Forward modelling the multiply scattered 2.5-D teleseismicPwaves accelerated by the multilevel fast multipole method

Abstract

S U M M A R YThe 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.

A New Method for Selecting the Phase and Group Velocity Dispersion Curves of Rayleigh and Love Surface Waves: Real Data Case of Central Anatolia, Turkey (Türkiye)

“…For instance, the joint inversion is followed in studying the surface waves and receiver functions for the structural inversion where the joint inversion is shown to delineate the subsurface velocity discontinuities better compared to these data sets inverted alone (Çakır & Erduran, 2003;Wu et al, 2022). In this respect, the current findings have the great potential to be jointly evaluated with the receiver functions as a future work (Ammon, 1991;Çakır, 2009;Erduran et al, 2022).…”

Fast 3‐D large‐scale gravity and magnetic modeling using unstructured grids and an adaptive multilevel fast multipole method

“…The number of source center points in each leaf cell is less than or equal to the presupposed number. The source center points of all leaf cells must be the same as the entire set of source center points to equivalently represent the source tetrahedral elements [Blome et al, 2009;Hackbusch and Nowak, 1989;Ren et al, 2013a]. The octree for the observation site is established in a very similar way.…”

“…Bapat et al ., ]. Its concept has only been sparsely used by the geophysical community with applications reported for the 3‐D direct current resistivity problem [ Blome et al ., ], the seismic wave propagation problem [ Çakir , ; Çakır , ], and the 3‐D electromagnetic induction problem [ Ren et al ., , ]. As for gravity modeling problems, only geometrically simple Earth models with 3‐D structured grids were considered [ May and Knepley , ].…”