Physics-Informed Deep Learning for Wave-Based Seismic Imaging

Kurzfassung

This thesis investigates using a physics-informed continuous conditional Generative Adversarial Network (CcGAN) for simulating seismic wave propagation. Seismic wave simulations are a key element in seismic imaging used for subsurface exploration and discovery. In recent years, physics-informed machine learning (ML) and deep learning (DL) methods have emerged as valuable additions or substitutes to classical numerical simulation of partial differential equations (PDEs), one of their main benefits being fast computing time after training. We extend Kadeethum, et al. [1]'s CcGAN designed to solve a time-dependent PDE on a 2D domain by adding a physics consistency-based loss. The time-depended PDE of interest in this thesis is the acoustic wave equation. A CcGAN allows for generalization across velocity distribution inputs and handling continuous conditional variables like time. To our knowledge, this is the first use of a physics-informed CcGAN. We first compare a traditional CcGAN to a physics-informed one using uniform velocity distributions. Contrary to expectations, the traditional one outperformed the physics-informed one. Despite this, we applied the physics-informed CcGAN to a data set consisting of horizontally layered velocity distributions, hypothesizing that the advantages of using a physics-informed approach would become apparent with a more complex problem. However, the model showed mode collapse on the validation and test data sets, generating identical pressure wavefields regardless of the input velocity distributions. This mode collapse, a common issue in training traditional GANs, persisted despite employing a Wasserstein gradient-penalty GAN, which should have mitigated this problem. Encouragingly, our model generated varied pressure wavefields on the training dataset. Additionally, it demonstrated the ability to handle wavefield progression based on input times, thereby enabling the possibility of querying wavefields at individual timesteps without the need for preceding ones. Unfortunately, continuous time-stepping defaulted back on timesteps used during training. These findings underscore the need for additional research to address the unexpected physics-informed CcGAN behavior. Despite the challenges, the possibility of querying wavefields at arbitrary time steps highlights the potential of using DL methods to contribute to computational speed-ups in seismic simulation and imaging.