spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver
<p>In this article, we introduce spyro, a software stack to solve wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite-element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Copernicus Publications
2022-11-01
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| Series: | Geoscientific Model Development |
| Online Access: | https://gmd.copernicus.org/articles/15/8639/2022/gmd-15-8639-2022.pdf |
| _version_ | 1798016570077741056 |
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| author | K. J. Roberts A. Olender L. Franceschini R. C. Kirby R. S. Gioria B. S. Carmo |
| author_facet | K. J. Roberts A. Olender L. Franceschini R. C. Kirby R. S. Gioria B. S. Carmo |
| author_sort | K. J. Roberts |
| collection | DOAJ |
| description | <p>In this article, we introduce spyro, a software stack to solve wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite-element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite-element method. The capability of the software is demonstrated by using a continuous Galerkin approach to perform FWI for seismic velocity model building, considering realistic geophysics examples. A time domain FWI approach that uses meshes composed of variably sized triangular elements to discretize the domain is detailed. To resolve both the forward and adjoint-state equations and to calculate a mesh-independent gradient associated with the FWI process, a fully explicit, variable higher-order (up to degree <span class="inline-formula"><i>k</i>=5</span> in 2D and <span class="inline-formula"><i>k</i>=3</span> in 3D) mass-lumping method is used. We show that, by adapting the triangular elements to the expected peak source frequency and properties of the wave field (e.g., local <span class="inline-formula"><i>P</i></span>-wave speed) and by leveraging higher-order basis functions, the number of degrees of freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both 2D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material properties.</p> |
| first_indexed | 2024-04-11T15:51:45Z |
| format | Article |
| id | doaj.art-d56ed992f525435f90d03a1eea3a3e16 |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-04-11T15:51:45Z |
| publishDate | 2022-11-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-d56ed992f525435f90d03a1eea3a3e162022-12-22T04:15:16ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032022-11-01158639866710.5194/gmd-15-8639-2022spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solverK. J. Roberts0A. Olender1L. Franceschini2R. C. Kirby3R. S. Gioria4B. S. Carmo5Department of Mining and Petroleum Engineering, Escola Politécnica, University of São Paulo, São Paulo, BrazilDepartment of Mechanical Engineering, Escola Politécnica, University of São Paulo, São Paulo, BrazilDepartment of Mechanical Engineering, Escola Politécnica, University of São Paulo, São Paulo, BrazilDepartment of Mathematics, Baylor University, Waco, USADepartment of Mining and Petroleum Engineering, Escola Politécnica, University of São Paulo, São Paulo, BrazilDepartment of Mechanical Engineering, Escola Politécnica, University of São Paulo, São Paulo, Brazil<p>In this article, we introduce spyro, a software stack to solve wave propagation in heterogeneous domains and perform full waveform inversion (FWI) employing the finite-element framework from Firedrake, a high-level Python package for the automated solution of partial differential equations using the finite-element method. The capability of the software is demonstrated by using a continuous Galerkin approach to perform FWI for seismic velocity model building, considering realistic geophysics examples. A time domain FWI approach that uses meshes composed of variably sized triangular elements to discretize the domain is detailed. To resolve both the forward and adjoint-state equations and to calculate a mesh-independent gradient associated with the FWI process, a fully explicit, variable higher-order (up to degree <span class="inline-formula"><i>k</i>=5</span> in 2D and <span class="inline-formula"><i>k</i>=3</span> in 3D) mass-lumping method is used. We show that, by adapting the triangular elements to the expected peak source frequency and properties of the wave field (e.g., local <span class="inline-formula"><i>P</i></span>-wave speed) and by leveraging higher-order basis functions, the number of degrees of freedom necessary to discretize the domain can be reduced. Results from wave simulations and FWIs in both 2D and 3D highlight our developments and demonstrate the benefits and challenges with using triangular meshes adapted to the material properties.</p>https://gmd.copernicus.org/articles/15/8639/2022/gmd-15-8639-2022.pdf |
| spellingShingle | K. J. Roberts A. Olender L. Franceschini R. C. Kirby R. S. Gioria B. S. Carmo spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver Geoscientific Model Development |
| title | spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver |
| title_full | spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver |
| title_fullStr | spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver |
| title_full_unstemmed | spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver |
| title_short | spyro: a Firedrake-based wave propagation and full-waveform-inversion finite-element solver |
| title_sort | spyro a firedrake based wave propagation and full waveform inversion finite element solver |
| url | https://gmd.copernicus.org/articles/15/8639/2022/gmd-15-8639-2022.pdf |
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