Forward modelling the multiply scattered 2.5-D teleseismic P waves accelerated by the multilevel fast multipole method

The present study introduces an algorithm to compute the forward modelling of multiple scattering. The propagating medium is defined, in general, by 3-D heterogeneities embedded in a 1-D layered structure, assumed as the reference structure. The 3-D formulation is consequently modified to suit 2.5-D scattering modelling. The basic formulation relies on the Green's function method and employs (1) the reflectivity method (RM) to acquire the 1-D multilayered, half-space Green's function, (2) the multilevel fast multipole method (MLFMM) to gain speed and (3) the generalized minimal residual method (GMRES) to iteratively solve the linear system in a memory efficient manner. The heterogeneities are modelled as point scatterers, creating a secondary wavefield that superimposes on the waves in the reference structure. The algorithm is efficient since the CPU time increases logarithmically with the size of the model. The test cases included various anomalous lithosphere structures, ranging from a simple point scatterer to a suture zone.