation</value></json:item><json:item><value>GEODESY AND GRAVITY</value></json:item><json:item><value>Rheology of the lithosphere and mantle</value></json:item><json:item><value>HYDROLOGY</value></json:item><json:item><value>Uncertainty assessment</value></json:item><json:item><value>INFORMATICS</value></json:item><json:item><value>Uncertainty</value></json:item><json:item><value>MATHEMATICAL GEOPHYSICS</value></json:item><json:item><value>Inverse theory</value></json:item><json:item><value>Uncertainty quantification</value></json:item><json:item><value>SEISMOLOGY</value></json:item><json:item><value>Lithosphere</value></json:item><json:item><value>Computational seismology</value></json:item><json:item><value>Seismology</value></json:item></subject></host><namedEntities><unitex><date><json:string>2012</json:string><json:string>1970s</json:string></date><geogName></geogName><orgName><json:string>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</json:string><json:string>North Carolina Central University</json:string><json:string>National Collaborative Research Infrastructure Strategy</json:string><json:string>Department of Innovation, Industry, Science and Research</json:string><json:string>Environmental, Earth</json:string><json:string>Australian Research Council Discovery</json:string><json:string>NCRIS</json:string><json:string>American Geophysical Union</json:string></orgName><orgName_funder></orgName_funder><orgName_provider></orgName_provider><persName><json:string>P. Arroucau</json:string><json:string>J. Geophys</json:string><json:string>Agostinetti</json:string><json:string>Malinverno</json:string><json:string>Scales</json:string><json:string>Ligorria</json:string><json:string>N. Rawlinson</json:string><json:string>Lombardi</json:string><json:string>O. Gudmundsson</json:string><json:string>M. Sambridge</json:string><json:string>Red</json:string><json:string>Valette</json:string><json:string>Sisson</json:string><json:string>The</json:string><json:string>Tarantola</json:string><json:string>Snieder</json:string><json:string>Ammon</json:string><json:string>K. Gallagher</json:string><json:string>H. 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[2005]</json:string><json:string>[1995, 2003]</json:string><json:string>Graeber et al., 2002</json:string><json:string>[108]</json:string><json:string>Agostinetti and Malinverno, 2010</json:string><json:string>Gelman et al., 2004</json:string><json:string>[100]</json:string><json:string>[73]</json:string><json:string>Juliá et al., 2000</json:string><json:string>Stehly et al., 2009</json:string><json:string>Reading et al., 2010</json:string><json:string>Box and Tiao, 1973</json:string><json:string>[2009]</json:string><json:string>Hetényi and Bus, 2007</json:string><json:string>Tkalčić et al. [2011]</json:string><json:string>[2]</json:string><json:string>Arroucau et al. [2010]</json:string><json:string>[57]</json:string><json:string>Vinnik et al., 2004, 2006</json:string><json:string>Zhao et al., 1996</json:string><json:string>Tokam et al., 2010</json:string><json:string>Gallagher et al., 2011</json:string><json:string>[105]</json:string><json:string>[124]</json:string><json:string>[2004]</json:string><json:string>Juliá et al., 2000, 2003</json:string></ref_bibl><bibl></bibl></unitex></namedEntities><ark><json:string>ark:/67375/WNG-9MH9K420-W</json:string></ark><categories><wos><json:string>1 - science</json:string><json:string>2 - geosciences, multidisciplinary</json:string></wos><scienceMetrix><json:string>1 - natural sciences</json:string><json:string>2 - earth & environmental sciences</json:string><json:string>3 - meteorology & atmospheric sciences</json:string></scienceMetrix><scopus><json:string>1 - Physical Sciences</json:string><json:string>2 - Earth and Planetary Sciences</json:string><json:string>3 - Palaeontology</json:string><json:string>1 - 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This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.</p></abstract><abstract style="short"><head>Key Points</head><p xml:id="jgrb16993-para-0002"><list style="bulleted"><item>Novel scheme for joint inversion of receiver function</item><item>Transdimensional algorithm where the number of layers is an unknown</item><item>Bayesian formulation correctly accounts for data and model uncertainties</item></list></p></abstract><textClass><keywords><term xml:id="jgrb16993-kwd-0001">Bayesian inference</term><term xml:id="jgrb16993-kwd-0002">Monte Carlo methods</term><term xml:id="jgrb16993-kwd-0003">inverse theory</term><term xml:id="jgrb16993-kwd-0004">receiver function</term><term xml:id="jgrb16993-kwd-0005">surface waves</term><term xml:id="jgrb16993-kwd-0006">time series analysis</term></keywords><classCode scheme="http://psi.agu.org/subset/ESE">Seismology</classCode><classCode scheme="http://psi.agu.org/taxonomy5/0500">COMPUTATIONAL GEOPHYSICS</classCode><classCode scheme="http://psi.agu.org/taxonomy5/1200">GEODESY AND GRAVITY</classCode><classCode scheme="http://psi.agu.org/taxonomy5/1800">HYDROLOGY</classCode><classCode scheme="http://psi.agu.org/taxonomy5/1900">INFORMATICS</classCode><classCode scheme="http://psi.agu.org/taxonomy5/3200">MATHEMATICAL GEOPHYSICS</classCode><classCode scheme="http://psi.agu.org/taxonomy5/7200">SEISMOLOGY</classCode><keywords rend="articleCategory"><term>Seismology</term></keywords><keywords rend="tocHeading1"><term>Seismology</term></keywords></textClass><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/31ED01A1129DBF445173C8C77E9ACB291D43297B/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 type="serialArticle" version="2.0" xml:lang="en" xml:id="jgrb16993"><header><publicationMeta level="product"><doi>10.1002/(ISSN)2156-2202b</doi><issn type="print">0148-0227</issn><issn type="electronic">2156-2202</issn><idGroup><id type="product" value="JGRB"></id><id type="coden" value="JGREA2"></id></idGroup><titleGroup><title type="main" xml:lang="en" sort="JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH">Journal of Geophysical Research: Solid Earth</title><title type="short">J. Geophys. Res.</title></titleGroup></publicationMeta><publicationMeta level="part" position="20"><doi>10.1002/jgrb.v117.B2</doi><idGroup><id type="focusSection" value="2"></id></idGroup><titleGroup><title type="focusSection" xml:lang="en">Journal of Geophysical Research: Solid Earth</title></titleGroup><numberingGroup><numbering type="journalVolume" number="117">117</numbering><numbering type="journalIssue">B2</numbering></numberingGroup><coverDate startDate="2012-02">February 2012</coverDate></publicationMeta><publicationMeta level="unit" type="article" position="350" status="forIssue"><doi>10.1029/2011JB008560</doi><idGroup><id type="editorialOffice" value="2011JB008560"></id><id type="society" value="B02301"></id><id type="unit" value="JGRB16993"></id></idGroup><countGroup><count type="pageTotal" number="24"></count></countGroup><titleGroup><title type="articleCategory">Seismology</title><title type="tocHeading1">Seismology</title></titleGroup><copyright ownership="thirdParty">Copyright 2012 by the American Geophysical Union</copyright><eventGroup><event type="manuscriptReceived" date="2011-06-05"></event><event type="manuscriptRevised" date="2011-11-17"></event><event type="manuscriptAccepted" date="2011-11-18"></event><event type="firstOnline" date="2012-02-03"></event><event type="publishedOnlineFinalForm" date="2012-02-03"></event><event type="xmlConverted" agent="SPi Global Converter:AGUv5.2_TO_WileyML3Gv1.0.3 version:1.1; WileyML 3G Packaging Tool v1.0; AGU2WileyML3G Final Clean Up v1.0" date="2012-12-13"></event><event type="xmlConverted" agent="Converter:WILEY_ML3G_TO_WILEY_ML3GV2 version:3.8.8" date="2014-01-31"></event><event type="xmlConverted" agent="Converter:WML3G_To_WML3G version:4.3.4 mode:FullText" date="2015-02-25"></event></eventGroup><numberingGroup><numbering type="pageFirst">n/a</numbering><numbering type="pageLast">n/a</numbering></numberingGroup><subjectInfo><subject href="http://psi.agu.org/subset/ESE">Seismology</subject><subject href="http://psi.agu.org/taxonomy5/0500">COMPUTATIONAL GEOPHYSICS</subject><subjectInfo><subject href="http://psi.agu.org/taxonomy5/0520">Data analysis: algorithms and implementation</subject></subjectInfo><subject role="crossTerm" href="http://psi.agu.org/taxonomy5/1200">GEODESY AND GRAVITY</subject><subjectInfo><subject role="crossTerm" href="http://psi.agu.org/taxonomy5/1236">Rheology of the lithosphere and mantle</subject></subjectInfo><subject role="crossTerm" href="http://psi.agu.org/taxonomy5/1800">HYDROLOGY</subject><subjectInfo><subject role="crossTerm" href="http://psi.agu.org/taxonomy5/1873">Uncertainty assessment</subject></subjectInfo><subject role="crossTerm" href="http://psi.agu.org/taxonomy5/1900">INFORMATICS</subject><subjectInfo><subject role="crossTerm" href="http://psi.agu.org/taxonomy5/1990">Uncertainty</subject></subjectInfo><subject href="http://psi.agu.org/taxonomy5/3200">MATHEMATICAL GEOPHYSICS</subject><subjectInfo><subject href="http://psi.agu.org/taxonomy5/3260">Inverse theory</subject><subject href="http://psi.agu.org/taxonomy5/3275">Uncertainty quantification</subject></subjectInfo><subject href="http://psi.agu.org/taxonomy5/7200">SEISMOLOGY</subject><subjectInfo><subject href="http://psi.agu.org/taxonomy5/7218">Lithosphere</subject><subject href="http://psi.agu.org/taxonomy5/7290">Computational seismology</subject></subjectInfo></subjectInfo><selfCitationGroup><citation xml:id="jgrb16993-cit-0000" type="self"><author><familyName>Bodin</familyName>, <givenNames>T.</givenNames></author>, <author><givenNames>M.</givenNames> <familyName>Sambridge</familyName></author>, <author><givenNames>H.</givenNames> <familyName>Tkalčić</familyName></author>, <author><givenNames>P.</givenNames> <familyName>Arroucau</familyName></author>, <author><givenNames>K.</givenNames> <familyName>Gallagher</familyName></author>, and <author><givenNames>N.</givenNames> <familyName>Rawlinson</familyName></author> (<pubYear year="2012">2012</pubYear>), <articleTitle>Transdimensional inversion of receiver functions and surface wave dispersion</articleTitle>, <journalTitle>J. Geophys. Res.</journalTitle>, <vol>117</vol>, B02301, doi:<accessionId ref="info:doi/10.1029/2011JB008560">10.1029/2011JB008560</accessionId>.</citation></selfCitationGroup><objectNameGroup><objectName elementName="appendix">Appendix</objectName></objectNameGroup><linkGroup><link type="toTypesetVersion" href="file:JGRB.JGRB16993.pdf"></link></linkGroup></publicationMeta><contentMeta><countGroup><count type="wordTotal" number="18300"></count><count type="figureTotal" number="15"></count></countGroup><titleGroup><title type="main">Transdimensional inversion of receiver functions and surface wave dispersion</title><title type="shortAuthors">BODIN ET AL.</title><title type="short">TRANSDIMENSIONAL INVERSION OF RF AND SWD</title></titleGroup><creators><creator xml:id="jgrb16993-cr-0001" creatorRole="author" affiliationRef="#jgrb16993-aff-0001"><personName><givenNames>T.</givenNames><familyName>Bodin</familyName></personName><contactDetails><email>thomas.bodin@anu.edu.au</email></contactDetails></creator><creator xml:id="jgrb16993-cr-0002" creatorRole="author" affiliationRef="#jgrb16993-aff-0001"><personName><givenNames>M.</givenNames><familyName>Sambridge</familyName></personName></creator><creator xml:id="jgrb16993-cr-0003" affiliationRef="#jgrb16993-aff-0001"><personName><givenNames>H.</givenNames><familyName>Tkalčić</familyName></personName></creator><creator xml:id="jgrb16993-cr-0004" affiliationRef="#jgrb16993-aff-0002"><personName><givenNames>P.</givenNames><familyName>Arroucau</familyName></personName></creator><creator xml:id="jgrb16993-cr-0005" creatorRole="author" affiliationRef="#jgrb16993-aff-0003"><personName><givenNames>K.</givenNames><familyName>Gallagher</familyName></personName></creator><creator xml:id="jgrb16993-cr-0006" creatorRole="author" affiliationRef="#jgrb16993-aff-0001"><personName><givenNames>N.</givenNames><familyName>Rawlinson</familyName></personName></creator></creators><affiliationGroup><affiliation xml:id="jgrb16993-aff-0001" countryCode="AU" type="organization"><unparsedAffiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</unparsedAffiliation></affiliation><affiliation xml:id="jgrb16993-aff-0002" countryCode="US" type="organization"><unparsedAffiliation>Environmental, Earth and Geospatial Sciences, North Carolina Central University, Durham, North Carolina, USA</unparsedAffiliation></affiliation><affiliation xml:id="jgrb16993-aff-0003" countryCode="FR" type="organization"><unparsedAffiliation>Géosciences Rennes, Université de Rennes 1, Rennes, France</unparsedAffiliation></affiliation></affiliationGroup><keywordGroup type="author"><keyword xml:id="jgrb16993-kwd-0001">Bayesian inference</keyword><keyword xml:id="jgrb16993-kwd-0002">Monte Carlo methods</keyword><keyword xml:id="jgrb16993-kwd-0003">inverse theory</keyword><keyword xml:id="jgrb16993-kwd-0004">receiver function</keyword><keyword xml:id="jgrb16993-kwd-0005">surface waves</keyword><keyword xml:id="jgrb16993-kwd-0006">time series analysis</keyword></keywordGroup><abstractGroup><abstract type="main"><p xml:id="jgrb16993-para-0001" label="1">We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.</p></abstract><abstract type="short"><title type="main">Key Points</title><p xml:id="jgrb16993-para-0002"><list style="bulleted"><listItem>Novel scheme for joint inversion of receiver function</listItem><listItem>Transdimensional algorithm where the number of layers is an unknown</listItem><listItem>Bayesian formulation correctly accounts for data and model uncertainties</listItem></list></p></abstract></abstractGroup></contentMeta></header></component></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Transdimensional inversion of receiver functions and surface wave dispersion</title></titleInfo><titleInfo type="abbreviated" lang="en"><title>TRANSDIMENSIONAL INVERSION OF RF AND SWD</title></titleInfo><titleInfo type="alternative" contentType="CDATA" lang="en"><title>Transdimensional inversion of receiver functions and surface wave dispersion</title></titleInfo><name type="personal"><namePart type="given">T.</namePart><namePart type="family">Bodin</namePart><affiliation>E-mail: thomas.bodin@anu.edu.au</affiliation><affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</affiliation><affiliation>E-mail: thomas.bodin@anu.edu.au</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">M.</namePart><namePart type="family">Sambridge</namePart><affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">H.</namePart><namePart type="family">Tkalčić</namePart><affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, Australia</affiliation></name><name type="personal"><namePart type="given">P.</namePart><namePart type="family">Arroucau</namePart><affiliation>Environmental, Earth and Geospatial Sciences, North Carolina Central University, Durham, North Carolina, USA</affiliation></name><name type="personal"><namePart type="given">K.</namePart><namePart type="family">Gallagher</namePart><affiliation>Géosciences Rennes, Université de Rennes 1, Rennes, France</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">N.</namePart><namePart type="family">Rawlinson</namePart><affiliation>Research School of Earth Sciences, Australian National University, Canberra, ACT, 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><dateIssued encoding="w3cdtf">2012-02</dateIssued><dateCaptured encoding="w3cdtf">2011-06-05</dateCaptured><dateValid encoding="w3cdtf">2011-11-18</dateValid><edition>Bodin, T., M. Sambridge, H. Tkalčić, P. Arroucau, K. Gallagher, and N. Rawlinson (2012), Transdimensional inversion of receiver functions and surface wave dispersion, J. Geophys. Res., 117, B02301, doi:10.1029/2011JB008560.</edition><copyrightDate encoding="w3cdtf">2012</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><physicalDescription><extent unit="figures">15</extent><extent unit="words">18300</extent></physicalDescription><abstract>We present a novel method for joint inversion of receiver functions and surface wave dispersion data, using a transdimensional Bayesian formulation. This class of algorithm treats the number of model parameters (e.g. number of layers) as an unknown in the problem. The dimension of the model space is variable and a Markov chain Monte Carlo (McMC) scheme is used to provide a parsimonious solution that fully quantifies the degree of knowledge one has about seismic structure (i.e constraints on the model, resolution, and trade‐offs). The level of data noise (i.e. the covariance matrix of data errors) effectively controls the information recoverable from the data and here it naturally determines the complexity of the model (i.e. the number of model parameters). However, it is often difficult to quantify the data noise appropriately, particularly in the case of seismic waveform inversion where data errors are correlated. Here we address the issue of noise estimation using an extended Hierarchical Bayesian formulation, which allows both the variance and covariance of data noise to be treated as unknowns in the inversion. In this way it is possible to let the data infer the appropriate level of data fit. In the context of joint inversions, assessment of uncertainty for different data types becomes crucial in the evaluation of the misfit function. We show that the Hierarchical Bayes procedure is a powerful tool in this situation, because it is able to evaluate the level of information brought by different data types in the misfit, thus removing the arbitrary choice of weighting factors. After illustrating the method with synthetic tests, a real data application is shown where teleseismic receiver functions and ambient noise surface wave dispersion measurements from the WOMBAT array (South‐East Australia) are jointly inverted to provide a probabilistic 1D model of shear‐wave velocity beneath a given station.</abstract><abstract type="short">Novel scheme for joint inversion of receiver function Transdimensional algorithm where the number of layers is an unknown Bayesian formulation correctly accounts for data and model uncertainties</abstract><subject><genre>keywords</genre><topic>Bayesian inference</topic><topic>Monte Carlo methods</topic><topic>inverse theory</topic><topic>receiver function</topic><topic>surface waves</topic><topic>time series analysis</topic></subject><relatedItem type="host"><titleInfo><title>Journal of Geophysical Research: Solid Earth</title></titleInfo><titleInfo type="abbreviated"><title>J. Geophys. 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