The 3-D Finite Difference Time Domain Algorithm of Responses of Multi-component Electromagnetic Well Logging in a Deviated and Layered Anisotropic Formation

In this paper, we advance an algorithm of numerical modeling for responses of multicomponent electromagnetic well logging in a deviated and layered anisotropic formation through the 3-D finite difference time domain approach (FDTD). First, we use a Yee's staggered grid and linear interpolation formula to discretize the Maxwell equation in the time domain in an anisotropic medium and determine the non-defined components of electromagnetic (EM) field in the staggered grid in order to obtain the time recursive equation of the EM field on all staggered grids in an arbitrary anisotropic media. At the same time, area weighted average and transformation matrix are utilized to calculate the effective conductive tensors on the grids, and an absorbing boundary condition is executed to reduce the reflection of outer-boundary on the base of uniaxial anisotropic perfectly matched layer (UPML). Then, we apply three mutually orthogonal transmitter coils with a singlefrequency sinusoidal current to excite EM fields in the time domain and extract the amplitude and phase of EM from the EM field through a special two-equation and two-unknown (2E2U) approach to obtain the responses of multicomponent EM propagation logging tool. Finally, by numerical results we validate the algorithm and examine systematically the influence of changes in bed thickness, formation dipping angle and radius of invasion zones on responses of the tool.