The role of model weighting functions in the gravity and DC resistivity inversion

Abstract

Summary The role of the model weighting function is decisive to give a correct reconstruction of the source properties in geophysical inversion. We analyze three different types of weighting functions for the gravity problem and for the linearized DC resistivity problem. While weighting functions based on depth weighting and compactness have been used in gravity inversion, they are not adopted in resistivity inversion. The comparison of the behaviors of these weighting functions in these two different problems is meaningful: both gravity and resistivity inversions are sensitive to the exponent of the depth weighting; but if compactness is also considered, gravity inversion depends only slightly on it, while the opposite occurs for DC resistivity. Finally, the roughness matrix, frequently assumed in DC resistivity algorithms, leads to a poor resolution at large depths, especially for pole-dipole and pole-pole arrays and give different models for the different arrays. Instead, the weighting function based on both compactness and depth weighting makes the inversion for different arrays consistent.