Propagation of seismic shear and surface waves in a laterally heterogeneous mantle by multiple forward scattering

A method for modelling the propagation and scattering of seismic shear and surface waves in the upper 1000 km of the Earth's mantle is proposed. Its intended application is the computation of the seismic displacement field in a time window between the arrival of the S wave and the end of the first surface-wave train for epicentral distances of less than 50 degrees. The displacement is synthesized in the frequency domain by superimposing contributions from all surface-wave overtones with phase velocities less than a pre-defined upper bound. It is shown that for each overtone the displacement can be derived from a potential defined on the unit sphere. The potentials satisfy a system of coupled integral equations, one for each overtone, that is equivalent to the eigenvalue problem of quasi-degenerate perturbation theory. A numerical approach is used to solve these equations in which the total potential for a given overtone is formed from its value in a spherically symmetric earth plus scattered potentials that originate at scattering cells on the unit sphere and are excited through coupling of the overtone to itself and to all other overtones. In the near field of the source, the Born approximation is used. while in the far field multiple forward scattering is taken into account. The method is applied to idealized models of a subducted slab and a plume head. Snapshots of the displacement field at the surface and on vertical cross-sections passing through the heterogeneity together with record sections along different profiles are shown. In addition, sensitivity kernels in the time domain are presented that exhibit their largest amplitude in the neighbourhood of the geometrical ray path; however, they show significant and extended off-path sensitivity.