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      FWIGAN: Full‐Waveform Inversion via a Physics‐Informed Generative Adversarial Network

      1 , 2
      Journal of Geophysical Research: Solid Earth
      American Geophysical Union (AGU)

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          Abstract

          Full‐waveform inversion (FWI) is a powerful geophysical imaging technique that reproduces high‐resolution subsurface physical parameters by iteratively minimizing the misfit between the simulated and observed seismograms. Unfortunately, conventional FWI with a least‐squares loss function suffers from various drawbacks, such as the local‐minima problem and human intervention in the fine‐tuning of parameters. It is particular problematic when applied with noisy data and inadequate starting models. Recent work relying on partial differential equations and neural networks show promising performance in two‐dimensional FWI. Inspired by the competitive learning of generative adversarial networks, we propose an unsupervised learning paradigm that integrates the wave equation with a discriminative network to accurately estimate physically consistent velocity models in a distributional sense (FWIGAN). The introduced framework does not require a labeled training dataset or pretraining of the network; therefore, this framework is flexible and able to achieve inversion with minimal user interaction. We experimentally validate our method for three baseline geological models, and a comparison of the results demonstrates that FWIGAN faithfully recovers the velocity models and consistently outperforms other traditional or deep learning‐based algorithms. A further benefit from the physics‐constrained learning used in this method is that FWIGAN mitigates the local‐minima issue by reducing the sensitivity to initial models or data noise.

          Plain Language Summary

          We propose a method for inverting seismic data to estimate seismic velocities in 2D using deep learning techniques combined with physical principles. Unlike traditional full‐waveform inversion (FWI) methods, we use the wave equation to generate simulated seismic data and use a neural network to measure the difference between the simulated and observed data. Velocity models of the subsurface can be recovered by minimizing this difference. A key feature of the proposed framework is that it can simultaneously reconstruct multiple parameters during the optimization process. By adding white noise, we show that our method is able to produce accurate results even for noisy observed data. Moreover, this method does not need labeled training data or pretraining and is flexible due to certain automated features of deep learning platforms. Our method requires minimal user intervention and is easily implemented for applications. We use numerical examples to show that the proposed method represents a substantial improvements over traditional and deep learning‐based FWI methods, as well as being more generalizable and robust.

          Key Points

          • We proposed a physics‐informed unsupervised learning framework for two‐dimensional full‐waveform inversion of stress‐free surfaces

          • This method does not require labeled training data or network pretraining, which makes it more generalizable and easier to implement in applications

          • Our framework can produce high‐quality velocity models by solving a min‐max competitive learning problem based on the Wasserstein distance

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          Deep learning allows computational models that are composed of multiple processing layers to learn representations of data with multiple levels of abstraction. These methods have dramatically improved the state-of-the-art in speech recognition, visual object recognition, object detection and many other domains such as drug discovery and genomics. Deep learning discovers intricate structure in large data sets by using the backpropagation algorithm to indicate how a machine should change its internal parameters that are used to compute the representation in each layer from the representation in the previous layer. Deep convolutional nets have brought about breakthroughs in processing images, video, speech and audio, whereas recurrent nets have shone light on sequential data such as text and speech.
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            U-Net: Convolutional Networks for Biomedical Image Segmentation

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              Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations

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                Author and article information

                Contributors
                Journal
                Journal of Geophysical Research: Solid Earth
                JGR Solid Earth
                American Geophysical Union (AGU)
                2169-9313
                2169-9356
                April 2023
                April 20 2023
                April 2023
                : 128
                : 4
                Affiliations
                [1 ] Department of Mathematics Harbin Institute of Technology Harbin China
                [2 ] School of Earth and Space Sciences Institute of Artificial Intelligence Peking University Beijing China
                Article
                10.1029/2022JB025493
                37fee5cd-ef11-4d3e-bb78-ca4c32556a9c
                © 2023

                http://onlinelibrary.wiley.com/termsAndConditions#vor

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