Computation of Large Anisotropic Seismic Heterogeneities (CLASH)

A general tomographic technique is designed in order (i) to operate in anisotropic media; (ii) to account for the uneven seismic sampling and (iii) to handle massive data sets in a reasonable computing time. One modus operandi to compute a 3-D body wave velocity model relies on surface wave phase velocity measurements. An intermediate step, shared by other approaches, consists in translating, for each period of a given mode branch, the phase velocities integrated along ray paths into local velocity perturbations. To this end, we develop a method, which accounts for the azimuthal anisotropy in its comprehensive form. The weakly non-linear forward problem allows to use a conjugate gradient optimization. The Earth's surface is regularly discretized and the partial derivatives are assigned to the individual grid points. Possible lack of lateral resolution, due to the inescapable uneven ray path coverage, is taken into account through the a priori covariances on parameters with laterally variable correlation lengths. This method allows to efficiently separate the 2ψ and the 4ψ anisotropic effects from the isotropic perturbations. Fundamental mode and overtone phase velocity maps, derived with real Rayleigh wave data sets, are presented and compared with previous maps. The isotropic models concur well with the results of Trampert & Woodhouse. Large 4ψ heterogeneities are located in the tectonically active regions and over the continental lithospheres such as North America, Antarctica or Australia. At various periods, a significant 4ψ signature is correlated with the Hawaii hotspot track. Finally, concurring with the conclusions of Trampert & Woodhouse, our phase velocity maps show that Rayleigh wave data sets do need both 2ψ and 4ψ anisotropic terms.     

裂隙型单斜介质中弹性系数的计算及波的传播特性研究

根据Hudson等关于裂隙介质弹性系数计算的扰动理论及Bond变换矩阵原理，给出了各向同性介质中含多组垂直裂隙时等效弹性系数的计算方法。计算了含两组斜交的垂直裂隙形成的单斜各向异性介质中的等效弹性系数，并根据Christoffel方程推导、得出水平面内平面波传播的相速度和群速度随方位变化的特性。     

Relation of the Wave-Propagation Metric Tensor to the Curvatures of the Slowness and Ray-Velocity Surfaces

The contravariant components of the wave-propagation metric tensor equal half the second-order partial derivatives of the selected eigenvalue of the Christoffel matrix with respect to the slowness-vector components. The relations of the wave-propagation metric tensor to the curvature matrix and Gaussian curvature of the slowness surface and to the curvature matrix and Gaussian curvature of the ray-velocity surface are demonstrated with the help of ray-centred coordinates.