The boundary integral method for the D.C. geoelectric problem in the 3-layered earth with a prismoid inhomogeneity in the second layer

Abstract

The paper presents algorithm and numerical results for the boundary integral equations (BIE) method of the forward D.C. geoelectric problem for the three-layered earth which contains the prismoidal body with sloped faces in the second layer. This situation occurs in the sedimentary basins. Although the numerical calculations are more complicated in comparison with faces orthogonal to the x, y, z axes, the generalization to the sloped faces enables treatment of the anomalous fields for the bodies of more general shapes as rectangular prisms. The graphs with numerical results present isoline maps of the perturbing potential as well as the resistivity profiles when the source field is due to the pair of D.C. electrodes at the surface of the earth. Also presented apparent resistivity curves for the Schlumberger array AMNB sounding.

Out‐of‐plane effects in 2D borehole‐to‐surface resistivity tomography and applications in mineral exploration

“…Numerical techniques have been applied to solve the forward problem of the geoelectric field, including the finite‐difference (FD) method (Mufti ; Dey and Morrison , b; Spitzer ; Zhang, Sun and Sun ; Demirci, Erdogan and Candansayar ), the finite‐element (FE) method (Coggon ; Bing and Greenhalgh ; Vachiratienchai, Boonchaisuk and Siripunvaraporn ; Vachiratienchai and Siripunvaraporn ), and the boundary integral method (Schulz ; Schulz ; Hvoždara ). Generally, the FD methods are numerical methods for differential equations using FD equations to mathematically approximate derivatives.…”