Study Of Surface Wave Tomography And Inversion For 3-D Crustal Azimuthal Anisotropy

Surface wave tomography is one of the most important methods to investigate crust and upper mantle structure and deformation characteristics.Surface wave tomography based on continuous regionalization of model parameters is widely used to invert for 2-D phase or group velocity maps.An inevitable problem is that the distribution of ray paths is far from regular due to the spatially uneven distribution of stations and seismic events,which often affects the spatial resolution of the tomographic model.We present an improved tomographic method with a spatially varying smoothing scheme that is based on the continuous regionalization approach.The smoothness of the inverted model is constrained by the Gaussian a priori model covariance function with spatially varying correlation lengths based on ray path density.In addition,a two-step inversion procedure is used to suppress the effects on tomographic models of data outliers.Both synthetic and real data are used to evaluate this newly developed tomographic algorithm.In the synthetic tests,when the contrived model has different scales of anomalies and uneven ray path distribution,we compare the performance of our spatially varying smoothing method with the traditional inversion method and show that the new method is capable of improving the recovery in the regions of dense ray sampling.For real data applications,the resulting phase velocity maps of Rayleigh waves in SE Tibet produced using spatially varying smoothing method show similar features to results with the traditional method,however,the new results contain more detailed structures and appears to better resolve the amplitude of anomalies better.From both synthetic and real data tests we demonstrate that our new approach is useful to achieve spatially varying resolution when used in regions with heterogeneous ray path distribution.Besides velocity structure,azimuthal anisotropy in seismic wave speeds has long been investigated using surface waves and is recognized to reflect the orientation of anisotropic minerals/cracks under strain/stress and depth-varying deformation patterns in the crust and upper mantle.Depth-dependent azimuthal anisotropy has generally been obtained from point-wise inversion of period-dependent Rayleigh wave dispersion data with azimuthal anisotropy.Here we propose a method to directly invert all path-dependent Rayleigh wave dispersion data for 3-D variation of shear wave speed and azimuthal anisotropy without the intermediate step of 2-D phase or group velocity tomography.In a former study,we have developed a two-step method that uses the Neighborhood Algorithm(NA)for 1-D inversion of depth-dependent shear wavespeeds and azimuthal anisotropy(Yao 2015).This method has been further improved with the improved MINEOS code to compute the Rayleigh-wave phase velocity sensitivity kernel to the five elastic parameters of the transversely isotropic medium(A,C,L,F,N).In addition,we have previously proposed a method that directly inverts all path-dependent dispersion data for 3-D isotropic shear wavespeed structure based on ray tracing(Fang et al.2015).Then,based on these two methodological advancements,we propose the direct inversion method of surface wave dispersion for three-dimensional anisotropic structure,using frequency-dependent ray tracing based on the fast marching method,which avoids the assumption of great-circle propagation of surface waves that is generally applied in most surface wave tomographic studies,but not appropriate in complex media.A series of synthetic tests have been performed to evaluate this new method.Initially,by comparison with the input model,we prove the reliability of direct inversion,when using the true isotropic model as the reference isotropic model.Furthermore,in the second synthetic test,we give a complete process on how to process real data using the direct inversion method to achieve the three-dimensional isotropic shear wave speed structure and anisotropic structure.Finally,by using synthetic data with different noise levels,we prove the newly developed direct inversion is stable to some extent,but it is pretty hard to retrieve the amplitude of azimuthal anisotropy when using the data with the large noise level.Through synthetic data tests,we demonstrate that our new approach is useful to achieve a reliable three-dimensional anisotropic structure in regions with good ray path coverage when the input Rayleigh wave dispersion data are precise enough.