Quantifying location uncertainties in seismicity catalogues: application to the Pyrenees

Abstract

Linearised least-square inversions are commonly used to locate small-magnitude earthquakes, as they are fast and simple to implement. These methods are based on minimising the root-mean-square (RMS) of travel time residuals to find the best-fitting location coordinates and origin time. There are two well-known problems that affect location estimates: (1) the linearisation of the inverse problem causes dependence on the initial guess; (2) regularisation produces solutions that depend on the chosen damping coefficient and biased uncertainty estimates. In this work, we propose a method to quantify unbiased uncertainties with a series of synthetic tests. We first generate travel times for events from all possible coordinates on a 3D grid and then locate each synthetic event by using HYPOCENTER software (this can be applied to any location method). We show that the uncertainties estimated from the standard linearised inversion are strongly underestimated, and we propose another method to compute uncertainties. We produce a 3D error map, where at each grid point we plot the location error, defined as the distance between the event at the given grid point and its inverted location. Moreover, we show how this error map varies with the quantity and quality of the data, and with user-defined parameters such as maximum event–station distance or station corrections. We also provide a methodology to tune the seismic location parameters and calculate the corresponding uncertainties for users who are using similar earthquake location software. Finally, we present an application to the Pyrenean region.