A stretched grid finite-difference time-domain scheme implemented with anisotropic perfectly matched layers

Abstract

A stable 2.5D finite difference time-domain (FDTD) scheme is developed to study wave propagation in heterogeneous media. On example is the logging while drilling configuration where small features such as the annulus between the drill pipe and the formation, only about 1/10 or even smaller than the wavelength in the steel pipe, affect the wave field significantly. The FDTD scheme proposed in this paper improves computational efficiency and accuracy from three aspects: griding, differencing, and numerical truncation. Coordinate stretching, proving to be more accurate, stable, and easy to implement, is employed to achieve variable griding. A wavelet-based differencing scheme is derived and compared with conventional FDTD schemes with spatial truncation accuracy being 2nd, 4th, 6th and 8th order. Because the wavelet-based and higher order FDTD scheme exhibits higher linear dispersion properties, it allows courser griding and is therefore more efficient. Reflections and transmission coefficients estimated from all FDTD schemes at a sharp boundary show that the wavelet-based FDTD solution outperforms the others. Efficient numerical truncation is realized by an anisotropic perfectly matched layer.