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Geophysical Prospecting: Reconstructing frequency‐magnitude statistics from detection limited microseismic data

Microseismic monitoring, particularly the monitoring of hydraulic fracturing in gas‐ and oil‐bearing shales, has developed significantly over the last ten years. Early work focused on the location of microseismic events but more recently there have been attempts to extract more of the information afforded by this rich data source. In particular, the recovery of the frequency‐magnitude distribution, which is expected to follow a Gutenberg‐Richter distribution, may provide insights into the prevailing effective stress regime in the vicinity of the events. This stress regime varies with distance from the hydraulic fracturing: at the propagating fracture one expects conditions for tensile or shear failure, away from the fracture one may broadly expect microseismicity associated with pre‐existing weakness in the rock, occurring at effective stress conditions close to the conditions existing prior to the treatment.All geophysical experiments are detection limited and the microseismic monitoring case does not differ in this regard. In constructing a statistical indicator such as the distribution of moment magnitudes we would like the estimate to be robust and use as much of the data as possible. In analysing earthquake catalogues the predominant practise is to determine a magnitude of completeness denoting the detection limit of the catalogue. This approach defines a minimum magnitude above which all events are thought to have been reliably recorded. In effect, this imposes an artificial, conservative detection limit to replace the unknown detection limit of the catalogue. We present the case of an arbitrary detection limit and introduce an approach from astronomy that is particularly suited to the single‐well observing geometry most prevalent in hydraulic fracture monitoring.We calculate b‐values for a set of event magnitudes from the Barnett Shale formation, where multiple stimulation treatments were applied in a pair of wells (‘zipper frac’) followed by a four‐stage treatment in a third well and find significant variations in the b‐value between the pumped stages.

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