Parallel joint inversion of three-dimensional DC resistivity and seismic travel-time data with cross-gradient constraints

Abstract:

A major challenge in interpreting geophysical data is to obtain consistent three-dimensional (3D) earth models of different physical properties from spatially and temporally limited measurements. One solution is to apply structurally constrained joint inversion of different geophysical data by imposing constraints that encourage correlation between different geophysical properties in space or time. Here, we present a joint inversion of 3D direct-current (DC) resistivity and seismic travel-time data by imposing structural similarities between electrical conductivity and seismic velocity using cross-gradient constraints. The code is massively parallelized and built upon E4D, an open-source software for DC resistivity and seismic travel-time data simulation and inversion. It utilizes existing E4D frameworks for parallel unstructured-mesh finite-element forward simulation, distributed storage and computation of the Jacobian matrix of the forward operator, and parallel execution of matrix-vector multiplication during a Gauss-Newton optimization. To accommodate unstructured tetrahedral mesh in E4D, a least-square gradient method is applied to compute the gradients of model parameters to impose cross-gradient constraints. Although it involves matrix inversion and hence has more computational overhead, the least-square method provides higher accuracy than the direct methods (e.g. Green-Gauss gradient method), especially, when the shape and size of the mesh cells vary widely. The code consists of two levels of iterations: the outer iterations update the Jacobian of forward operators and cross-gradients; the inner iterations solve the normal equations assembled per outer iteration using a preconditioned nonlinear conjugate gradient algorithm. We demonstrate the efficiency of the joint inversion code by considering 3D synthetic borehole surveys of DC resistivity and seismic travel-time data. The results show that the joint inversion with cross-gradient constraints enhances correlations between inverted conductivity and velocity models and results in more accurate geometry and position of anomalies than the separate inversions.