Machine learned Green's functions that approximately satisfy the wave equation

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2020Machine learned Green's functions that approximately satisfy the wave equationAuthors: Tariq AlkhalifahChao SongUmair bin WaheedTariq AlkhalifahKAUSTSearch for more papers by this author, Chao SongKAUSTSearch for more papers by this author, and Umair bin WaheedKFUPMSearch for more papers by this authorhttps://doi.org/10.1190/segam2020-3421468.1 SectionsAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail AbstractGreen’s functions are wavefield solutions for a particular point source. They form basis functions to build wavefields for modeling and inversion. However, calculating Green’s functions are both costly and memory intensive. We formulate frequency-domain machine-learned Green’s functions that are represented by neural networks (NN). This NN outputs a complex number (two values representing the real and imaginary part) for the scattered Green’s function at a location in space for a specific source location (both locations are input to the network). Considering a background homogeneous medium admitting an analytical Green’s function solution, the network is trained by fitting the output perturbed Green’s function and its derivatives to the wave equation expressed in terms of the perturbed Green’s function. The derivatives are calculated through the concept of automatic differentiation. In this case, the background Green’s function absorbs the point source singularity, which will allow us to train the network using random points over space and source location using a uniform distribution. Thus, feeding a reasonable number of random points from the model space will ultimately train a fully connected 8-layer deep neural network, to predict the scattered Green’s function. Initial tests on part of the simple layered model (extracted from the left side of the Marmousi model) with sources on the surface demonstrate the successful training of the NN for this application. Using the trained NN model for the Marmousi as an initial NN model for solving for the scattered Green’s function for a 2D slice from the Sigsbee model helped the NN converge faster to a reasonable solution.Presentation Date: Wednesday, October 14, 2020Session Start Time: 1:50 PMPresentation Time: 2:15 PMLocation: 360APresentation Type: OralKeywords: modeling, frequency-domain, neural networks, machine learningPermalink: https://doi.org/10.1190/segam2020-3421468.1FiguresReferencesRelatedDetailsCited byPINNup: Robust Neural Network Wavefield Solutions Using Frequency Upscaling and Neuron Splitting15 June 2022 | Journal of Geophysical Research: Solid Earth, Vol. 127, No. 6Wavefield Reconstruction Inversion via Physics-Informed Neural NetworksIEEE Transactions on Geoscience and Remote Sensing, Vol. 60High-dimensional wavefield solutions based on neural network functionsTariq Alkhalifah, Chao Song, and Xinquan Huang1 September 2021A modified physics-informed neural network with positional encodingXinquan Huang, Tariq Alkhalifah, and Chao Song1 September 2021Solving the frequency-domain acoustic VTI wave equation using physics-informed neural networks11 January 2021 | Geophysical Journal International, Vol. 225, No. 2 SEG Technical Program Expanded Abstracts 2020ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2020 Pages: 3887 publication data© 2020 Published in electronic format with permission by the Society of Exploration GeophysicistsPublisher:Society of Exploration Geophysicists HistoryPublished Online: 30 Sep 2020 CITATION INFORMATION Tariq Alkhalifah, Chao Song, and Umair bin Waheed, (2020), "Machine learned Green's functions that approximately satisfy the wave equation," SEG Technical Program Expanded Abstracts : 2638-2642. https://doi.org/10.1190/segam2020-3421468.1 Plain-Language Summary Keywordsmodelingfrequency-domainneural networksmachine learningPDF DownloadLoading ...