Inversion algorithm determining sharp boundaries in electrical resistivity tomography

Abstract

Blurred resistivity boundaries resulting from smoothness-regularized inversions of electrical resistivity tomography (ERT) data can lead to inaccurate interpretations of sharp boundary structures. To address this issue, various ERT inversion algorithms have introduced localized adjustments (localized discontinuities) in the regularization operator at positions where sharp boundaries are anticipated. Current approaches rely on prior information about sharp boundary locations, obtained from complementary geophysical, geologic, and drilling data, to determine the positions and weights for these regularization adjustments. However, such prior information is frequently insufficient, limiting the application of localized regularization adjustments. Accordingly, we develop a sharp boundary inversion (SBI) algorithm using the Akaike Bayesian information criterion (ABIC) that determines the optimal positions and weights for localized regularization adjustments by testing various configurations and selecting the one that minimizes ABIC. A synthetic modeling study demonstrates that the SBI algorithm correctly delineated the sharp boundaries of a conductor. Its application to field data demonstrates that it delineated the sharp boundaries of a utility tunnel, and the size and horizontal position of the recovered tunnel were consistent with the estimated dimensions from the blueprint. As it does not rely heavily on prior information, the SBI algorithm can be applied to a wide range of geophysical survey data, even when prior knowledge of sharp boundary locations is limited.