Cross spectral analysis of Swabian Jura (SW Germany) three-component microearthquake recordings

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F. Scherbaum
J. Wendler


Similar three-component microearthquake records have been observed in the Swabian Jura (SW Germany) seismic zone for different source-receiver geometries. This data set is used to study the resolution power of cross spectral analysis techniques for the estimation of relative differential times as well as the applicability to velocity monitoring. The differential times are estimated in the frequency domain by assuming a linear-phase cross spectrum with the slope indicating the individual time difference. All earthquakes have been relocated with respect to a master event, using the relative P and S delay times from the cross spectral analysis as a measure of source mislocation. The overall location error is strongly dependent on the inital distance between master and studied event. For earthquakes initially located farther apart than approximately 1.5 km, the relocalization result in terms of total location error was poorer, whereas for events initially located closer than 1 km the precision of the relocalization was improved. The remaining residuals are of the order of 10 ms, which is approximately 3 times the digitization interval. In order to test the applicability of cross spectral analysis to velocity monitoring, synthetic data were used to model the influences of noise and source time function differences. The effect of additive white noise seems to be acceptable in cases where the S/N ratio is sufficiently high. Small changes in the shape of the source time function, however, were found to be of great influence to the differential time estimates. Variation of rise, sustain and decay times, which were negligible in the coherence spectrum, spuriously introduced phase differences which, in terms of delay times, easily reach the magnitude of the digitization interval. Thus, velocity monitoring using cross spectral analysis techniques seems to depend strongly on the equality - in contrast to similarity - of the source time functions of the events which are compared. The coherence spectrum is not a sufficient measure to detect all the significant differences.

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Scherbaum, F., & Wendler, J. (1986). Cross spectral analysis of Swabian Jura (SW Germany) three-component microearthquake recordings. Journal of Geophysics, 60(1), 157-166. Retrieved from
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