Nonstationary Bayesian kriging: a predictive technique to generate spatialcorrections for seismic detection, location and identification

Seismic characterization works to improve the detection, location and ident ification of seismic events by correcting for inaccuracies in geophysical m odels. These inaccuracies are caused by inherent averaging in the model and , as a result, exact data values cannot be directly recovered at a point in the model. Seismic characterization involves cataloging reference events s o that inaccuracies in the model can be mapped at these points and true dat a values can be retained through a correction. Application of these correct ions to a new event requires the accurate prediction of the correction valu e at a point that is near, but not necessarily coincident with the referenc e events. Given that these reference events can be sparsely distributed geo graphically, both interpolation and extrapolation of corrections to the new point are required. In this study, we develop a closed form representation of Bayesian kriging (linear prediction) that incorporates variable spatial damping. The result is a robust nonstationary algorithm for spatially inte rpolating geophysical corrections. This algorithm extends local trends when data coverage is good and allows for damping (blending) to an a priori bac kground mean when data coverage is poor. Benchmark tests show that the tech nique gives reliable predictions of the correction value along with an appr opriate uncertainty estimate. Tests with travel-time residual data demonstr ate that combining variable damping with an azimuthal coverage criterion re duces the large errors that occur with more classical linear prediction tec hniques, especially when values an extrapolated in poor coverage regions. I n the travel-time correction case, this technique generates both seismic co rrections along with uncertainties and can properly incorporate model error in the final location estimate. Results favor the applicability of this no nstationary algorithm to other types of seismic corrections such as amplitu de and attenuation measures. Since this studies original publication, sever al studies have demonstrated that nonstationary Bayesian kriging provides s ignificant improvement over more conventional correction techniques. Applic ations have been performed in location and identification and each has demo nstrated that this technique can combine the best theoretical earth models with empirical corrections to obtain a more accurate solution. These result s and their broad implications for the future calibration of monitoring net works are discussed in a new section that follows the conclusions, (C) 1999 Seism. Sec. Am. Published by Elsevier Science B.V. All rights reserved.