Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California

doi:10.1785/0120050067

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Comparison of Short-Term and Time-Independent Earthquake Forecast Models for Southern California

Agnès Helmstetter¹, Yan Y. Kagan² and David D. Jackson²

¹ Lamont-Doherty Earth Observatory
61 Route 9W
Palisades, New York 10964
agnes{at}ldeo.columbia.edu
(A.H.)

² Department of Earth and Space Sciences
University of California
Los Angeles, California 90095-1567
djackson{at}ucla.edu
ykagan{at}ucla.edu
(D.D.J., Y.Y.K.)

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Figure 1. Declustered catalog, obtained with Reasenberg's (1985) algorithm, including 6,861 m $≥$ 3 earthquakes in the time window 1932–1979 and 46,937 earthquakes with m $≥$ 2 for 1980–2003.

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Figure 2. Time-independent density obtained by declustering and smoothing the ANSS catalog.

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Figure 3. Time-independent seismicity density for the Kagan and Jackson (1994) model (left) and for the present work (right). White circles represent m $≥$ 5 earthquakes that occurred between 1990 and 2004.

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Figure 4. Time-independent density of m $≥$ 5 earthquakes for the Frankel et al. (1997) model (left) and for our model (right). White circles represent m $≥$ 5 earthquakes that occurred between 1996 and 2004.

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Figure 5. Plot of the magnitude versus time for a few days in the ANSS catalog, which illustrates the fact that a significant fraction of earthquakes that will occur in the next day (between the present time t_p and t_p + T) may be triggered by earthquakes that will occur in the next day (t_p < t < t_p + T).

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Figure 6. Magnitude versus time since mainshock for aftershocks of Joshua Tree m 6.1 (a), San Simeon m 6.5 (b), and Landers m 7.3 earthquakes (c). The continuous line represents the threshold magnitude estimated from (15) and includes the effect of all m $≥$ 5 earthquakes. The vertical lines in (c) are due to the increase of m_c(t) after large m $≥$ 5 aftershocks. Dates of these earthquakes are shown in Table 2.

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Figure 7. Density of aftershocks estimated by smoothing the location of early aftershocks (white circles) that occurred less than 2 hr after the Landers mainshock (m 7.3, 28 June 1992), using either a Gaussian kernel (18) (a) or a power-law kernel (17)(b).

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Figure 8. Results of the optimization of the log likelihood LL for the unconstrained model 1 by using a Gaussian kernel. Value of LL as a function of each model parameter (a)–(e) and as a function of the number of iterations (f).

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Figure 9. (a) Forecasted number of events with m $≥$ 2 per cell for 23 October 2004 (logarithmic scale). Black circles represent observed earthquakes with m $≥$ 2 that occurred during this day. Two of these events are aftershocks of the m 6.5, 22 December 2003 San Simeon earthquake (located at latitude 35.7° and longitude –121.1°), three are associated with the m 6 28 September 2004 Parkfield mainshock (latitude 35.81° and longitude –120.37°), and one is an aftershock of a m 3.7 9 September 2004 earthquake (latitude 35.09° and longitude –117.52°). The predicted number of events for this day was 8.39 and the observed number was 6. Most of these earthquakes are better predicted by the ETES model than by the time-independent model (i.e., N_p > µ in the cells within which these earthquakes occurred). Only one event, which occurred at 11 km away from the San Simeon earthquake (latitude 35.81° and longitude –121.02°), was better predicted by the time-independent model, because it occurred just outside of the main aftershock zone. (b) Ratio of the forecasted number of events estimated using the ETES and the time-independent models (logarithmic scale). High values of N_p/µ (up to 800) are associated with recent large earthquakes, such as Parkfield, San Simeon, Landers, Hector Mine, and Northridge.

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Figure 10. Observed (solid black line) and predicted number of m $≥$ 2 earthquakes per day as a function of the time since the Landers mainshock, for model 2 (circles), model 3 (crosses), and model 5 (diamonds). The saturation at t $≤$ 10 days is due to the incompleteness of the catalog for small magnitudes (see Fig. 6).

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Figure 11. (a) Observed (black) and predicted (gray) number of m $≥$ 2 earthquakes per day in southern California for model 3 (see Table 1). Dashed line is the background rate µ_s = 2.81/day. (b) Probability gain per earthquake defined in (25).

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Figure 12. Predicted number of m $≥$ 2 earthquakes per day for model 3 (see Table 1) as a function of the observed number, for the period 1985–2003. The dashed line represents the perfect fit. The horizontal line is the background rate µ_s = 2.81/day.