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Application of a Cepstral F Statistic for Improved Depth Estimation

Weston Geophysical Corporation
Lexington, Massachusetts
(J.L.B., D.T.R.)
University of California at Davis
Department of Statistics
Davis, California
(R.H.S.)

Manuscript received 25 February 2001.

The depth of a seismic event can be determined using peaks corresponding to depth phase-delay times found in the cepstrum of the seismic signal. Until now, however, there has been no method available to determine the significance of various peaks in the cepstrum. We have formulated a cepstral F statistic by using a classic approach to detect a signal in a number of stationarily correlated time series. The method attaches a statistical significance level to peaks in the cepstrum of seismic data caused by echoes in the signal. The method is particularly well suited for detecting depth phase echoes (pP and sP) recorded on regional seismic arrays. Detections determined from the peaks in the cepstral F statistic are then stacked as a function of pP-P and sP-P travel times predicted from the IASPEI global 1-D model (Kennett and Engdahl, 1991), using a modification of the method of depth-phase beamforming (Woodgold, 1998; Murphy et al., 1999). Tests on synthetic data show the method is most successful when the P-wave arrival has a signal-to-noise ratio (SNR) greater than 4-7 and the depth phase exhibits an SNR greater than 2. Tests on complex regional data suggest that the depth-phase SNR must be between 4 and 8 for consistent successful application of the method. We tested the method by using events from the Hindu-Kush region of Afghanistan with well-determined depths as recorded on arrays at teleseismic distances. We determined the correct depths for 14 of the 19 events in this dataset (74% success rate), and we determined incorrect depths for two events, for a false-alarm rate of 10.5%. The difference between the depths calculated by the cepstral method and the prototype International Data Center (pIDC) decrease with increasing magnitude. For events with m_b > 3.8, the average difference between the cepstral and pIDC depths was 7.9 km, with no false alarms.

To test the operational capabilities of this method as a tool for data center use, we first analyzed 32 events that occurred on 12 February 2000 as located by the pIDC. Additionally, we analyzed 29 events located in Central and South America between 05 May and 15 June 2000 with event characteristics published by the International Data Center (IDC). Most of these events were also located by the National Earthquake Information Center. Our method determined statistically significant depths for 40 of these 61 events, with 11 having a low SNR at three or more recording arrays, while another 10 were either too shallow for analysis or did not exhibit depth phases. Only seven of the 61 events had depth phases listed in the Reviewed Event Bulletin produced by the pIDC and IDC. For these events, the average difference between the reported and cepstral F-statistic depths was 4.0 km. The pIDC/IDC fixed the depth of 26 of 61 events to 0.0. The cepstral F-statistic method determined depths ranging from 16 to 92 km for 15 of the events that had been constrained as surface foci. Overall, we believe the method would be most valuable when used by analysts to detect possible depth phases that could then verify or improve network-calculated focal depths.

This article has been cited by other articles:

				R. Heyburn and D. Bowers Earthquake Depth Estimation Using the F Trace and Associated Probability Bulletin of the Seismological Society of America, February 1, 2008; 98(1): 18 - 35. [Abstract] [Full Text] [PDF]

				L. M. Warren and P. M. Shearer Using the Effects of Depth Phases on P-wave Spectra to Determine Earthquake Depths Bulletin of the Seismological Society of America, February 1, 2005; 95(1): 173 - 184. [Abstract] [Full Text] [PDF]