Investigation of a Coupled Deterministic Inversion for the Interior of the Earth by using Gravity-Anomaly, Acoustic-Wavefield and Geodetic Velocity measurements

Conventionally, exploration in geology involves distinct research groups, each looking at a different observable and performing separate inversions for subsurface structure. In this work we discuss the advantages and performance of a combined inversion coupling gravity-anomaly, acoustic-wavefield and surface velocities as observables in one single framework. The gravity potential, which varies across the Earth, is sensitive to density anomalies at depth and can be obtained by solving a Poisson type equation. Its inversion is ill-posed since its solutions are non-unique in the depth and the density of the inverted anomaly. We also consider the surface displacement caused by a compressible wave as a consequence of an earthquake at depth. This inversion results in a wavespeed reconstruction but lacks interpretability, i.e. whether the anomaly is thermal or chemical in origin. The surface velocity, caused by the motion of highly viscous rocks in the subsurface, is the third observable. It can be modelled by the (nonlinear) Stokes equations, which account for the density and viscosity of a subsurface anomaly.

All three equations and their adjoints are implemented in one single Python framework using the finite element library FeNICS. To investigate the shape of the cost function, a grid search in the parameter space for three geological settings is presented. Additionally, the performance of gradient-based inversions for each observable separately or in combination, respectively, is presented. We further investigate the performance of a shape-optimizing inversion method, assuming the material parameters are known, while the shape is unknown.