Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks
Incorporating anisotropy is crucial for accurately modeling seismic wave propagation. However, numerical solutions are susceptible to dispersion artifacts, and they often require considerable computational resources. Moreover, their accuracy is dependent on the size of discretization, which is a fun...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-08-01
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| Series: | Frontiers in Earth Science |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/articles/10.3389/feart.2023.1227828/full |
| _version_ | 1797739295137595392 |
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| author | Ali Imran Sandhu Umair bin Waheed Chao Song Oliver Dorn Pantelis Soupios |
| author_facet | Ali Imran Sandhu Umair bin Waheed Chao Song Oliver Dorn Pantelis Soupios |
| author_sort | Ali Imran Sandhu |
| collection | DOAJ |
| description | Incorporating anisotropy is crucial for accurately modeling seismic wave propagation. However, numerical solutions are susceptible to dispersion artifacts, and they often require considerable computational resources. Moreover, their accuracy is dependent on the size of discretization, which is a function of the operating frequency. Physics informed neural networks (PINNs) have demonstrated the potential to tackle long-standing challenges in seismic modeling and inversion, addressing the associated computational bottleneck and numerical dispersion artifacts. Despite progress, PINNs exhibit spectral bias, resulting in a stronger capability to learn low-frequency features over high-frequency ones. This paper proposes the use of a simple fully-connected PINN model, and evaluates its potential to interpolate and extrapolate scattered wavefields that correspond to the acoustic VTI wave equation across multiple frequencies. The issue of spectral bias is tackled by incorporating the Kronecker neural network architecture with composite activation function formed using the inverse tangent (atan), exponential linear unit (elu), locally adaptive sine (l-sin), and locally adaptive cosine (l-cos) activation functions. This allows the construction of an effectively wider neural network with a minimal increase in the number of trainable parameters. The proposed scheme keeps the network size fixed for multiple frequencies and does not require repeated training at each frequency. Numerical results demonstrate the efficacy of the proposed approach in fast and accurate, anisotropic multi-frequency wavefield modeling. |
| first_indexed | 2024-03-12T13:56:08Z |
| format | Article |
| id | doaj.art-aef3f5fc3a3c45ef804f0dc299060ba4 |
| institution | Directory Open Access Journal |
| issn | 2296-6463 |
| language | English |
| last_indexed | 2024-03-12T13:56:08Z |
| publishDate | 2023-08-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Earth Science |
| spelling | doaj.art-aef3f5fc3a3c45ef804f0dc299060ba42023-08-22T15:50:38ZengFrontiers Media S.A.Frontiers in Earth Science2296-64632023-08-011110.3389/feart.2023.12278281227828Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networksAli Imran Sandhu0Umair bin Waheed1Chao Song2Oliver Dorn3Pantelis Soupios4Center for Integrative Petroleum Research, College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi ArabiaCollege of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi ArabiaDepartment of Geophysics, Jilin University, Changchun, ChinaDepartment of Mathematics, The University of Manchester, Manchester, United KingdomCollege of Petroleum Engineering and Geosciences, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi ArabiaIncorporating anisotropy is crucial for accurately modeling seismic wave propagation. However, numerical solutions are susceptible to dispersion artifacts, and they often require considerable computational resources. Moreover, their accuracy is dependent on the size of discretization, which is a function of the operating frequency. Physics informed neural networks (PINNs) have demonstrated the potential to tackle long-standing challenges in seismic modeling and inversion, addressing the associated computational bottleneck and numerical dispersion artifacts. Despite progress, PINNs exhibit spectral bias, resulting in a stronger capability to learn low-frequency features over high-frequency ones. This paper proposes the use of a simple fully-connected PINN model, and evaluates its potential to interpolate and extrapolate scattered wavefields that correspond to the acoustic VTI wave equation across multiple frequencies. The issue of spectral bias is tackled by incorporating the Kronecker neural network architecture with composite activation function formed using the inverse tangent (atan), exponential linear unit (elu), locally adaptive sine (l-sin), and locally adaptive cosine (l-cos) activation functions. This allows the construction of an effectively wider neural network with a minimal increase in the number of trainable parameters. The proposed scheme keeps the network size fixed for multiple frequencies and does not require repeated training at each frequency. Numerical results demonstrate the efficacy of the proposed approach in fast and accurate, anisotropic multi-frequency wavefield modeling.https://www.frontiersin.org/articles/10.3389/feart.2023.1227828/fullHelmholtz equationphysics informed neural networks (PINNs)wavefield modelingseismic anisotropywave propagation |
| spellingShingle | Ali Imran Sandhu Umair bin Waheed Chao Song Oliver Dorn Pantelis Soupios Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks Frontiers in Earth Science Helmholtz equation physics informed neural networks (PINNs) wavefield modeling seismic anisotropy wave propagation |
| title | Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks |
| title_full | Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks |
| title_fullStr | Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks |
| title_full_unstemmed | Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks |
| title_short | Multi-frequency wavefield modeling of acoustic VTI wave equation using physics informed neural networks |
| title_sort | multi frequency wavefield modeling of acoustic vti wave equation using physics informed neural networks |
| topic | Helmholtz equation physics informed neural networks (PINNs) wavefield modeling seismic anisotropy wave propagation |
| url | https://www.frontiersin.org/articles/10.3389/feart.2023.1227828/full |
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