面波有限频率法3-D灵敏度核函数的计算

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

高分辨率面波成像应克服射线理论的高频近似假设,考虑有限频率效应。该文给出了一种计算面波有限频率3-D灵敏度核函数的方法。该方法可直接计算球壳层状地球模型中面波振型特征值和特征函数,而不再需要采用球化平变换来近似计算球壳层状地球模型中面波频散参数。作者计算了相位延迟、振幅扰动和群到时延迟的3-D灵敏度核函数,并对面波有限频率效应进行了讨论。分析结果显示:面波相位延迟的3-D灵敏度核函数同2-D体波走时的核函数形状类似,说明面波具有二维传播特性。对相速度数据而言,Fresnel带方法适用于低频面波的反演,射线方法适用于高频面波的反演,而对于中等频率的面波反演应采用有限频率方法。频率的高低是相对于所要取得的分辨率而言的。在反演地壳上地幔细结构方面,群频散数据更具有优越性;然而,群到时延迟核函数的极强的旁瓣可能使得反演变得不稳定。

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.