Physics-embedded inverse analysis with algorithmic differentiation for the earth’s subsurface

Abstract

Inverse analysis has been utilized to understand unknown underground geological properties by matching the observational data with simulators. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented with embedded physics and a technique known as algorithmic differentiation. We use a physics-embedded generative model, which takes statistically simple parameters as input and outputs subsurface properties (e.g., permeability or P-wave velocity), that embeds physical knowledge of the subsurface properties into inverse analysis and improves its performance. We tested the application of this approach on four geologic problems: two heterogeneous hydraulic conductivity fields, a hydraulic fracture network, and a seismic inversion for P-wave velocity. This physics-embedded inverse analysis approach consistently characterizes these geological problems accurately. Furthermore, the excellent performance in matching the observational data demonstrates the reliability of the proposed method. Moreover, the application of algorithmic differentiation makes this an easy and fast approach to inverse analysis when dealing with complicated geological structures.

Feature scale and identifiability: How much information do point hydraulic measurements provide about heterogeneous head and conductivity fields?

“…Where the loss function is expensive to compute and the parameter space is high dimensional, it is generally not feasible to estimate the gradient naively via successive parameter perturbation. Various solutions exist, including automatic differentiation Elizondo et al (2002); Sambridge et al (2007); Wu et al (2023), and the adjoint state method, initially applied to the groundwater inverse problem by Sykes et al (1985). Adjoint state formulations for groundwater model inversion commonly incorporate head data only (Sykes et al, 1985;Carrera and Neuman, 1986b;Lu and Vesselinov, 2015;Delay et al, 2019), although they have been formulated to incorporate other forms of information (Cirpka and Kitanidis, 2001).…”

GaussianRandomFields.jl: A Julia package to generate and sample from Gaussian random fields

“…GaussianRandomFields.jl provides Julia implementations of Gaussian random fields with stationary separable and non-separable isotropic and anisotropic covariance functions. It has been used in a number of recent works, including (Blondeel et al, 2020), (Robbe et al, 2021) and (Wu et al, 2023).…”

Early steps toward practical subsurface computations with quantum computing

“…Traditionally, a seismic inverse problem of this nature could be solved using imaging methods such as reverse time migration (Baysal et al, 1983) or full waveform inversion (Virieux and Operto, 2009). Hydrologic inverse problems are usually solved using variants of the geostatistical approach such as the principal component geostatistical approach (Kitanidis and Lee, 2014) and sometimes more modern techniques leveraging machine learning are used (Kadeethum et al, 2021;Wu et al, 2023).…”