Non-linear Smoothness-constrained Model Error and Resolution Estimates

Abstract

A comparison of error and resolution properties of 2-D models of electrical resistivity from single and joint inversions of direct-current resistivity (DCR) and radiomagnetotelluric (RMT) data is presented. Linearized model resolution and error estimates are computed from the Jacobian and its smoothness-constrained generalized inverse. As a novelty, linearized model errors are compared to most-squares error estimates to better account for non-linearity. For a synthetic example, linearized analyses yield model errors up to 30 to 40 per cent for data errors of two per cent and resolving kernels spread over several cells in the vicinity of the investigated cell. Most importantly, linearized errors are in good agreement with most-squares errors and, hence, linearized model errors can be representative. DCR data can constrain both resistive and conductive structures whereas RMT data provide superior constraints for conductive structures. For structures within the depth ranges of exploration of both methods, error and resolution of joint inverse models are equal to or better than those of single inversions. For structures outside the depth range of exploration of one method, error and resolution of joint inverse models are close to those of the best single inversion given appropriate data weighting.