Numerical calculation of All‐Time Apparent Resistivity for Central Loop Transient Electromagnetic Method

Abstract

AbstractWe propose a numerical method for calculating exact all‐time apparent resistivity for time‐domain transient electromagnetic method. According to the behaviour of the kernel function Y'(Z) for ∂Bz/∂T, the transient can be distinguished into early‐time (Z > 1.6), transition point (Z = 1.6) and late‐time (Z < 1.6) stages for a central loop configuration. First the exact early‐time and late‐time apparent resisitivities are calculated using the earlytime and late‐time expressions , then the exact all‐time curve is founded by combining the two over the transition point. Although the kernel function Y (Z) for BZ is single valued, there is also a transition point Z = 1.6 and the early‐time and late‐time expressions should be used for Z > 1.6 and Z ≤ 1.6, respectively. For the numerical calculation an iterative procedure is employed. The relative error in the all‐time apparent resistivity will be less than 0.5% when the variation of the parameter Z is defined as ΔZ < 0.005Z in the iteration. Model calculation and field data experiments show that the resulting all‐time apparent resistivity can be easily determined with greater accuracy and higher resolution than that based on early‐time and late‐time asymptotic definitions.