Transient electromagnetic response of a three‐dimensional body in a layered earth

Abstract

by a large rectangular loop is substantial when host currents are strong near the conductor. The more con ductive the host, the longer the galvanic responses will The three-dimensional (3-D) electromagnetic scatter persist. Large galvanic responses occur if a 3-D conduc ing problem is tirst formulated in the frequency domain tor is in contact with a conductive overburden. For a in terms of an electric field volume integral equation.thin vertical dike embedded within a conductive host, Three-dimensional responses are then Fourier trans the 3-D response is similar in form but differs in mag formed with sine and cosine digital filters or with the nitude and duration from the 2-D response generated decay spectrum. The digital filter technique is applied to by two infinite line sources positioned parallel to the a sparsely sampled frequency sounding, which is re strike direction of the 2-D structure.placed by a cubic spline interpolating function prior to We have used the 3-D solution to study the appli convolution with the digital filters. Typically, 20 to 40 cation of the central-loop method to structural interpre frequencies at five to eight points per decade are re tation. The results suggest variations of thickness of quired for an accurate solution. A calculated transient is conductive overburden and depth to sedimentary struc usually in error after it has decayed more than six ture beneath volcanics can be mapped with one orders in magnitude from early to late time. The decay dimensional inversion. Successful 1-D inversions of 3-D spectrum usually req uires ten frequencies for a satisfac transient soundings replace a 3-D conductor by a con tory solution. However, the solution using the decay ducting layer at a similar depth. However, other pos spectrum appears to be less accurate than the solution sibilities include reduced thickness and resistivity of the using the digital filters, particularly after early times.(-0 host containing the body. Many different l-D Checks on the 3-D solution include reciprocity and con models can be fit to a transient sounding over a 3-D vergence checks in the frequency domain, and a com structure. Near-surface, 3-D geologic noise will not per parison of Fourier-transformed responses with results manently contaminate a central-loop apparent resistivi from a direct time-domain integral equation solution. ty sounding. The noise is band-limited in time and even The galvanic response of a 3-D conductor energized tually vanishes at late times.

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An electromagnetic induction method for underground target detection and characterization

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