Cross-Correlation – An Objective Tool to Indicate Induced Seismicity

The qualitative correlation between earthquake rates and the injected volume has been an established tool for investigating possible induced or triggered seismicity. The method using direct values of earthquake rates and the injected volume in normalized cross-correlation (NCC) is a recent development. We show theoretically and by numerical example that the mathematical definition of NCC provided by a set of positive random functions, exhibits high cross-correlation values with a limit equal to 1 for large mean and low standard deviation time histories. Instead of positive-value time histories, their “Useful Functions” (the original functions with their weighted running mean subtracted) should be used for NCC. Then the NCC of such functions may be close to zero or oscillating between positive and negative values of +0.5 and -0.5 in cases where seismicity is probably not induced by injection. If the positive and negative peaks of NCC were statistically significant, it would mean that the increased seismicity is related to either lower or higher injection volumes. However, a NCC dominated by a positive maximum with a zero (or small) time-lag, indicates that seismicity is induced by the injection. We apply the method for case studies of known natural and triggered/induced seismicity.