Probabilistic earthquake location in 3D and layered models - Introduction of a Metropolis-Gibbs method and comparison with linear locations

Probabilistic earthquake location with non-linear, global search methods al lows the use of 3D models and produces comprehensive uncertainty and resolu tion information represented by a probability density function over the unk nown hypocentral parameters. We describe a probabilistic earthquake locatio n methodology and introduce an efficient Metropolis-Gibbs, non-linear, glob al sampling algorithm to obtain such locations. Using synthetic travel time s generated in a 3D model, we examine the locations and uncertainties given by an exhaustive grid-search and the Metropolis-Gibbs sampler using 3D and layered velocity models, and by a iterative, linear method in the layered model. We also investigate the relation of average station residuals to kno wn static delays in the travel times, and the quality of the recovery of kn own focal mechanisms. With the 3D model and exact data, the location probab ility density functions obtained with the Metropolis-Gibbs method are nearl y identical to those of the slower but exhaustive grid-search. The location PDFs can be large and irregular outside of a station network even for the case of exact data. With location in the 3D model and static shifts added t o the data, there are systematic biases in the event locations. Locations u sing the layered model show that both linear and global methods give system atic biases in the event locations and that the error volumes do not includ e the "true" location - absolute event locations and errors are not recover ed. The iterative, linear location method can fair for locations near sharp contrasts in velocity and outside of a network. Metropolis-Gibbs is a prac tical method to obtain complete, probabilistic locations for large numbers of events and for location in 3D models. It is only about 10 times slower t han linearized methods but is stable for cases where linearized methods fai l. The exhaustive grid-search method is about 1000 times slower than linear ized methods but is useful for location of smaller number of events and to obtain accurate images of location probability density functions that may b e highly-irregular.