The matter of size; on the moment magnitude of microseismic events

We investigated the method of estimating seismic moment and moment magnitude for microseismic events. We determined that the M (super T) (sub 0) defined by Bowers and Hudson is the proper scalar moment to be used in microseismic studies for characterizing the size of an event and calculating its moment magnitude. For non-double-couple sources, the proportional relationship between body-wave amplitude and seismic moment in the Brune model breaks down. So under such situations, the Brune model is not an appropriate way to estimate the seismic moment and magnitude. Moreover, the S-wave alone is not sufficient for determining the total seismic moment. Instead, the P-wave must be analyzed. An example Barnett Shale data set was studied, and the results concluded that the magnitudes estimated with the Brune model could be off by as much as 1.92, with an absolute average of 0.35. The moment magnitudes based on the scalar moment M (super T) (sub 0) also gave a significantly different event size distribution and b-value estimation. Finally, attenuation also played a role in estimating the moment magnitude. With a typical average attenuation factor of Q=70, the average magnitude correction for our field data set was on the order of 0.15. However, it could reach 0.3 for events far away from the monitoring well.