Improved diagonal tensor approximation (DTA) and hybrid DTA/BCGS–FFT method for accurate simulation of 3D inhomogeneous objects in layered media

This paper presents an improved diagonal tensor approximation (DTA) and its hybridization with the stabilized biconjugate-gradient fast Fourier transform (BCGS–FFT) algorithm to solve a volume integral equation for three-dimensional (3D) objects in layered media. The improvement in DTA is obtained for lossy media through a higher-order approximation. The interaction between the dyadic Green’s function and the contrast source is efficiently evaluated by the (FFT) algorithm through the convolution and correlation theorems. For the hybrid implementation, the DTA solution is used as an initial estimate and a preconditioner in the BCGS–FFT algorithm in order to solve the forwards modelling problem accurately with fewer iterations than the conventional BCGS–FFT algorithm. The accuracy and convergence of the DTA, BCGS–FFT and hybrid DTA/BCGS–FFT methods are compared extensively with several numerical examples. Numerical results show that (a) the improved DTA formulation enhances the accuracy and (b) the DTA/BCGS–FFT method can produce results as accurate as the conventional BCGS–FFT but with fewer iterations if the contrast is moderate. For very high contrasts, the hybrid method does not seem to improve further on the BCGS–FFT iteration convergence.