Determination ofS-wave slowness from a linear array of borehole receivers

Locations of seismic events from a linear array of receivers may require determination of slowness vectors of arriving waves. In an isotropic medium, P waves are polarized along the slowness vector, which enables direct determination of backazimuth (i.e. azimuth to a source from a receiver) from P-wave polarization. In contrast, S waves usually have much larger signal-to-noise ratio than P waves, but are polarized in a plane perpendicular to their slowness vectors, which prevents direct determination of their backazimuth. We have developed a novel technique to determine the slowness vector of S waves detected in a linear array of receivers in an isotropic medium. We combine the S-wave polarization measurement with the derivative of the S-wave travel times along the array to obtain the full slowness vector and backazimuth. The proposed method allows one to determine direction to sources of seismic events from a single linear array of receivers, using only S waves. This technique is not affected by SV waves, which is shown by a test on a synthetic data set. We also test the method on two real microseismic data sets from hydraulic fracturing treatments and show that it outperforms the backazimuth determination from P waves and from horizontal polarization of S waves.