Parkfield Research

Robert M. Nadeau, Lane R. Johnson and Tom V. McEvilly

Earthquake Forecasting

In its various reports since 1988, the Working Group on California Earthquake Probabilities (WGCEP) has consistently made use of statistical models of time-dependent earthquake recurrence to help estimate earthquake probabilities in California. In all WGCEP reports, the need for a larger database of earthquake recurrence intervals is emphasized. Additional data are necessary to select from competing statistical models of earthquake recurrence and to better define the model parameters. The most recent working group reports (WG99, 1999; WG02, 2002) introduced recurrence intervals from numerous small and characteristically repeating microearthquake sequences occurring along the San Andreas fault and, in particular, at Parkfield (Ellsworth et al., 1999). They included only a small fraction of the Parkfield data yet that nearly doubled the available data base from which estimates of the model parameters were made. However, even this expanded data set was considered less than adequate by the working groups. At Parkfield a significantly larger set of small repeating sequences than was used by the working groups exists (184 total sequences composed of 1073 events and 889 recurrence intervals; compared to 17 Parkfield sequences of 117 events and 100 recurrence intervals used for the WG model) and many additional sequences and events have recently been identified by our research group along the central SAF between Parkfield and the southeast terminus of the Loma Prieta rupture (Nadeau and McEvilly, 2003). In total, our group has now identified a total of 515 sequences yielding 2079 recurrence intervals from sequences whose characteristic magnitudes range from $M_{w}$-0.7 to $M_{w}$3.5 (Figure 17.1).

The potential of such a large data set for helping select and refine time-dependent recurrence models is considerable, yet serious questions remain regarding the use of small earthquake data for forecasting large earthquakes (e.g. Is the variance of earthquake recurrence intervals independent of magnitude, and what normalization (if any) should be used to account for variations in magnitude among characteristic sequences?). Nadeau and Johnson (1998) found that the average recurrence interval of sequences scales reasonably well for sequence magnitudes ranging from -0.7 to 6 under similar fault loading conditions. However, they did not analyze the variance of intervals as a function of magnitude. Ellsworth et al. (1999) analyzed magnitude dependent variance for the small data used by the working groups, and noted that the variance for both the small and large sequences was comparable. However results of their analysis, admittedly based on a small data set, had a large uncertainty. Adding to the difficulties in evaluating magnitude dependent variance are problems associated with spatial and temporal variations of fault loading rates on recurrence time variance. For example if significant slip rate transients occur over time scales comparable to the recurrence intervals of sequences (as has been observed at Parkfield) the variance of the intervals should be significantly greater than for sequences whose recurrence times are long compared to the transients.

Previous efforts at variance determinations have also relied on data dependent normalizations where the intervals for each sequence were divided by the average recurrence time of the sequences (Figure 17.1, top). However as pointed out by Matthews et al. (2002), this significantly under estimates the variance for typical characteristic sequences where the total number of repetitions are typically small. Matthews et al. also point out that discrimination between competing probability models of interval variance for earthquakes is a difficult task, even when normalization is ignored and relatively large synthetic data sets are used (e.g. 50 intervals).

Preliminary Findings

The unique attributes of our recurrence interval data set and auxiliary geodetic measurements of fault loading rates have the potential of overcoming many of these difficulties and of greatly expanding our understanding of the time-dependent earthquake recurrence process. Since our data set is large and since recurrence times scale with magnitude, our data can also be used to establish a scaling relationship between average recurrence time and magnitude that is relatively insensitive to the average intervals of any individual sequence. This scaling can then be used to normalize the entire recurrence interval data set in a way that is also insensitive to the average recurrence intervals. This approach effectively circumvents the small sample bias problem discussed by Matthews et al. The bottom panel of Figure 17.1 shows our first attempt at normalizing our data set in this way. A significantly better fit to a lognormal-like distribution is observed compared to the distribution shown in the top panel of Figure 17.1 where individual sequence average recurrence intervals are used for normalization. Also of significance is the larger intrinsic uncertainty determined for our scale normalized data (0.63 compared to 0.46). This result is entirely consistent with the remarks of Matthews et al., and supports the potential of the scaled normalization for overcoming bias problems associated with the sequence average recurrence interval normalization approach. The large number of data also significantly reduces the confidence bounds of the intrinsic uncertainty estimate.

Our 2079 recurrence intervals significantly exceed the 50 used by Matthews et al. in their synthetic dataset used for assessing the practicality of discriminating between competing recurrence models. This leaves some hope that discrimination between models may be feasible after all using real earthquakes and a scale-normalized dataset. Further investigation of the characteristics of the recurrence-magnitude scaling and normalization will be required before reliable conclusions can be reached in these regards, but our initial results do appear promising. The spatial and temporal characteristics of fault loading rate variations are also exceptionally well characterized in the regions where most of our repeating sequences are occurring. This information can be used to remove and/or asses any bias in the variance of recurrence interval data that variations in spatial and temporal fault loading rates introduce into their distributions. Though our dataset contains only small magnitude events, the "range" in magnitude that it spans is over 4 magnitude units. This should also allow us to test (at least for small magnitudes) the validity of the hypothesis that recurrence interval variance is independent of magnitude, an implicit assumption used by WG99 and WG02.

Finally, an additional attractive feature of our dataset is that it continues to increase in size as ongoing repeating events (typically repeats for each of the 515 sequences occur on the order of every few years or less). Using these ongoing events to continually add to the recurrence interval data set can not only provide more data for constraining the forecast model parameters, but it also can be used to test forecast models on real events. This can be done by making probabilistic forecasts for the future small and frequently recurring earthquakes using competing models and then by assessing the success and failure rates of the various forecasts.

Our future research plans include integration of the auxiliary fault loading rate and recurrence interval data as discussed above, augmentation of the recurrence interval archive with the ongoing small characteristic events, parameterizing competing forecast models using our recurrence and other available recurrence interval data, making small earthquake forecasts using the competing models and comparing the forecasts' relative success rates.

Figure 17.1: Normalized recurrence interval distributions from repeat times of 2594 characteristic small earthquakes (-0.8 $< M_{w} <$ 3.6) occurring along the central SAF from 15 km southeast to 160 km northwest of Parkfield, CA. (Top) Histogram and lognormal fit to recurrence intervals normalized by the average interval for each sequence. (Bottom) Histogram and fit for data normalized by the empirical scaling relationship of average recurrence time with magnitude for all the data. No corrections for spatial or temporal variations in fault slip rates have been applied, and all sequences, regardless of the number of member events, have been included. The exceptionally large number of characteristically repeating small earthquakes makes normalization by the scaling relationship insensitive to the biases that plague Tav normalized data. The surprisingly well behaved Ts scaled results and the large number of intervals available suggest it might be possible to discriminate between competing time-dependent earthquake recurrence models and to test the assumption used by the WG99 and WG02 recurrence model subgroup that aperiodicity of earthquake recurrence is scale independent.
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Acknowledgements

We appreciate support for this project by the USGS NEHRP program through grant numbers 02HQGR0067 and 03HQGR0065, by NSF through award number 9814605, and by the U.S. Department of Energy (DOE) under contract No. DE-AC03-76SF00098.

References

Ellsworth, W.L., M.V. Matthews, R.M. Nadeau, S.P. Nishenko, P.A. Reasenberg, and R.W. Simpson, A physically based earthquake recurrence model for estimation of long-term earthquake probabilities, U.S. Geol. Surv. Open-File Rept. 99-522, 1999.

Matthews, M.V., W.L. Ellsworth and P.A. Reasenberg, A Brownian Model for Recurrent Earthquakes, Bull. Seism. Soc. Am., 92, 2233-2250, 2002.

Nadeau, R.M. and L.R. Johnson, Seismological Studies at Parkfield VI: Moment Release Rates and Estimates of Source Parameters for Small Repeating Earthquakes, Bull. Seismol. Soc. Amer., 88, 790-814, 1998.

Nadeau, R.M. and T.V. McEvilly, Periodic Pulsing of the San Andreas Fault, Science, submitted, 2003.

Working Group on California earthquake Probabilities (WG99), Earthquake probabilities in the San Francisco Bay Region: 2000 to 2030-a summary of findings, U.S. Geol. Surv., Open-File Rept. 99-517, 1999

Working Group on California earthquake Probabilities (WG02), Earthquake probabilities in the San Francisco Bay Region: 2003 to 2032-a summary of findings, U.S. Geol. Surv., Open-File Rept. (to be determined), 2002.

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