回线源瞬变电磁法有限体积三维任意各向异性正演及分析

目前,瞬变电磁法(TEM)数据基本都是基于各向同性模型进行反演解释,这对于存在明显电性各向异性的勘探区域会产生较大的反演解释误差.为分析电各向异性对回线源瞬变电磁信号的影响方式与程度,本文通过求解离散化的全张量电导率时间域Helmholtz方程,实现了基于有限体积法的TEM任意各向异性的三维正演算法.该算法采用基于交错网格的拟态有限体积法(MFV)对时域Maxwell方程组进行空间域离散,并利用后退欧拉算法(Backward Euler Method)进行时间域离散.为提高时域电磁场的求解精度与效率,该算法将时间分段等步长算法与方程直接求解法相结合.通过对一维各向异性模型以及三维复杂各向同性模型进行测试,验证了本算法对于回线源瞬变电磁响应计算的正确性及有效性.最后,通过对几类典型电各向异性介质中大回线源瞬变电磁信号响应的分析,总结了不同电各向异性类型对TEM电磁信号的影响模式,结果表明,主轴各向异性情况下TEM信号主要受水平方向电导率的影响,倾斜各向异性对TEM信号的影响程度远大于水平各向异性,而通过水平各向异性信号能较清晰判断出各向异性主轴方向.

3D forward modeling and analysis of the loop-source transient electromagnetic method based on the finite-volume method for an arbitrarily anisotropic medium

Electrical anisotropy of strata has been long recognized by field and laboratory observations. However, nearly all of interpretations of transient electromagnetic (TEM) data is based on the assumption of electric isotropy of media, which can cause misleading data interpretation in regions with strong electrical anisotropy. To clarify the influence of electrical anisotropy on loop-source TEM responses, we present a three dimensional (3D) robust finite-volume (FV) algorithm for simulating TEM responses in an arbitrarily anisotropic medium through solving Helmholtz equations in the time domain. The time domain Maxwell equations are discretized using the mimetic finite-volume method (MFV) on a conventional staggered grid in the space domain and discretized in the time domain using the backward Euler method. To reduce time steps required by computation, the modeling time is first divided into several intervals, each of which has a constant time step size. Then, the resulting system matrix in each interval is factored and solved by a direct solver, which allows the factored matrix to be used to calculate the TEM responses for subsequent time steps in the same time interval. The accuracy of our algorithm is validated against quasi-analytic solutions of a 1-D layered anisotropic model. Finally, by numerical experiments for 3D models with different types of electrical anisotropy, we analyze the influences of electrical anisotropy on TEM responses. The results demonstrate that TEM responses are mainly affected by the horizontal conductivity. The effect of dipping anisotropy on TEM responses is much greater than horizontal anisotropy. Besides, the horizontal principle-axis direction of electrical anisotropy could be inferred from the TEM signal.