2.5 Resolution test
Checkerboard tests have often been used in seismic tomography studies to demonstrate how well an inversion can recover a model with a fixed pattern of heterogeneity distribution. A comprehensive assessment of the resolution of an inversion, however, requires the knowledge of the resolution matrix (e.g., Backus & Gilbert, 1968; Ritsemaetal et al., 2004), which has been used in the analyses spatial resolutions in tomography studies (e.g., Thurber, 1983; Barmin et al, 2001; Soldati and Boschi, 2005). However, in most inversion practices the exact resolution matrices require prohibitive amount of efforts to compute numerically, and various techniques have been developed to probe the properties of the resolution matrices without actually computing them. Here, we use the statistical resolution matrix approach of An (2012) to examine the spatial resolving power of our inversion. By inverting the synthetic data from a limited number of random models and comparing the input and recovered model pairs, we can probe the resolution matrix and determine the distribution of spatial resolution lengths of the tomography inversion. In this study, we use a total of 1200 random models, each of which is generated by adding random perturbations with maximum amplitude of ±7% to the initial model, to determine the horizontal spatial resolution lengths at different depths. The results are shown in Figure 6. Although still involving a large amount of computational labor, this is a practical and effective approach to evaluating the resolving power of the dataset in the inversion.
Figure 6 shows clearly that the resolutions are quite good for most part of the Sichuan-Yunnan region at all depths between 25 and 70 km with resolutions of ~0.4° in some regions in the lower crust and ~0.2° in most parts of the uppermost mantle, consistent with our earlier assessment from the ray path distributions seen in Figures 2 and 4. In the lower crust, the region around the Longmenshan Fault Zone and most part of northern Yunnan are dominated by a resolution length of over 0.5°. The uppermost mantle under the Sichuan Basin, Yangtze Block and eastern part of the Songpan-Ganzi Block are mainly characterized by a resolution length of ~0.2°. With regard to the Sichuan-Yunnan Rhombic Block (SYRB), the resolution to the velocity in the uppermost mantle changes clearly with depth. For example, the small region southeast of the Lijiang-Xiaojinhe Fault Zone has excellent resolution at 55-km depth, while there is a large area northwest of the fault zone having excellent resolution at 70-km depth.