Incorporating prior information into geophysical inversion: from regularized inversion of thermal data to a framework using conditional variational autoencoders

Abstract

Geophysical inversion provides physical property models which are essential to understanding and characterizing the subsurface. However, traditional inversion methods recover models with smooth features that do not resemble geologic structures. Incorporating prior information into inversion can encourage geologic realism in recovered models, but how best to do so remains an open research question. I develop methods to inject prior information into inversion to recover more geologically realistic models. First, I develop methods for generalized inversion of temperature and heat flow data. While thermal data containing information about the subsurface distribution of thermal conductivity are widely available, methods to invert thermal data are underexplored. I formulate Tikhonov inversion algorithms to recover continuously varying distributions of thermal conductivity from borehole temperature data and surface heat flow data. The naïve application of Tikhonov inversion produces unrealistically smooth models that only contain structure near data locations, so I employ sensitivity-based model weighting and an lp model norm to improve the inversion results. Next, I develop a framework that is capable of promoting complicated geologic structures in inverted models. Geological realism is challenging to quantify, but recently, generative neural networks have proven capable of capturing complex spatial and petrophysical information from a set of example models. I train a conditional variational autoencoder to incorporate learned information into geophysical inversion and generate models that resemble the example models while honoring the specific data to be inverted. I apply this framework to two different problems. First, I invert gravity data, using synthetic layered and faulted density models as a training set. I show that the method can recover models that exhibit faulting, layering, compact bodies, and sharp boundaries, all difficult characteristics to enforce using traditional inversion methods. Second, I apply the framework to magnetotelluric inversion, using publicly available borehole logs to construct a set of conductivity models for training. By training on models that exemplify how conductivity is distributed in the subsurface, I incorporate geologic information from a widely available yet vastly underutilized type of data into the inversion results.