BAYESIAN TOMOGRAPHY APPLIED TO SEISMIC EVENT IDENTIFICATION PROBLEMS

The advantages of a Bayesian approach to tomography are that large-scale and high-resolution tomographic models available from other well-accepted studies can be used as prior background models. The resulting refined tomographic model blends into these prior background models. Moreover, the error budget is well established in a Bayesian framework. We assume a general linear Gaussian (least squares) model, where the covariance matrix is partitioned into data and prior model components. Uncertain data are naturally down weighted and certain model components will be subject to small perturbations. Bayesian attenuation tomography (Tarantola, 1987) is being incorporated into the Magnitude and Distance Amplitude Correction (MDAC) methodology used for amplitude corrections to seismic discriminants (Taylor et al., 1999). Because a signal-to-noise criterion is used to select amplitudes for the inversion, the data are left-censored and the resulting Q0 models will be biased high. We examine the utility of the Expectation Maximization (EM) algorithm to the left-censored data problem (Dempster et al., 1977). In this case, we can define only an upper bound to measured amplitudes based on pre-phase noise. The EM algorithm can be used to fill in the missing data values with their conditional expectation based on the relationship of amplitudes with other related completely observed variables. We have initially chosen a bivariate Gaussian model for filling in missing amplitudes based on the relationship between amplitude and pre-phase noise. The methodology can be extended to the multivariate case by the incorporation of other variables such as magnitude and distance, background noise, and Pn velocity tomography. We apply the technique to eastern Asia for Pn, Pg, Sn, and Lg signals at 1 Hz using data from 1651 earthquakes recorded at 12 stations. Tomographic patterns correlate well with those expected from geophysical considerations (e.g. high attenuation in Tibet and low attenuation up into the stable regions of Kazakhstan). Interestingly, many of the large cratonic basins surrounding the Tibet Plateau (e.g. Tarim, Junggar) show reduced attenuation. Application of the EM algorithm tends to increase attenuation in Tibet (particularly western Tibet) and the cratonic basins to the north of but not to the east of Tibet. We are refining regionalized surface slowness models in a number of regions for surface wave magnitude measurements to be used for mb — Ms discriminants. Regional MS can be measured at lower magnitudes through the application of phase-match filters. The filters can be constructed from tomographic group velocity maps from which path-specific dispersion curves can be calculated. Global and regional group velocity maps are available from previous studies (e.g., Stevens and Adams, 2000; Levsin et al., 2000) and Bayesian slowness tomography provides a framework for utilizing existing global and regional models as priors on which to improve resolution in specific regions. Tomography provides only an approximation to the propagation effects a seismic wave may experience. For example, phase blockage can occur over relatively short distances in the absence of any anelastic effects. Station-centric kriged amplitude or slowness correction surfaces on top of the tomographic models may assist in quantifying departures from the smooth tomographic model (Pasyanos, 2000).