An examination of linear and non-linear earthquake locations using synthetic travel times from a 3D model

Anthony Lomax and Jean Virieux
UMR Geosciences Azur, 250 Rue A. Einstein, 06560 Valbonne, France

Philippe Volant and Catherine Berge
IPSN, BP 6, 92265 Fontenay-aux-Roses, France


We generate synthetic P and S travel-times in a 3D velocity model for known sources at various depths on a vertical plane passing through a station network with the geometry of the IPSN-Durance micro-seismic network in southern France. With these times we "locate" the sources using non-linear grid and Metropolis-Gibbs searches (valid in 3D models) to obtain a probability density function and equivalent Gaussian uncertainty statistics, and we use the linear method Hypoellipse (Lahr, 1989; valid for layered models) to obtain hypocentres and associated Gaussian uncertainties. We also obtain estimates of the known focal mechanisms using synthetic P wave first motions. To validate the non-linear algorithms and to study a near ideal, but unrealizable location scenario, we examine the locations and uncertainties obtained from the 3D synthetic times using the correct 3D velocity model.

To investigate a more realistic location scenario, we use the 3D travel times with added station static shifts, and locate with a 1D layered model. We compare the locations, uncertainties, and focal mechanisms obtained with the linear and non-linear location methods. We find that with both methods the locations can be strongly biased with respect to the "true" locations of the known sources. For events inside of the network, the linear and non-linear locations and uncertainties are similar, but they can differ significantly (particularly in depth) outside of the network. These differences reflect the limitations of linear inversion in the presence of irregular, highly non-gaussian location uncertainties.