Resolution matrices in time‐lapse gravity‐gradiometry imaging

Abstract

We partially form the nonlinear resolution matrix for a synthetic time‐lapse gravity gradiometry experiment based on an actual survey acquired in Colorado in 2005. Through computing the columns of the resolution matrix, we quantify the resolution as a function of the sparseness of data coverage and as a function of LP‐norm ( 1 ⩽ p ⩽ 2 ) applied to the model space. The results of this work can be used to optimize sensor placement in time‐lapse surveys as well as understand if the changes observed in time‐lapse imaging are real (i.e. sufficient resolution exists within the model). This is, in essence, a nonlinear model appraisal due to the LP‐norm, which favors the recovery of sharp density contrasts, and the use of logarithmic barrier constraints in the inversion process which provides realistic bounds for the recovered density. Therefore, the resolution matrix can be used in a post‐processing mode or for planning a deployment. In pre‐deployment calculations, the resolution matrix is used to understand the balance between maximizing sensor placement and unrealistic computation time due to use of an LP‐norm to recover increased model performance.