Adaptive waveform inversion for transmitted wave data
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arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915057484431360 |
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| author | Symes, William W. |
| author_facet | Symes, William W. |
| contents | Adaptive Waveform Inversion (AWI) applied to transient transmitted wave data can yield estimates of index of refraction (or wave velocity) similar to those obtained by travel time inversion. The AWI objective function measures normalized mean-square dispersion about zero time of a family of filters, one filter for each source-reeciver pair, designed to match predicted data to observed data. Provided that the data contain a single smooth wavefront, this function approaches the mean square traveltime error as data wavelength tends to zero. The scaling of each filter to have unit norm is responsible for the simple relation with travel time tomography. A similar approach, Matched Source Waveform Inversion (MSWI), does not normalize the filters and has a looser relation with mean-square travel time error. If substantial energy is spread amongst multiple arrivals, on the other hand, neither AWI nor MSWI objectives approximate the travel time mean square erorr, and attempts to minimize them by local (Newton-related) optimization are as likely to stagnate at models predicting erroneous travel times as is least-square Full Waveform Inversion (FWI). The matching filter at the heart of this approach must be ``pre-whitened'', that is, computed by solving a regularized least squares problem for filtered data misfit. In order for the relation to traveltime tomography to hold, and for the filtered data misfit to stay relatively small, the regularization weight must be coupled to data wavelength. These objective functions can also be used as penalty terms in a homotopy of objectives connecting AWI or MSWI with FWI. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17696 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Adaptive waveform inversion for transmitted wave data Symes, William W. Optimization and Control Analysis of PDEs 35R30 Adaptive Waveform Inversion (AWI) applied to transient transmitted wave data can yield estimates of index of refraction (or wave velocity) similar to those obtained by travel time inversion. The AWI objective function measures normalized mean-square dispersion about zero time of a family of filters, one filter for each source-reeciver pair, designed to match predicted data to observed data. Provided that the data contain a single smooth wavefront, this function approaches the mean square traveltime error as data wavelength tends to zero. The scaling of each filter to have unit norm is responsible for the simple relation with travel time tomography. A similar approach, Matched Source Waveform Inversion (MSWI), does not normalize the filters and has a looser relation with mean-square travel time error. If substantial energy is spread amongst multiple arrivals, on the other hand, neither AWI nor MSWI objectives approximate the travel time mean square erorr, and attempts to minimize them by local (Newton-related) optimization are as likely to stagnate at models predicting erroneous travel times as is least-square Full Waveform Inversion (FWI). The matching filter at the heart of this approach must be ``pre-whitened'', that is, computed by solving a regularized least squares problem for filtered data misfit. In order for the relation to traveltime tomography to hold, and for the filtered data misfit to stay relatively small, the regularization weight must be coupled to data wavelength. These objective functions can also be used as penalty terms in a homotopy of objectives connecting AWI or MSWI with FWI. |
| title | Adaptive waveform inversion for transmitted wave data |
| topic | Optimization and Control Analysis of PDEs 35R30 |
| url | https://arxiv.org/abs/2402.17696 |