Moment and moment magnitude of seismic events located by stacking

Determination of moment and moment magnitude for seismic events located by stacking has been an unsolved problem because current methodologies cannot be applied. To solve this problem, we have developed a methodology for moment magnitude M-w estimation of (micro) seismic events. Our method was designed for stacking waveforms. We found that magnitude can be determined from the stack of amplitudes corrected for radiation pattern and propagation effects such as geometric spreading, attenuation, and free-surface boundary. From the stack of corrected waveforms, we found the low-frequency limit corresponding to the stack of particle displacement and calculated seismic moment. We found that an unstacked method of estimating moment magnitude on each trace and averaging these estimates was consistent with the method we developed although it was limited to higher magnitude events and more sensitive to noise. We benchmarked our methodology with a case study and found improvement in M-w estimation resulting in determination of magnitude for weaker events when unstacked methodology cannot be used.