Semi‐Supervised Surface Wave Tomography With Wasserstein Cycle‐Consistent GAN: Method and Application to Southern California Plate Boundary Region

Abstract

Machine learning algorithm has been applied to shear wave velocity (Vs) inversion in surface wave tomography, where a set of starting 1‐D Vs profiles and their corresponding synthetic dispersion curves are used in network training. Previous studies showed that the performance of such trained network is dependent on the diversity of the training data set, which limits its application to previously poorly understood regions. Here, we present an improved semi‐supervised algorithm‐based network that takes both model‐generated and observed surface wave dispersion data in the training process. The algorithm is termed Wasserstein cycle‐consistent generative adversarial networks (Wasserstein Cycle‐GAN [Wcycle‐GAN]). Different from conventional supervised approaches, the GAN architecture enables the inclusion of unlabeled data (the observed surface wave dispersion) in the training process that can complement the model‐generated data set. The cycle‐consistency and Wasserstein metric significantly improve the training stability of the proposed algorithm. We benchmark the Wcycle‐GAN method using 4,076 pairs of fundamental mode Rayleigh wave phase and group velocity dispersion curves derived in periods from 3 to 16 s in Southern California. The final 3‐D Vs model given by the best trained network shows large‐scale features consistent with the surface geology. The resulting Vs model has reasonable data misfits and provides sharper images of structures near faults in the top 15 km compared with those from conventional machine learning methods.

Machine Learning Developments and Applications in Solid‐Earth Geosciences: Fad or Future?

“…Most studies in this category design deep neural networks that are capable to capture the complex transformation from the measured data space to the desired model parameter space, train these machines using paired models and their corresponding synthetic data, and apply the trained machines to field datasets. Applications of such a framework range across the whole spectrum of geophysical inverse problems, including surface wave dispersion inversion and tomography (Cai et al, 2022;X. Zhang & Curtis, 2021), seismic-to-petrophysics inversion (Xiong et al, 2021;C.…”

Fault2SeisGAN: A method for the expansion of fault datasets based on generative adversarial networks

“…These will case the vanishing gradient problem which could lead to generated data loss its diversity even become abnormal. To solve this problem, the Wasserstein distance (Cai et al, 2022) was used in this study instead of the JS divergence to improve the stability of the GAN and reduce the training difficulty. The Wasserstein distance is defined as:…”

“…In recent years, deep learning technology has been developed rapidly and applied in various fields. In contrast to traditional model-driven methods, deep learning is data-driven and has been well applied by geophysicists in various branches including end-to-end seismic data denoising (Herrmann and Hennenfent, 2008;Zhang et al, 2017;Yu et al, 2019;Zhu et al, 2019), missing data recovery and reconstruction (Mandelli et al, 2018;Wang et al, 2019;Wang et al, 2020), first arrival picking (Wu et al, 2019a;Hu et al, 2019;Yuan et al, 2020), deeplearning velocity inversion (Araya-Polo et al, 2018;Adler et al, 2019;Cai et al, 2022), deep-learning seismology inversion (Wang et al, 2022) and fault interpretation (Wu et al, 2019c;Wu et al, 2019d;Cunha et al, 2020;Yang et al, 2022).…”

Characterization of Subsurface Hydrogeological Structures With Convolutional Conditional Neural Processes on Limited Training Data

“…With the extraordinary ability to extract complex characteristics of deep learning technique, various generative models are applied to hydrogeological modeling (Cai et al., 2022; Laloy et al., 2018; Lopez‐Alvis et al., 2022; Yang et al., 2022; Zhan et al., 2022; K. Zhang et al., 2021). In the majority of relevant research, generative models are trained to learn the distribution of training data and reproduce the probability distribution according to the test data.…”

“…With the extraordinary ability to extract complex characteristics of deep learning technique, various generative models are applied to hydrogeological modeling (Cai et al, 2022;Laloy et al, 2018;Lopez-Alvis et al, 2022;Yang et al, 2022;Zhan et al, 2022;K. Zhang et al, 2021).…”