Sensitivity of frequency-dependent traveltimes to laterally heterogeneous, anisotropic Earth structure

We investigate the effect of lateral heterogeneity on the frequency-dependent traveltime residuals of various seismic arrivals, for example P, S, sS, SS, sSS, SSS, Love and Rayleigh waves. These residuals, which are examples of generalized seismological data functionals (GSDFs), are measured from narrow-band cross-correlagrams between observed seismograms and isolated waveforms (isolation filters) synthesized by weighted (partial ) normal-mode summations. The effect of lateral heterogeneity is incorporated through the coupling between normal-mode multiplets with the help of first-order perturbation theory. Based upon the normal-mode coupling matrix for the eigenfrequency shifts, the sensitivity kernels of the frequency-dependent traveltime residuals to the model parameter perturbations are derived by an application of the Born approximation. In order to reduce the computational labour so that tomographic inversions can practically be conducted, 2-D sensitivity kernels of the traveltime residuals to the lateral structure within the source–receiver great-circle plane are obtained with a stationary-phase integration. In addition, a normal-mode coupling scheme is adopted to increase further the computational efficiency in which a pair of modes are coupled only when the differences between their eigenfrequencies and group velocities are small. We present numerical examples for the 2-D Frechet kernels of frequency-dependent traveltime residuals for various model parameters in a transversely isotropic model, namely the velocities of vertically and horizontally polarized and/or propagating shear and compressional waves and the topographies of the 410 and 660 km discontinuities. Wherever possible, physical explanations are also provided on the different aspects of the 2-D Frechet kernels with emphasis on the complex phenomenon of interference among multiple seismic waves. We also demonstrate, both algebraically and numerically, that when the waveforms used in the measurements involve multiple travelling waves, the frequency-dependent traveltime kernels can be counterintuitive, i.e. velocity increase in some places can lead to increased traveltimes.

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