Bayesian attenuation tomography (Tarantola, 1987) is being used to refine existing Lg attenuation models in eastern Asia. 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 will blend into these prior background models. Moreover, the uncertainties are 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 model components with small errors will be subject to little change. Amplitude 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 correction surfaces on top of the tomographic models may assist in identifying blocked paths.
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 a maximum-likelihood data augmentation method to the left-censored data problem (Schafer, 1997). In this case, we can only measure an upper bound to measured amplitudes on the basis of prephase noise. Data augmentation is used to impute the missing data values with their conditional expectation based on the relationship of amplitudes with other completely observed variables. We have initially chosen a bivariate Gaussian model for filling in missing amplitudes based on the relationship between amplitude and prephase noise.
We apply the technique to eastern Asia for 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). Many of the large cratonic basins surrounding the Tibet Plateau (e.g., Tarim, Junggar) show reduced attenuation consistent with the hypothesis that they represent regions of stronger lithosphere. Data augmentation tends to increase attenuation in Tibet (particularly western Tibet) and the cratonic basins to the North of but not to the East of Tibet. In addition, the resulting models are much smoother than models that do not account for censoring.