PNNL

Abstract

For event discrimination, operational implementation of a regional seismic station requires three sequential calibration analyses. 1) Magnitude, distance and amplitude corrections (MDAC) made to observed regional amplitudes are necessary so that what remains in the corrected amplitude is mostly information about the seismic source-type. Corrected amplitudes can be used in ratios to discriminate between earthquakes and explosions. Calibration of MDAC can be accomplished with empirical Bayes estimation, which naturally provides metrics to determine when adequate calibration data have been acquired, and provides statistical assurance that the errors associated with MDAC calibration are negligible in future operational discrimination analysis. 2) MDAC corrected amplitudes can then be used in ratios to discriminate between earthquakes and explosions. However, there remain source effects such as those due to depth, focal mechanism, local material property and apparent stress variability that cannot easily be determined and applied as amplitude corrections. We have developed a mathematical model to capture these near source effects as random (unknown) giving an error partition of three sources: model inadequacy, station noise and amplitude correlation. This mathematical model is the basis for a general multi-station regional discriminant. Calibration analysis for the standard error of the discriminant includes the calculation of the variances of model inadequacy and station noise, and amplitude correlation. 3) Likelihood-based seismic event identification analysis with MDAC discriminants requires estimated source population means and covariance matrices for the discriminants from each of the possible source types (e.g., deep earthquake, shallow earthquake, and explosion). Anderson et al. (2007) note that source population covariance matrices and the pooled covariance matrix are best estimated element-wise to fully utilize available calibration events. We propose an algorithm that may be used to mildly adjust an element-wise covariance matrix to ensure positive definiteness and non-singular behavior. The algorithm uses the Frobenius norm as the calibration metric because it minimally adjusts the variance terms of an element-wise covariance relative to the off-diagonal covariance terms to achieve a stable, positive semi-definite covariance matrix.