IDENTIFYING FORESHOCKS BY THEIR SENSITIVITY TO REMOTE TRIGGERING
Grant Number: 1434-HQ-97-GR-03078
Terry E. Tullis
Phone: (401) 863-3829
Program Element IV: Providing Real-time Hazard and Risk Assessment
Key Words: Earthquake forecasting
The purpose of this research is to evaluate a proposed earthquake prediction scheme briefly presented by Whiteside and Ben-Zion (1995). They orally reported results suggesting that free oscillations of the earth were able to trigger earthquakes and that this triggering occurred preferentially in time and space prior to impending earthquakes. The underlying physical idea was that in the hypocentral region of an impending earthquake the stress was close enough to the failure strength of the rock, or the frictional strength of minor faults. Their suggestion was that the stresses involved in normal mode vibrations of the earth are high enough to trigger microseismicity, perhaps only by advancing their time of occurrence by a few minutes. Thus the proposed method can be thought of as a way of distinguishing foreshocks from normal background microseismicity by their sensitivity to triggering. Although the idea has some appeal, the magnitudes of free oscillation stresses are much smaller than tidal stresses; since tides apparently seldom trigger earthquakes, the likelihood that free oscillations could trigger earthquakes seems low.
However, the data presented by Whiteside and Ben-Zion (1995) suggested that before several major earthquakes, notably the Loma Prieta earthquake of 1989, there was a significant increase in free-oscillation-triggered earthquakes in the epicentral area. Thus although the physical plausibility of the method seemed low, the suggestive results presented warranted an independent study of the situation.
The results of our evaluation of the method of Whiteside and Ben-Zion (1995) indicate that the method is not a viable method of earthquake forecasting. The triggering reported is in fact not real and results from random chance. Comparisons of results generated with real data and with random data show virtually no difference. Furthermore, the temporal and spatial variation previously reported can be shown to result from variations in the numbers of earthquakes and consequent variations in the opportunities for apparent triggering by random chance. We have devised a triggering parameter that takes into account the opportunities for such random apparent triggering. We find that this triggering parameter is never significantly different from zero in any of the examples for which Whiteside and Ben-Zion (1995) suggested free-oscillation triggering occurred.
The Method Being Evaluated
The method of Whiteside and Ben-Zion (1995) considers that an earthquake may have been triggered by a free oscillation mode if the time interval between the earthquake and any other earthquake in the region is equal to the period of that mode, or a multiple thereof. Both earthquakes of the pair are considered to have been triggered. Only certain modes are used, and only as many multiples are considered as will fall within a specified time interval. A match between the inter-event time and the free oscillation period is considered to occur if they are within a specified tolerance of one another. The modes used are 0S0, 0S2, 0S3, 1S2, 0T2, 0T3, and 1T2 and take mode splitting into account. The tolerance allowed for a match is plus or minus 9 seconds.
Since one earthquake may be a member of several pairs, an earthquake that is multiply paired is, by definition, multiply triggered. The study area is subdivided into 0.1-degree bins and the number of earthquake triggers (greater or equal to the number of triggered events) is counted in each bin. The ratio of the number of triggers to the number of total events is calculated and cast as a percentage. Because many events in a single bin may have been multiply triggered, a bin may have a percentage in excess of 100%.
Plots of percent triggering for a region over several years allows the establishment of a baseline value and therefore detection of times of greater sensitivity of earthquakes to triggering which may be foreshocks to a large event.
Recreating the Proposed Method and What it Appears to Show
In order to verify that we have successfully recreated the Whiteside method, we used our independently written computer program to examine a data set also examined by Whiteside. For the ten-month span from 8/1/88 to 5/31/89, the results of this comparison are shown in Figure 1.
Figure1. Percentage of earthquakes that appear to be triggered in 0.1 degree bins, using the method described above in the text. The epicenter of the Loma Prieta earthquake is shown as a black star on these and all other maps. (a-left) These results, computed and kindly provided by Lowell Whiteside, have been transferred into our map base. (b-right) These results have been computed by us using the same data and same method, but using our own independently written computer program.
The virtually identical results in Figure 1a and 1b show that we have successfully duplicated the method of Whiteside. We have also prepared a difference map between our results and those computed by Whiteside and it shows very small differences that are related primarily to different bin boundaries.
In Figure 1 (and more clearly on Figure 2a) note the region of high triggering percentage near the future location of the Loma Prieta earthquake that may indicate foreshocks to the large event. Also of note is the very high level in the Mammoth Mountain region. Several regions in the study area exhibit similar magnitude of triggering percentage to that seen in the Loma Prieta location.
On the maps presented by Whiteside and Ben-Zion (1995) the triggering shown in Figure 1 around the location of the Loma Prieta earthquake was significantly larger than the observed background level of prior years. This formed the basis for their claim that sensitivity to triggering increases in the time and space window where a future large earthquake will occur.
Tests vs. Random Data
The apparent earthquake triggering shown in Figure 1 could be due to matches occurring by random chance between the inter-event times for "triggered" pairs of earthquakes and the periods of the Earth's normal modes. In order to test this we have randomized the data in various ways to see if the triggering disappears, as is should if it is due to physical triggering by the normal modes. We have randomized the earthquake inter-event times, the times of the earthquakes themselves, and the periods of the normal modes. In every test the randomized data is very similar to the real data, showing that the triggering is only apparent and is occurring by random chance. This is shown in Figure 2 for the case in which the earthquake inter-event times have been randomized.
Figure 2. Comparison between (a-left) real data and (b-right) data for which the earthquake inter-event times have been randomized. The two results are nearly identical. The percentages are slightly higher in these maps than in Figure 1. This is because we have corrected an error of Whiteside's incorporated into both Figures 1a and 1b, in which he had used a smaller number of period multiples than he originally intended and a 2 day time window for matching pairs of events to period multiples. After this was fixed, we switched to using arithmetic multiples of periods and a two hour time window. The result of the two changes kept the percentage triggering levels similar to those observed previously, but somewhat higher.
Improved Method for Analyzing Data
The use of triggering percentage as employed by Whiteside is not a suitable parameter for quantitative analysis. If there are a large number of earthquakes in the study region, each event in a particular bin has an increased chance of being in a "triggered" pair of events. Also, if either the plus or minus 9 second tolerance or the time window used for matching is lengthened, each earthquake may be paired with many more events. To remove this bias, we form a null hypothesis that there is not a statistically greater number of matches than should be observed by random chance. More explicitly, for each earthquake the number of triggers relative to the number of pairs available for matching (fractional triggers) should equal the ratio of the time available for matching in the window to the full window width (fractional window). The ratio of fractional triggers to fractional window should equal unity for random data. The triggering parameter is then defined as,
Values of Tr greater than zero indicate that normal mode forcing enhances triggering of earthquakes while a value less than zero indicates that triggering is inhibited by normal mode forcing. We find that the statistical distribution of Tr is essentially Gaussian.
The means of the distributions for both real and random data were found to have slightly negative values. For clarity, plots of Tr were made by subtracting the mean of the distribution for randomized inter-event times, thus showing the deviations from random data. Such plots of Tr for four time periods leading up to the Loma Prieta earthquake are shown in Figure 3.
Figure 3. Maps of Triggering Parameter Tr for four time periods leading up to the Loma Prieta earthquake.
Figure 3c (lower left) is the map of Tr for the same ten-month interval used for Figures 1 and 2. For this and all the time periods we have examined most values are very close to zero, and almost no value in this binned data is beyond one standard deviation from zero. Thus not only is the apparent triggering in Figure 1 and 2a due to random chance, there is no significant difference in the triggering parameter as one approaches the time of the Loma Prieta earthquake.
The earthquake prediction method proposed by Whiteside and Ben-Zion (1995) is found upon closer inspection not to be a viable means of earthquake prediction. Results using random data are indistinguishable from those using real data. Casting the results in terms of a newly defined triggering parameter that takes into account opportunities for random apparent triggering, our results support the null hypothesis that the apparent triggering by free oscillations is not real.
Whiteside, L. S., and Y. Ben-Zion, Universal triggering patterns in earthquake sequences and the use of triggering for earthquake prediction, Eos. Trans. Am. Geophys, Union, Fall Meeting Suppl., 76, F532, 1995.
We have evaluated a previously proposed earthquake prediction method and found that it does not work. The method envisioned that very small stresses associated with vibrations of the earth called free oscillations could cause small earthquakes to be triggered in areas where the stress was already high because the area was getting ready for a major earthquake. Several examples were presented that seemed to show that an unusually large number of small earthquakes were triggered before previous major earthquakes. Unfortunately, we have found that the apparent triggering was not real and was due merely to random chance.
Costello, S. W., and T. E. Tullis, Investigation of a proposed earthquake prediction method that envisions foreshock triggering by free oscillations, Eos. Trans. Am. Geophys, Union, Fall Meeting Suppl., 78, 490, 1997.
Costello, S., and T.E. Tullis, Can free oscillations trigger foreshocks that allow earthquake prediction?, Geophys. Res. Lett., 26, 891-894, 1999.