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A trade-off solution between model resolution and covariance in surface-wave inversion

Pure and Applied Geophysics

By:
, , , and
DOI: 10.1007/s00024-010-0107-z

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Abstract

Regularization is necessary for inversion of ill-posed geophysical problems. Appraisal of inverse models is essential for meaningful interpretation of these models. Because uncertainties are associated with regularization parameters, extra conditions are usually required to determine proper parameters for assessing inverse models. Commonly used techniques for assessment of a geophysical inverse model derived (generally iteratively) from a linear system are based on calculating the model resolution and the model covariance matrices. Because the model resolution and the model covariance matrices of the regularized solutions are controlled by the regularization parameter, direct assessment of inverse models using only the covariance matrix may provide incorrect results. To assess an inverted model, we use the concept of a trade-off between model resolution and covariance to find a proper regularization parameter with singular values calculated in the last iteration. We plot the singular values from large to small to form a singular value plot. A proper regularization parameter is normally the first singular value that approaches zero in the plot. With this regularization parameter, we obtain a trade-off solution between model resolution and model covariance in the vicinity of a regularized solution. The unit covariance matrix can then be used to calculate error bars of the inverse model at a resolution level determined by the regularization parameter. We demonstrate this approach with both synthetic and real surface-wave data. ?? 2010 Birkh??user / Springer Basel AG.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
A trade-off solution between model resolution and covariance in surface-wave inversion
Series title:
Pure and Applied Geophysics
DOI:
10.1007/s00024-010-0107-z
Volume
167
Issue:
12
Year Published:
2010
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
Larger Work Title:
Pure and Applied Geophysics
First page:
1537
Last page:
1547
Number of Pages:
11