Beyond chi-squared: Additional measures of the closeness of a model to data

Abstract

Subtle, and not so subtle, features in our increasingly large and complex datasets are being missed because of our reliance on a single number, typically chi-squared based, to describe the distance between a plausible model and the data. Additional measures need to be used. Here I propose that the autocorrelations of the residuals between the data and the model responses be minimized as part of the objective function during inversion. I demonstrate the use on a toy example and three 1D magnetotelluric examples, one a synthetic “impossible” problem and two real ones.