Resolution, Uncertainty and Data Predictability of Tomographic Lg Q Models - Application to Eastern Eurasia

We focus on new methodologies of Q tomography using two-station based Q measurements and apply them on the amplitude data observed in Eastern Eurasia for the Lg Q model at 1Hz. The amplitude data for Lg Q tomography are substantially compromised due to their complex errors dominated by the 1D assumptions in the stochastic modeling for spectral amplitude. In this paper, we address the statistical properties of such errors that were never systematically studied before. For the first time, we quantitatively characterize the structure and magnitude of modeling errors in the compromised data by stochastic modeling. It turns out that all errors contained in the log-spectral ratio data can be modeled as a Gaussian random variable with well-calibrated mean and variance. We also extend our statistical methodology to characterize the statistical behavior of site responses through the measured site response ratios and numerical simulations. The results can provide statistically calibrated uncertainty in predicting site response of individual sites. We solve for the tomographic Q model by explicitly decomposing the kernel matrix based on the PROPACK software package. This matrix-solver approach makes it possible to formally construct a resolution matrix and map data variance into model variance while solving for the Q model parameters. The inverted Lg Q tomographic map of Eastern Eurasia suggests that the reliably retrieved Q values correlate well with the distinct tectonic blocks featured by the most recent major deformations. The model resolution can be quantitively analyzed by the spread functions defined by full resolution matrix as well as the diagonal elements of resolution matrix. With the Q tomographic model and its covariance matrix, we can not only predict any path-specific Lg Q value, but also provide formal estimates of the uncertainty of the Q prediction. This new capability will significantly benefit practical missions of source identification and source size estimation for which reliable uncertainty estimate is especially important.