Surface-Wave Finite-Frequency Tomography Theory And Its Application

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 author presents a method for the computation of 3-D finite frequency sensitive kernels for surface-waves. This method can compute directely 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 author computes the 3-D sensitive kernels for phase-delay,amplitude perturbation,group-delay and make a discussion of finite-frequency effects in surface-waves. The analysis reveals that the 3-D phase-delay sensitivity kernels for surface waves bear 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 is 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 is 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.Based on the discussion above, a two-step method for the inversion of group velocity using finite-frequency method is presented and a thorough discussion about the influence of model parameterization and regularization is given. After gridding the area 50~0E-165~0E, 20~0S-75~0N by 1°×1°, which is within China and its surrounding area, the finite-frequency method is used to retrieve the group velocity distribution in this area.The result represents:(1) In the period rang between 20 and 60 seconds the group velocity are mainly influenced by the thickness of the crust. As a result the group velocity maps in this period rang represent the crustal feature of China and its surrounding area: this area can be divided approximately along 105°E longitude into west and east parts because they show distinct crustal feature, namely the west part more thicker than the east part.(2) In the group velocity maps in periods rang between 60 and 85 seconds, Yangtze platform shows very prominent high velocity anomaly; the north India platform, the Tibetan platform, the Tarim platform, the west Daxingganling-Mongolian block show alternative high and low velocity anomaly. As the period increases, the amplitude of the low velocity anomaly in the Tibetan platform decreases gradually; the more prominent high velocity anomaly in Tarim platform migrates from the west to the east; the amplitude of the low velocity anomaly in the west Daxingganling-Mongolian block increases gradually, though weaker than the Tibetan platform.(3) There are three prominent low velocity anomaly zone while the Yangtze platform remains the prominent high velocity anomaly in the group velocity maps in periods rang between 85 and 150 seconds.