瞬变电磁全期视电阻率的弦截无限逼近算法

应用瞬变电磁法进行地质勘探的过程中，视电阻率的计算至关重要，反演视电阻率可以直观地描述地下地质体。利用传统的近似公式法计算的视电阻率误差过大，因此针对地面中心回线瞬变电磁法中全期视电阻率的隐函数特点，通过引进针对非线性函数的弦截求根方法，给出了视电阻率的弦截无限逼近求解方法及其计算步骤。该方法可避免对复杂函数的导数计算。仿真计算与应用实例表明，弦截法具有比二分法更快的收敛速度，并可以任意精度求解地面中心回线瞬变电磁法中的全期视电阻率。

A secant infinite approximation algorithm for the full-time apparent resistivity in transient electromagnetic method

In the geology exploration with the transient electromagnetic method (TEM),the apparent resistivity calculation is quite important as the appa-rent resistivity may intuitively indicate underground geological bodies.However,conventional approximation formulas usually lead a large error in the apparent resistivity calculation.According to the characteristics of implicit functions of apparent resistivity for half-space central-loop TEM,we propose in this paper a secant infinite approximation algorithm for the full-time apparent resistivity in the transient electromagnetic method,in which the secant method is used to calculate the roots of non-linear functions.The proposed algorithm avoids complicated derivative calculations of implicit functions.Simulation and real data examples show that the proposed algorithm has faster convergence than the bisection algorithm and can calculate with arbitrary accuracy the full-time apparent resistivity for half-space central-loop TEM.