Location of Seismic Events

Abstract

The location of seismic events is of fundamental importance, since all subsequent seismological processing depends, to some degree, upon the event position and the distances to the stations. Finding the location of a seismic event amounts to solving an inverse problem — a set of unknowns has to be retrieved from a set of data. The four unknowns consist of the location and origin time vector, x = (h, t₀)^T = (x₀, y₀, z₀, t₀)^T. In the case of a mine seismic network, the unknowns are to be retrieved from data consisting of P and S wave arrival times, the direction of the wavefronts, both of which are derived from waveforms, the velocity model and the station coordinates. The data have associated errors which can produce location errors. The location errors also depend on the spatial distribution of stations with respect to the position of the source, discussed in Section 5.4 below, and on the physics of the rupture process. If slow rupture starts at a certain point, the closest station(s) may record waves radiated from that very point while others may only record waves generated later in the rupture process by a high stress drop patch of the same source. In this case, care has to be taken in determining the arrival times if the location of rupture initiation is sought, otherwise the location will be a statistical average of different locations within the source. It is helpful therefore to think of a seismic source as a spatial event with characteristic size of the order of a metre for a moment magnitude m_M=−4 event, up to a few hundred metres for an event of m_M>4.