Modeling Travel-Time Correlations Based on Sensitivity Kernels and Correlated Velocity Anomalies

摘要

This project concerns the errors in predicted regional and teleseismic travel times resulting from velocity heterogeneity in the real Earth not represented in the reference Earth model used for travel-time calculation. We are developing techniques for calculating the covariances between such prediction errors associated with different event-station paths, based on a statistical characterization of the velocity heterogeneity and the theoretical travel-time sensitivity to the Earth's velocity structure for each path. This effort is motivated by previous discoveries that event location errors can be reduced when a locator uses the full covariance matrix for travel- time prediction errors, including off-diagonal elements to account for correlations. Moreover, a physical model for travel-time covariances potentially provides useful constraints in the construction of empirical travel- time correction surfaces. We have developed numerical algorithms that generate a covariance matrix for first-arrival P-wave travel times along paths to various station locations from a fixed event location. Calculations with various station geometries reveal a strong dependence of the travel-time variances and covariances on the spatial sampling of seismic rays. For example, we find that prediction-error variances are smaller for teleseismic P arrivals than for Pn arrivals since teleseismic rays travel a shorter, more vertical path in the upper mantle, whereas most of the Pn path is in the upper mantle where velocity heterogeneity is greatest. Our calculated travel-time variance vs. distance curve agrees well with empirical results for a Eurasian data set when the standard deviation of velocity heterogeneity decreases from 2% to 1% at the 410 km discontinuity. We further find that correlation between travel times can be parameterized by inter-station distance only when both stations observe the same travel-time branch, but distinct breaks in residual correlation occur at the cross-over of bran.