3‐D magnetotelluric inversion for resource exploration

Abstract

Summary The standard approach to solving nonlinear geophysical inverse problems is by iterative, linearized inversion, which when run to completion minimizes an objective function over the space of models. This method, however, requires computing a Jacobian (sensitivity) matrix and solving a nonsparse, linear system on the model space at each inversion iteration. These computational tasks, while tractable for one-dimensional (1-D) and two-dimensional (2-D) inverse problems, are prohibitive for larger and more complicated three-dimensional (3-D) problems. For 3-D magnetotelluric (MT) inversion, we use the method of nonlinear conjugate gradients (NLCG) applied directly to the minimization of the objective function. Given the structure of the MT problem, the NLCG method replaces computation of the Jacobian matrixand solution of a large linear system with computations equivalent to only three forward problems per inversion iteration, dramatically increasing the speed to convergence. The algorithm has been tested on both synthetic and real data. In both cases, the results are in good agreement with either the actual model or with known geology. The computation times are modest, taking approximately 10–12 hours on a 400 MHz desktop computer to invert 100 stations at 5 frequencies using 20 NLCG iterations.