New Bayesian formulation to integrate body-wave polarization in non-linear earthquake location

Abstract

Earthquake location is most of the time computed using arrival times of seismic waves observed on monitoring networks. However, three-component seismometers enable measurement of the seismic wave polarization which is also hypocentre dependent. Especially for local and sparse seismic networks, as can be encountered in local reservoir applications such as geothermal field monitoring, this information can be used in addition to the travel-times to better constrain the hypocentre of local earthquakes.
We propose a new Bayesian formulation for the likelihood function of an earthquake hypocentre associated with the P-wave polarization information. The formulation is consistent with directional statistics contrarily to existing ones. The whole information of the P-wave covariance matrix is used. The non-linearity of the location problem is kept with this approach. Hence, the polarization information can be treated at the same level as the time information to build a joint probability density function of the earthquake location. Earthquake hypocentres are therefore provided with a realistic uncertainty domain.