Comparative appraisal of linear inverse models constructed via distinctive parameterizations (comparing distinctly inverted models)

Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus‐Gilbert's theory demonstrates that the resolvable model variation is the truth viewed through the resolution kernel that is woven by the data kernels. The actual numerical resolution amoun...

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Published in:	Journal of Geophysical Research: Solid Earth Vol. 115; no. B7
Main Authors:	Chiao, Ling-Yun, Fang, Hui-Yuan, Gung, Yuan-Cheng, Chang, Yu-Hsuan, Hung, Shu-Huei
Format:	Journal Article
Language:	English
Published:	Washington, DC Blackwell Publishing Ltd 01.07.2010 American Geophysical Union
Subjects:	Assessments covariance matrix Earth Earth sciences Earth structure Earth, ocean, space Exact sciences and technology finite parameterization Geophysics Inverse inverse problem Kernels Mathematical analysis Mathematical models Mathematics multiresolution representation Parametrization regularization resolution kernel Seismology transformation operator Wavelet transforms Far East Asia Taiwan experimental studies models inverse problem Consistency covariance splines lead offshore Regularization method Earth parametrization tomography noise wavelet Inner product Spherical harmonic plate boundaries tectonics theory
ISSN:	0148-0227, 2169-9313, 2156-2202, 2169-9356
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Abstract	Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus‐Gilbert's theory demonstrates that the resolvable model variation is the truth viewed through the resolution kernel that is woven by the data kernels. The actual numerical resolution amounts to the inversion of the Gram matrix formed by the inner products among data kernels. However, due to the usually sizable amount of data constraints and/or imperfection of the forward theory, the practical implementations are usually tackled through certain a priori finite parameterizations based on rather arbitrary choices of bases such as spatial voxels, splines, spherical harmonics, or spherical wavelets. The cross assessment on the consistency among inverse models parameterized or regularized differently has long been downplayed. It is shown in this study that straightforward conversions among different model representations also enable the direct conversions of the Gram matrices. This leads to significant flexibility in formulating the forward data rule in one representation and then carrying out the actual inversion in an alternate domain. Furthermore, it is also fairly easy to convert both the model covariance and resolution matrices across different representations. These conversions thus enable direct assessments across inverse models obtained via different parameterizations and different regularization schemes. An example utilizing preliminary results of an experiment of ambient noise tomography of a plate boundary region of complex tectonics for the northeast coast and offshore area of Taiwan is shown to demonstrate such comparisons.
AbstractList	Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus-Gilbertʼ s theory demonstrates that the resolvable model variation is the truth viewed through the resolution kernel that is woven by the data kernels. The actual numerical resolution amounts to the inversion of the Gram matrix formed by the inner products among data kernels. However, due to the usually sizable amount of data constraints and/or imperfection of the forward theory, the practical implementations are usually tackled through certain a priori finite parameterizations based on rather arbitrary choices of bases such as spatial voxels, splines, spherical harmonics, or spherical wavelets. The cross assessment on the consistency among inverse models parameterized or regularized differently has long been downplayed. It is shown in this study that straightforward conversions among different model representations also enable the direct conversions of the Gram matrices. This leads to sig Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus‐Gilbert's theory demonstrates that the resolvable model variation is the truth viewed through the resolution kernel that is woven by the data kernels. The actual numerical resolution amounts to the inversion of the Gram matrix formed by the inner products among data kernels. However, due to the usually sizable amount of data constraints and/or imperfection of the forward theory, the practical implementations are usually tackled through certain a priori finite parameterizations based on rather arbitrary choices of bases such as spatial voxels, splines, spherical harmonics, or spherical wavelets. The cross assessment on the consistency among inverse models parameterized or regularized differently has long been downplayed. It is shown in this study that straightforward conversions among different model representations also enable the direct conversions of the Gram matrices. This leads to significant flexibility in formulating the forward data rule in one representation and then carrying out the actual inversion in an alternate domain. Furthermore, it is also fairly easy to convert both the model covariance and resolution matrices across different representations. These conversions thus enable direct assessments across inverse models obtained via different parameterizations and different regularization schemes. An example utilizing preliminary results of an experiment of ambient noise tomography of a plate boundary region of complex tectonics for the northeast coast and offshore area of Taiwan is shown to demonstrate such comparisons.
Author	Gung, Yuan-Cheng Chiao, Ling-Yun Chang, Yu-Hsuan Fang, Hui-Yuan Hung, Shu-Huei
Author_xml	– sequence: 1 givenname: Ling-Yun surname: Chiao fullname: Chiao, Ling-Yun email: chiao@ntu.edu.tw organization: Institute of Oceanography, National Taiwan University, Taipei, Taiwan – sequence: 2 givenname: Hui-Yuan surname: Fang fullname: Fang, Hui-Yuan organization: Institute of Oceanography, National Taiwan University, Taipei, Taiwan – sequence: 3 givenname: Yuan-Cheng surname: Gung fullname: Gung, Yuan-Cheng organization: Department of Geosciences, National Taiwan University, Taipei, Taiwan – sequence: 4 givenname: Yu-Hsuan surname: Chang fullname: Chang, Yu-Hsuan organization: Department of Geosciences, National Taiwan University, Taipei, Taiwan – sequence: 5 givenname: Shu-Huei surname: Hung fullname: Hung, Shu-Huei organization: Department of Geosciences, National Taiwan University, Taipei, Taiwan
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Keywords	experimental studies models inverse problem Consistency covariance splines lead offshore Regularization method Earth parametrization tomography noise wavelet Inner product Spherical harmonic plate boundaries tectonics theory
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Snippet	Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus‐Gilbert's theory demonstrates that the resolvable... Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus-Gilbert's theory demonstrates that the resolvable... Most geophysical inverse problems deal with models of the continuous Earth structure. The classical Backus-Gilbertʼ s theory demonstrates that the resolvable...
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SubjectTerms	Assessments covariance matrix Earth Earth sciences Earth structure Earth, ocean, space Exact sciences and technology finite parameterization Geophysics Inverse inverse problem Kernels Mathematical analysis Mathematical models Mathematics multiresolution representation Parametrization regularization resolution kernel Seismology transformation operator Wavelet transforms
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Title	Comparative appraisal of linear inverse models constructed via distinctive parameterizations (comparing distinctly inverted models)
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