A maximum a posteriori probability time-delay estimation for seismic signals

• Published in: Geophysical journal international Vol. 198; no. 3; pp. 1543 - 1553
• Main Authors: Carrier, A., Got, J.-L.
• Format: Journal Article
• Language: English
• Published: Oxford University Press 01.09.2014
• Subjects: Probability distributions; Earthquake interaction, forecasting, and prediction; Inverse theory; Rheology and friction of fault zones; Seismicity and tectonics; Seismic tomography
• ISSN: 0956-540X; 1365-246X
• DOI: 10.1093/gji/ggu218

Cross-correlation and cross-spectral time delays often exhibit strong outliers due to ambiguities or cycle jumps in the correlation function. Their number increases when signal-to-noise, signal similarity or spectral bandwidth decreases. Such outliers heavily determine the time-delay probability density function and the results of further computations (e.g. double-difference location and tomography) using these time delays. In the present research we expressed cross-correlation as a function of the squared difference between signal amplitudes and show that they are closely related. We used this difference as a cost function whose minimum is reached when signals are aligned. Ambiguities may be removed in this function by using a priori information. We propose using the traveltime difference as a priori time-delay information. By modelling the probability density function of the traveltime difference by a Cauchy distribution and the probability density function of the data (differences of seismic signal amplitudes) by a Laplace distribution we were able to find explicitly the time-delay a posteriori probability density function. The location of the maximum of this a posteriori probability density function is the maximum a p osteriori time-delay estimation for earthquake signals. Using this estimation to calculate time delays for earthquakes on the south flank of Kilauea statistically improved the cross-correlation time-delay estimation for these data and resulted in successful double-difference relocation for an increased number of earthquakes. This robust time-delay estimation improves the spatiotemporal resolution of seismicity rates in the south flank of Kilauea.