Probabilistic forecasting of earthquakes

Abstract

We present long‐term and short‐term forecasts for magnitude 5.8 and larger earthquakes. We discuss a method for optimizing both procedures and testing their forecasting effectiveness using the likelihood function. Our forecasts are expressed as the rate density (that is, the probability per unit area and time) anywhere on the Earth. Our forecasts are for scientific testing only; they are not to be construed as earthquake predictions or warnings, and they carry no official endorsement. For our long‐term forecast we assume that the rate density is proportional to a smoothed version of past seismicity (using the Harvard CMT catalogue). This is in some ways antithetical to the seismic gap model, which assumes that recent earthquakes deter future ones. The estimated rate density depends linearly on the magnitude of past earthquakes and approximately on a negative power of the epicentral distance out to a few hundred kilometres. We assume no explicit time dependence, although the estimated rate density will vary slightly from day to day as earthquakes enter the catalogue. The forecast applies to the ensemble of earthquakes during the test period. It is not meant to predict any single earthquake, and no single earthquake or lack of one is adequate to evaluate such a hypothesis. We assume that 1 per cent of all earthquakes are surprises, assumed uniformly likely to occur in those areas with no earthquakes since 1977. We have made specific forecasts for the calendar year 1999 for the Northwest Pacific and Southwest Pacific regions, and we plan to expand the forecast to the whole Earth. We test the forecast against the earthquake catalogue using a likelihood test and present the results. Our short‐term forecast, updated daily, makes explicit use of statistical models describing earthquake clustering. Like the long‐term forecast, the short‐term version is expressed as a rate density in location, magnitude and time. However, the short‐term forecasts will change significantly from day to day in response to recent earthquakes. The forecast applies to main shocks, aftershocks, aftershocks of aftershocks, and main shocks preceded by foreshocks. However, there is no need to label each event, and the method is completely automatic. According to the model, nearly 10 per cent of moderately sized earthquakes will be followed by larger ones within a few weeks.

Comment on ‘Testing earthquake prediction methods: “The West Pacific short-term forecast of earthquakes with magnitude MwHRV ≥5.8”’ by V.G. Kossobokov

“…The forecast algorithm running since 1999/1/1 in a test mode for the west Pacific regions (Jackson and Kagan, 1999;Kagan and Jackson, 2000), combines two procedures: the shortterm statistical method (Kagan and Knopoff, 1987) and the long-term program (Kagan and Jackson, 1994). When we started this experiment, we hoped to test the algorithm thoroughly in both short-and long-term applications, and then develop a probabilistic procedure to combine both methods in a comprehensive model.…”

“…When we started this experiment, we hoped to test the algorithm thoroughly in both short-and long-term applications, and then develop a probabilistic procedure to combine both methods in a comprehensive model. We tested the long-term forecast (Jackson and Kagan, 1999;Kagan and Jackson, 2000); see also additional results for years [2000][2001][2002] at http://scec.ess.ucla.edu/∼ykagan/tests index.html. Because of funding limitations, we were unable to develop the forecast method fully, create a permanent archive of forecasts, or thoroughly test the method's effectiveness.…”

“…They follow a power-law dependence on time (Jackson and Kagan, 1999;Kagan and Jackson, 2000). This rapid change necessitates frequent updating of forecasts.…”

“…In earlier papers (Jackson and Kagan, 1999;Kagan and Jackson, 2000), we introduced two earthquake forecast methods based on past seismicity, with an open invitation for others to test these forecasts on future earthquakes. Since then we have been updating these forecasts daily and posting results on the Web.…”

“…Earthquake occurrence is usually represented as a stochastic point process (Kagan and Jackson, 2000;Daley and Vere-Jones, 2003), and event occurrence rate is one of the most important parameters in the theory of point processes. In west Pacific regions we estimate the earthquake rate for cells 0.5 • × 0.5 • .…”