Three-dimensional preconditioned FM-IBEM solution to broadband-frequency seismic wave scattering in a layered sedimentary basin

Abstract

A three-dimensional (3-D) fast multipole indirect boundary element method (FM-IBEM) combined with an inner-outer preconditioned generalized minimal residual (GMRES) method algorithm is proposed to solve the broadband-frequency seismic wave scattering problem in complex sites. This method is established in three steps: first, the scattering wave field is developed with the dynamic Green's function; second, the dynamic Green's functions are expanded to generate a traditional FM-IBEM framework; and finally, the preconditioning matrix and GMRES algorithm are introduced to pre-process the dynamic Green's functions. Using this method, the broadband-frequency scattering of normally incident seismic waves in a hemispherical layered sedimentary basin is investigated in the frequency and time domains. The results show that the proposed method is highly accurate and efficient for solving low- and high-frequency seismic wave problems. Compared with the FM-IBEM without preconditioning, the computational time and storage space required for the FM-IBEM with preconditioning are reduced by 84% and 54%, respectively. The layered sedimentary basin has significant wave amplification (of up to 10 times) for dimensionless frequencies, η, in the range of 0.5–3.0; however, for η > 5, the amplification effect becomes weak.