Measure for the resolving power and bias effect in the nonlinear inverse analysis of geophysical potential fields

Abstract

Several measures are proposed for the power of resolution and the bias effect of nonlinearity in the inverse analysis of geophysical potential fields. They are the power of complete resolution for the entire system of both data and parameters, the power of partial resolution for individual data prediction and parameter estimation, and the bias for the effect of linearization of a nonlinear function. Relations between the measures for the resolution power and bias are derived. The tradeoff relations between the resolving power and estimation variance are also demonstrated. All these measures are tested on a synthetic gravity data set. A two‐dimensional (2-D) forward gravity model is employed to demonstrate the use of the measures proposed in this study. The selection of the reference depth [Formula: see text] and the number of nonzero eigenvalues (q) is highlighted based on the 2-D prism forward model. The “best” [Formula: see text] is that value that produces the least curvature in the plot of singular values versus q. The choice of q is considered “best” when it meets most of the critical requirements (e.g., small bias and high resolving power) and then satisfies secondary important needs (e.g., estimation variance).