Abstract

An introduction to the Deepwave Python package that implements wave propagation as a PyTorch module, enabling forward and backpropagation through the 2D wave equation (regular scalar, Born, and elastic). It can be used for seismic forward modelling, different types of seismic inversion (including FWI and LSRTM), and provides the flexibility to be more creative, such as integrating wave propagation into a deep neural network. Examples discussed will include joint migration-inversion, inversion for source amplitudes to produce a target final wavefield, and using the GSOT objective function.

 

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 little 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.