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.