Finite boundary perturbation theory for the elastic equation of motion

Abstract

S U M M A R YIn the waveform inversion for global 3-D heterogeneous mantle structure, it is critical to accurately compute the perturbation of synthetic seismograms caused by the crustal heterogeneities. In actual applications, to reduce the required CPU time, a weak form equation of motion in terms of global trial functions is widely used. For those trial functions, the principal difficulty is how to compute the effect of the perturbation in the location of boundaries (such as Moho and the surface). In previous studies, the formulation has been based on the first-order perturbation theory of the free oscillation. However, this method holds only for weakly heterogeneous media and for lower frequencies. In this study, we derive the exact weak form elastic equation of motion for finite boundary perturbations. Our method can be applied to arbitrary strongly heterogeneous media and to arbitrary frequencies, and should facilitates accurate crustal correction.

Whole mantle SH velocity model constrained by waveform inversion based on three-dimensional Born kernels

“…The crustal and ellipticity corrections are made using the method of Woodhouse (1980). Application of the more accurate method of Takeuchi (2005) is a subject for future research.…”

Particle relabelling transformations in elastodynamics

“…We could then use this mapping to transform the elastodynamic equations into an equivalent set on the spherically symmetric model, and the solution to these new equations could be expanded in terms of the eigenfunctions of the spherically symmetric model. A very similar approach to incorporate boundary topography has been implemented by Takeuchi (2005) in the non-self-gravitating case and in a Cartesian geometry based on the so-called direct solution method (Geller & Ohminato 1994). The main difficulty in applying the above method is transforming the elastodynamic equations between a geometrically aspherical earth model and a spherical one, and this is the problem we wish to address.…”

Theory and Obeservations - Forward Modeling and Synthetic Seismograms, 3D Numerical Methods

“…Takeuchi (2005) had recently extended the method to include arbitrary perturbations in boundary locations, as illustrated in Figure 9. Probably, the main restriction for the DSM, like the CMM, is the need for significant amount of shared memory to perform the necessary matrix-vector manipulations for fully 3D Earth models.…”