Waveform Cross-Correlation for Differential Time Measurement: Bias and Limitations

The waveform cross-correlation technique is a popular tool for estimating the differential times of seismic phases in a fast and reliable manner. Differential times are used for a variety of methods, with the double-difference relocation method HypoDD being the most popular. In this work, we analyzed the precision and possible error of cross-correlated differential times by conducting a simple comparison with reference manual datasets. Our study was carried out on two well-studied mainshock-aftershock datasets from the seismically active West Bohemia region (Czechia). We observed that the magnitude difference delta M-L between two cross-correlated earthquakes presents a significant bias, resulting in the over- or underestimation of the final differential time of both P and S waves. The earthquakes of differing magnitudes exhibit unequal first pulse durations in otherwise similar waveforms. As a result, the cross-correlated differential time, which shifts seismograms to the position of maximum cross-correlation, is different from the differential time between phase arrivals. Our test cases revealed that the resulting deviation from the true differential time depends on the actual delta M-L and can reach values higher than 0.025 s when delta M-L > 2. Hence, in standard differential time datasets, the error has a greater impact on the data related to strong events-mainshocks. In HypoDD applications, the error leads to mislocations of mainshocks, and at the same time, the locations of the weak events are improved. We demonstrate the mislocation potential of the error on relocated hypocenters of mainshock-aftershock sequences and earthquake swarms from West Bohemia, as well as on synthetic tests. The error cannot be avoided by changing the cross-correlated window length or filtration. We propose a few suggestions to suppress the consequences of the magnitude difference data bias. Nonetheless, the differential times error and its effects cannot currently be completely suppressed using the mentioned methods.