Abstract: In this paper, the numerical methods for improving the simulation accuracy of very late time response in Long-Offset TEM (LOTEM) sounding and its all-time apparent resistivity have been introduced. For the purpose, we use the direct numerical integration to get the low frequency response that fits in with the Hankel Transform. The integration is then recast into the form of the sum of the partial integration over the intervals constrained by the continuous roots of the Bessel Function of the first kind. And to accelerate the convergence speed of the sumation, continued fraction is adapted, and the coefficients of the continued fraction are evaluated from the partial integration over each integral subsection by a recursive method. In this way the direct integration of Hankel Transform can be fulfilled quickly and accurately. In consideration of the complexity of the electromagnetic response of LOTEM in half-space model, and basing on the idea that continued fraction has been utilized to solve nonlinear equations successfully, we try to adapt the method to obtain the all-time apparent resistivity from LOTEM responses, and to derive the iterative formulae for transforming the approximate solution into the continued fraction coefficients. Numerical simulation of theoretical models show that the combination of direct integration and continued fraction can greatly improve the calculation accuracy of rather low frequency response, and hence more accurate and stable late-time response of LOTEM can be obtained, while the range of the late time can be extended to about 100 seconds or more. A new method for estimating all-time apparent resistivity in LOTEM sounding is developed by using continued fraction expansion. The results of this study may provide scientific basis for the processing and interpretation of LOTEM data for understanding the electrical properties at greater depth.

Key words: LOTEM, numerical integration, very-late time, all-time apparent resistivity, continued fraction

摘要： 文中讨论了提高长偏移距瞬变电磁测深甚晚期响应计算精度及相应的全区视电阻率的计算方法。在频率域,利用直接数值积分结合连分式展开提高低频段响应的计算精度,从而提高时间域甚晚期响应的计算精度。同时,利用连分式渐进展开,将均匀半空间电阻率表示为该模型长偏移距瞬变电磁测深响应的反函数,利用迭代方法求出适合全时间段的全区视电阻率。数值结果表明,文中的方法可有效地提高长偏移距瞬变电磁测深(甚)晚期数据的模拟与解释精度。

关键词: 长偏移距瞬变电磁测深, 甚晚期, 数值积分, 全区视电阻率, 连分式