# Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows Source: [Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows]() Collection index: [llms.txt]() Data updated: 2025-10-25T07:58:42.546Z Authors: Feng Liu, Haipeng Li, Guangyuan Zou, Junlun Li Published: 2024-11-30T13:58:41.000Z ## Abstract Full waveform inversion (FWI) is able to construct high-resolution subsurface models by iteratively minimizing discrepancies between observed and simulated seismic data. However, its implementation can be rather involved for complex wave equations, objective functions, or regularization. Recently, automatic differentiation (AD) has proven to be effective in simplifying solutions of various inverse problems, including FWI. In this study, we present an open-source AD-based FWI framework (ADFWI), which is designed to simplify the design, development, and evaluation of novel approaches in FWI with flexibility. The AD-based framework not only includes forword modeling and associated gradient computations for wave equations in various types of media from isotropic acoustic to vertically or horizontally transverse isotropic elastic, but also incorporates a suite of objective functions, regularization techniques, and optimization algorithms. By leveraging state-of-the-art AD, objective functions such as soft dynamic time warping and Wasserstein distance, which are difficult to apply in traditional FWI are also easily integrated into ADFWI. In addition, ADFWI is integrated with deep learning for implicit model reparameterization via neural networks, which not only introduces learned regularization but also allows rapid estimation of uncertainty through dropout. To manage high memory demands in large-scale inversion associated with AD, the proposed framework adopts strategies such as mini-batch and checkpointing. Through comprehensive evaluations, we demonstrate the novelty, practicality and robustness of ADFWI, which can be used to address challenges in FWI and as a workbench for prompt experiments and the development of new inversion strategies. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Full Waveform Inversion on Overthrust model](): Full Waveform Inversion; Overthrust model; MSE: 0.0592. - [Full Waveform Inversion on Overthrust Model Smooth](): Full Waveform Inversion; Overthrust Model Smooth; MSE: 0.0592. - [Full Waveform Inversion on OpenFWI Style noisy](): Full Waveform Inversion; OpenFWI Style noisy; MSE: 27.66. - [Full Waveform Inversion on OpenFWI FaltVel noisy](): Full Waveform Inversion; OpenFWI FaltVel noisy; MSE: 21.3. - [Full Waveform Inversion on OpenFWI CurveVel noisy](): Full Waveform Inversion; OpenFWI CurveVel noisy; MSE: 57.07. - [Full Waveform Inversion on OpenFWI FaltFault noisy](): Full Waveform Inversion; OpenFWI FaltFault noisy; MSE: 48.23. - [Full Waveform Inversion on OpenFWI CurveFault noisy](): Full Waveform Inversion; OpenFWI CurveFault noisy; MSE: 99.14. - [Full Waveform Inversion on 3D Overthrust model SEG/EAGE (test)](): Full Waveform Inversion; 3D Overthrust model SEG/EAGE (test); Normalized MSE: 0.1469. - [Full Waveform Inversion on Salt Model Constant](): Full Waveform Inversion; Salt Model Constant; MSE: 0.6337. - [Full Waveform Inversion on Marmousi Model Smooth](): Full Waveform Inversion; Marmousi Model Smooth; MSE: 0.2132. - [Full Waveform Inversion on Marmousi Model Constant](): Full Waveform Inversion; Marmousi Model Constant; MSE: 1.1522. - [Full Waveform Inversion on BP Model Constant 2004](): Full Waveform Inversion; BP Model Constant 2004; MSE: 0.4281. - [Full-Waveform Inversion on 2D Marmousi Smooth initial velocity model](): Full Waveform Inversion; 2D Marmousi Smooth initial velocity model; SSIM: 0.626. - [Full Waveform Inversion on Marmousi Model G-Noise](): Full Waveform Inversion; Marmousi Model G-Noise; MSE: 0.5422. - [Full Waveform Inversion on Salt Model Smooth](): Full Waveform Inversion; Salt Model Smooth; MSE: 0.6462. - [Full-Waveform Inversion on 2D Marmousi Constant initial velocity model](): Full Waveform Inversion; 2D Marmousi Constant initial velocity model; SSIM: 5.49. - [Full-Waveform Inversion on 2D Marmousi Gaussian noise 4σ0](): Full Waveform Inversion; 2D Marmousi Gaussian noise 4σ0; SSIM: 21.67. - [Full-Waveform Inversion on 2D Marmousi Gaussian noise 8σ0](): Full Waveform Inversion; 2D Marmousi Gaussian noise 8σ0; SSIM: 14.01. - [Full Waveform Inversion on Marmousi Model F-Cutoff](): Full Waveform Inversion; Marmousi Model F-Cutoff; MSE: 0.4975. - [Full-Waveform Inversion on 2D Marmousi Linear initial velocity model](): Full Waveform Inversion; 2D Marmousi Linear initial velocity model; SSIM: 0.2689. - [Full-Waveform Inversion on 2D Marmousi Frequency cutoff 4 Hz](): Full Waveform Inversion; 2D Marmousi Frequency cutoff 4 Hz; SSIM: 25.94. - [Full-Waveform Inversion on 2D Marmousi Frequency cutoff 6 Hz](): Full Waveform Inversion; 2D Marmousi Frequency cutoff 6 Hz; SSIM: 0.2287. - [Full-Waveform Inversion on 2D Marmousi 5 shots](): Full Waveform Inversion; 2D Marmousi 5 shots; SSIM: 19.69. - [Full Waveform Inversion on Salt model](): Full Waveform Inversion; Salt model; SSIM: 0.377. - [Full Waveform Inversion on Marmousi Model S-Shots (MSE)](): Full Waveform Inversion; Marmousi Model S-Shots; MSE: 0.473. - [Full Waveform Inversion on BP model 2004](): Full Waveform Inversion; BP model 2004; MSE: 0.1003. ## Original sources and implementation [Original paper]() [PDF]()