The computation of 3-D finite-frequency sensitivity kernels for surface-waves

Abstract

High resolution surface-wave tomography must overcome the high frequency approximation assumption of ray theory and take the finite frequency effects into account. In this paper, the authors present a method to compute 3-D finite frequency sensitive kernels for surface-waves. This method can directely compute the surface-wave eigenvalues and eigenfunctions for the layered spherical earth model and the Earth-flattening procedure to approximately compute surface -wave dispersion for this model is not needed. The authors compute the 3-D sensitive kernels for phase-delay, amplitude perturbation and group-delay and discuss the finite-frequency effects in surface-waves. The analysis reveals that the 3-D phase-delay sensitivity kernels for surface waves bear a great resemblance to frechet kernels for the 2-D body-wave traveltimes. This suggests the 2-D propagation nature of surface waves. As far as the phase speed data are concerned, the Fresnel zone method is proper for the inversion of low-frequency waves, while the ray theory is proper for the inversion of high-frequency waves. However, the finite-frequency method should be taken for the inversion of intermediate-frequency waves. The terms high and low are resolution-dependent. The group dispersion data are better for the inversion of the fine structure of the crust and the upper mantle. But the strong sidebands of the group-delay kernels may lead to unstability of the inversion.