Method for computing uncertainties in parameters estimated from beamformed microseismic survey data

Abstract

A method for estimating uncertainties in determining hypocenters of seismic events occurring in subsurface formations according to one aspect includes determining estimates of event locations by choosing local peaks in summed amplitude of seismic energy detected by an array of sensors disposed above an area of the subsurface to be evaluated. For each peak, the following is performed: recomputing the summed amplitude response for a selected set of points of comprising small perturbations in time and space from the estimated event locations; computing second derivatives of log likelihood function from the stacked responses at the estimated location and the perturbed locations; assembling the second derivatives into a Fisher information matrix; computing an inverse of the Fisher information matrix; determining variances of estimated parameters from the elements from the diagonal of the inverted matrix; and computing standard deviations of the estimated parameters by calculating a square root of the variances.