Past exam of the physics of the Earth as a Planet course of the University of Cambridge / 2014 / Paper 1 / 1 / b / Solution

Identify the event and pick calibrated P wave and, where available, S wave arrivals at stations of known position. Associate each pick with a seismic phase and uncertainty. An earthquake location by arrival times fitsfor the three hypocentre coordinates and earthquake origin time, using travel times from a specified velocity model. A grid search can initialize iterative weighted least squares or a probabilistic inversion. Station coverage must constrain depth as well as horizontal position; merely having four observations does not ensure a well-conditioned solution.

Errors include uncertain or misidentified onsets, clock and station-coordinate errors, wrong velocities or neglected three-dimensional structure, poor azimuthal coverage, inadequate station distances and depth–origin-time tradeoffs. Examine residual patterns and resolution, not only the minimum residual. A small formal covariance within a wrong velocity model can accompany a systematically biased hypocentre.