Blocky regularization schemes for Full-Waveform Inversion

ABSTRACT With ill‐posed inverse problems such as Full‐Waveform Inversion, regularization schemes are needed to constrain the solution. Whereas many regularization schemes end up smoothing the model, an undesirable effect with FWI where high‐resolution maps are sought, blocky regularization does not:...

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Bibliographic Details
Published in:Geophysical Prospecting 2012-09, Vol.60 (5), p.870-884
Main Author: Guitton, Antoine
Format: Article
Language:English
Subjects:
Applied geophysics
Blocking
Discontinuity
Earth sciences
Earth, ocean, space
Exact sciences and technology
Full-Waveform Inversion
Geophysics
Illumination
Internal geophysics
Inverse problems
Inversions
Mathematical models
Preserves
Regularization
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Summary:ABSTRACT With ill‐posed inverse problems such as Full‐Waveform Inversion, regularization schemes are needed to constrain the solution. Whereas many regularization schemes end up smoothing the model, an undesirable effect with FWI where high‐resolution maps are sought, blocky regularization does not: it identifies and preserves strong velocity contrasts leading to step‐like functions. These models might be needed for imaging with wave‐equation based techniques such as Reverse Time Migration or for reservoir characterization. Enforcing blockiness in the model space amounts to enforcing a sparse representation of discontinuities in the model. Sparseness can be obtained using the ℓ1 norm or Cauchy function which are related to long‐tailed probability density functions. Detecting these discontinuities with vertical and horizontal gradient operators helps constraining the model in both directions. Blocky regularization can also help recovering higher wavenumbers that the data used for inversion would allow, thus helping controlling the cost of FWI. While the Cauchy function yields blockier models, both ℓ1 and Cauchy attenuate illumination and inversion artifacts.
ISSN:0016-8025
1365-2478
DOI:10.1111/j.1365-2478.2012.01025.x