A multilevel fast multiple method for computing the propagation of multiply scattered 2.5-D teleseismic surface waves underneath a linear or quasi-linear seismic station array

摘要

We introduce an algorithm for the forward modeling of multiple scattering of teleseismic surface waves where the underground structure beneath the linear (or quasi-linear) seismic station array is assumed two-dimensional and the teleseismic surface waves may be approached from an arbitrary direction. The current algorithm is two-and-half-dimensional since even though the structure is two-dimensional, the displacements are three-dimensional because of scattering outside the sagittal plane. The total displacement field is computed by applying a convolutional type integral equation for which the Green’s function is obtained by employing the normal mode theory in one-dimensional reference structure. When the number of data points gets large, the wavefield computations become awkward. In order to alleviate the computational burden, we employ the proficient multilevel fast multipole method where the central processing unit (CPU) time increases logarithmically with the size of the model.