Cross double-difference inversion for microseismic event location using data from a single monitoring well

The double-difference (DD) location method has long been applied for locating a cluster of earthquakes with data recorded at surface seismic stations. This method has also been used for locating microseismic events with multiple monitoring wells during hydraulic fracturing. We first extended the approach for locating a cluster of microseismic events with data recorded from a single well. To do this, we have reduced the 3D location problem to 2D by projecting all of the events onto a vertical (xz) plane, with a vertical z-axis and a horizontal x-axis representing the distance to the monitoring well, considering the symmetric character of the 1D velocity model and the vertical monitoring well. We then performed a 2D location inversion and projected the results back to 3D using the event azimuths, which were determined from a separate analysis of the initial P-wave polarizations. However, although the DD method could determine relative locations of events reasonably well, it yielded poor absolute locations. We have developed a cross DD (CDD) approach using the cross traveltime difference between the P-wave arrival of one event and the S-wave arrival of another event for inversion instead of the arrival-time differences of the same phases as in the DD method. The CDD method contains more information on absolute locations than the DD method, resulting in a much more stable absolute location determination. The synthetic and field data tests indicated that the CDD method could improve the accuracy of relative and absolute event locations in microseismic clusters.