An information-theoretic approach to microseismic source location

There has been extensive work on seismic source localization, going as far back as Geiger's 1912 paper, that is based on least-squares fitting of arrival times. The primary advantage of time-based methods over waveform-based methods (e.g. reverse-time migration and beam forming) is that simulated arrival times are considerably more reliable than simulated waveforms, especially in the context of an uncertain velocity model, thereby yielding more reliable estimates of source location. However, time-based methods are bedeviled by the unsolved challenges of accurate time picking and labelling of the seismic phases in the waveforms for each event. Drawing from Woodward's canonical 1953 text on the application of information theory to radar applications, we show that time-based methods can be applied directly to waveform data, thus capturing the advantages of time-based methods without being impacted by the aforementioned hindrances. We extend Woodward's approach to include an unknown distortion on wavelet amplitude and phase, showing that the related marginalization integrals can be analytically evaluated. We also provide extensions for correlation-based location methods such as relative localization and the S-P method. We demonstrate this approach through applications to microseismic event location, presenting formulations and results for both absolute and relative localization approaches, with receiver arrays either in a borehole or on the surface. By properly quantifying uncertainty in our location estimates, our formulations provide an objective measure for ranking the accuracy of microseismic source location methodologies.