Three-Dimensional Inversion Algorithm with A Footprint Computational Domain for Underground Engineering

Abstract

Granite bodies pose a common geohazard in urban underground engineering. The GEM-2 system, employing small coils as transmitter and receiver (Tx-Rx), has gained widespread adoption for efficiently and non-invasively delineating low resistivity targets with 1D results in the near-surface. In this paper, we propose a 3D inversion algorithm based on the footprint-guided compact finite element method and Gauss-Newton optimization to accurately delineate the 3D structure of granite boulders. To demonstrate the effectiveness of our 3D inversion method, we conducted a GEM-2 test survey in a scenario featuring a granite boulder. The inversion results exhibit superior horizontal resolution compared to the current 1D inversion methods. The three-dimensional contour of the boulder is clearly depicted by areas of relatively high resistance, showcasing the capability of our inversion algorithm.