Modeling in Subsurface Geophysics: Mathematics, Computation, and Machine Learning

Abstract

Understanding the structure of Earth’s subsurface is critical in many science, engineering, and business domains, from earthquake monitoring and forecasting to hydrocarbon exploration and carbon sequestration. Observations of seismic waves, from both anthropogenic and non-anthropogenic sources, yield many techniques for recovering models of subsurface structure. In this talk, I will introduce the concepts and challenges associated with reconstructing models of the subsurface through seismic tomography, imaging, and inversion. I will present the subsurface inversion workflow, from data acquisition, through modeling and computation, to interpretation and decision making. In this context, I will present the mathematics, computation, and intuition behind full-waveform inversion, an adjoint-based method for solving this inverse problem where the solution is constrained by the governing physics of the wave equation. Finally, looking forward, I will connect the mathematics and computation of FWI to related concepts in deep learning.