seismic gap hypothesis: ten years after - uclamoho.ess.ucla.edu/~kagan/jgr_1991_after.pdf ·...

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 96, NO. B13, PAGES 21,419-21,431, DECEMBER 10, 1991

Seismic Gap Hypothesis' Ten Years After

YAN Y. KAGAN

Institute of Geophysics and Planetary Physics, University of California, Los AngeJes

DAVID D. JACKSON

Department of Earth and Space Sciences, University of California, Los Angeles

The seismic gap hypothesis states that earthquake hazard increases with time since the last large earthquake on certain faults or plate boundaries. One of the earliest and clearest applications of the seismic gap theory to earthquake forecasting was by McCann et al. (1979), who postulated zones of high, medium, and low seismic potential around the Pacific rim. In the 10 years since, there have been over 40 large (M > 7.0) earthquakes, enough to test statistically the earlier forecast. We also analyze another forecast of long-term earthquake risk, that by Kelleher et al. (1973). The hypothesis of increased earthquake potential after a long quiet period can be rejected with a large confidence. The data suggest that, contrary to these forecasts, places of recent earthquake activity have larger than usual seismic hazard, whereas the segments of the circum-Pacific belt with no large earthquakes in recent decades have remained relatively quiet. The "clustering" of earthquake times does not contradict the plate tectonic model, which constrains only the long-term average slip rate, not the regularity of earthquakes.

INTRODUCTION

The seismic gap hypothesis implies that earthquake hazard is small immediately following the previous large earthquake and increases with time since the last large event on certain fault or plate boundaries [Sykes and Nishenko, 1984, p. 5911]. The hypothesis has re- cently been used in long-term forecasting of earthquakes around the whole Pacific rim [McCann et al., 1979; Nishenko, 1991], in Cahfornia [Sykes and Nishenko, 1984; Bakun and Lindh, 1985; Working Group on Cali- fornia Earthquake Probabilities, 1988], and in other Pa- cific regions [Sykes, 1971; Kelleher, 1972; and Kelleher et al., 1973]. Henceforth we shall refer to McCann et

[1991 [1991 to [191 as KSO [1973]. Because of the scientific and social im- portance of these forecasts, the seismic gap hypothesis deserves rigorous testing.

The times of large earthquakes in a given region can be studied by the statistics of "point processes" [Coz and Lewis, 1966]. These processes can be characterized well by their coefficient of variation, defined as the ratio of the standard deviation of interval times to the

mean interval time (or "recurrence time") T. At the one extreme a quasi-periodic process has a coefficient of variation less than 1, while a clustering process, at the other extreme, has a coefficient of variation greater than 1. For comparison the simple Poisson process serves as a useful benchmark' it has a coefficient of varia-

Copyright 1991 by the American Geophysical Union.

Paper number 91JB02210.

0148-0227/91/91JB-02210505.00

tion equal to 1, and predicts a seismic hazard independent of time and previous seismic activity. The seismic gap hypothesis assumes that earthquake occurrence is a quasi-periodic process, so that earthquake potential is low when the elapsed time since the last large earthquake is less than T and is high afterward.

Unfortunately, the record is too short in most seismic zones to estimate the distribution of event times

directly from the data. The palcoseismic record at Palette Creek, California, is the longest rehable record and suggests a clustering process, although a Poisson process cannot be rejected [$ieh et al., 1989]. Given the shortness of the seismic record, we test the seismic gap method using an ensemble of seismic zones, rather than an ensemble of times within a single zone.

The basic idea behind the seismic gap hypothesis has enjoyed intuitive appeal since the early work of Reid [1910]. He suggested that a large earthquake releases most of the stress in a given fault segment and that further earthquakes there would be unhkely until the stress is somehow restored. However, Gilbert [1909], the first to formulate this hypothesis, calling it the "rhythmic recurrence hypothesis," rejected it after analyzing seismicity in the United States during the nineteenth and early twentieth century: "The hypothesis of rhythmic recurrence has no sure support from observation, and is not in working order for either large or small areas. Its corollary of local immunity after local disaster is more alluring than safe" [Gilbert, 1909, p. 133].

The acceptance of plate tectonics in the 1960s as a behevable mechanism for resupplying stress added intuitive arguments for the seismic gap hypothesis. The standard explanation for quasi-periodicity is that the

21,419

21,420 KAOAN AND JACKSON: SEISMIC GAP HYPOTHESIS

stresses which cause earthquakes are slowly building up by plate movements after one event [Nishenko and McCann, 1981, p. 21]; a new, strong earthquake is less probable until the stress or deformational energy reaches a critical value [Shimazaki and Nakata, 1980].

Quasi-periodic occurrence of earthquakes, as suggested by the seismic gap hypothesis, does not follow as a required consequence of plate tectonics. The seismic gap hypothesis is based on several additional assumptions, for example, (1) that plate boundaries and major faults are subdivided into natural segments, (2) that tectonic stress within a segment must be relieved by the occurrence of an earthquake (sometimes called "characteristic earthquake") which ruptures the entire segment, (3) that such an earthquake reduces the stress significantly below the point where successive large earthquakes are immediately possible, and (4) that within a segment, stress accumulates slowly, requiring several decades to pass before another large earthquake is possible.

These assumptions may fa•l in several ways. For example, if earthquakes do not respect the segment boundaries of assumption 1, then the spatial extent of a seismic gap would be undefined [Thatcher, 1989], and estimating the recurrence time for a given gap becomes arbitrary because data selection is required. Even within a well-defined segment, events smaller than the characteristic earthquake of assumption 2 could collectively allow displacement and reduce stress. Of course, aseismic slip may also occur. It is also conceiv- able that the Earth remains in a near-critical state, even following a large earthquake, as proposed by the theory of "self-organized criticality" [Bak and Tang, 1989, and references therein]. This would violate assumption 3, and allow earthquakes to occur without a mandatory rest period. Finally, a ruptured fault segment might sometimes acquire stress rapidly, for example, by earthquakes or creep on nearby fault segments, thus violating assumption 4. Such coupling can, according to simula- tions by Rundle [1988], cause temporal clustering.

Nishenko [1989] lists 13 earthquakes which occurred since 1968 in previously identified seismic gaps, and many seismologists [e.g. Working Group on California Earthquake Probabilities, 1988, p. 5; Thatcher, 1989, p. 432; Oppenheimer et al., 1990, p. 8483] treat the seismic gap hypothesis as one confirmed by observations. How- ever, the hypothesis cannot be fairly evaluated by considering only successes; even if a few randomly selected seismic zones were labeled as "gaps," some earthquakes would occur in them purely by chance. If the seismic gap model is valid, it should be able to forecast future earthquakes better than a purely random scheme. A meaningful forecasting method must be testable against random occurrence. Many published forecasts do not satisfy this criterion because they do not clearly de- fine the events that would be considered successes and

failures. Some applications use only small regions, for

which the number of events occurring in the last 15-20 years is not sufficient for the statistical testing. Two forecasts satisfy the requirements necessary for successful statistical testing' (1) the K$O [1973] forecast which included previous results reported by Kelleher [1972] and Sykes [1971], and (2) the MNSK [1979] forecast. These papers provide the clearest early applications of the seismic gap model. According to the Science Cita- tion Indez [1988, and editions of previous years], they are the most often quoted references on the seismic gap hypothesis. Ten out of 13 successful forecasts listed by Nishenko [1989] are made in these two papers and their immediate predecessors.

The authors of both papers subdivided the circum- Pacific earthquake zone into many segments to which they assigned potential for large earthquakes (with magnitude M )_ 7.0). The probabilities of an earthquake occurrence have been expressed by MNSK [1979] through a scale of high, medium, and low potential; in the work of K$O [1973] the Pacific earthquake belt is subdivided into areas which we call, for convenience, dangerous and nondangerous. KSO [1973, p. 2553] suggested that "the most realistic test [of their forecasts] will lie in the locations of large earthquakes during the next few decades." MNSK also state that the seismic potential is forecasted for the next few decades. In this paper we do not con- test the methods and decisions by which MNSK and K$O arrived at their seismic hazard regionalization; we test statistically the final results of these papers, to see whether the forecasts have been validated by the seismicity of the last decade.

For several reasons we decided to test these forecasts

statistically: they provide a quite definitive explanation of the hypothesis; they state clearly what was forecasted, so that successes and failures can be clearly rec- ognized; and they forecasted for a large enough area that after 10 years for MNSK [1979] and 16 years for KSO [1973], there is a sufficient data set to make statistically valid conclusions. Indeed, according to the U.S. Department of the InteriorSGeological Survey, (USDIG$) [1988] Preliminary Determination of Epicen- •ers (PDE)list, in the time period from January 1, 1979, to June 24, 1988, about 60 shallow earthquakes (depth less than or equal to 70 km) with Ms _> 7.0 occurred in and around the circum-Pacific region covered by the MNSK forecast (Figure 1). MNSK forecasts of- fer a better opportunity for testing since the zones are defined more clearly, and we have two additional catalogs of seismic moment tensor inversions to test them. Hence, we start our discussion with the MNSK analysis.

MNSK [1979] PACIFIC FORr•C•ST

Nishenko [1988] reports that eight seismic gaps have been filled by large earthquakes in the decade following the publication of MNSK [1979], supporting the seismic gap hypothesis. However, a seismicity map for 1979-

KAOAN AND .lACKSON: SEISMIC GAP HYPOTHESIS 21,421

1988 (Figure 1), reveals that many of the above mentioned 60 shallow earthquakes occurred on segments where MArSK estimated low probability.

The MNSK [1979] forecast gives only qualitative statements about future seismic activity. We decided to verify the MNSK regionalization only in zones for which future earthquake potential had been definitely assessed. Thus, we use category 1 (red) segments which, according to MNSK, have the highest potential, category 2 (orange) areas with an intermediate potential, and category 6 (green) segments with the lowest potential. Segments of categories 3 to 5 have not been used here, since the seismic activity to be expected in these areas is unclear.

To avoid any ambiguity in interpreting the exposition, we used the color insert map MNSK [1979, Figure 1] as a final result in our testing. Several reasons exist for not using more detailed maps and discussion text in MNSK in assigning events: (1) We want to make data selection for statistical testing as formal and objective as possible; we would have to apply considerable sub- jective judgment and interpretation of our own to come up with a new uniform global map. (2) Some gaps on the detailed maps are shown as segments of lines, not regions; thus we need to project epicenters on those segments, a procedure subject to arbitrary decisions. (3) The seismic gaps in the detailed figures are not assigned an earthquake potential index, and the gaps do not correspond uniquely to the regions on the color map. Us- ing detailed maps for some event assignments and the global map for other events is also unsatisfactory, since it may bias the selection. Possibly questionable attri- butions of events using the color map of MNSK should cancel out over large time and area. Thus, statistical results should not be strongly affected by such selection.

The text and figures of MNSK [1979] contain quantitative information (such as seismic history and maximum known earthquake magnitude for specific zones) as well as qualitative information about the geology and plate interactions at specific zones. Most of this information we cannot use without introducing bias into our test. For example, the seismic gap hypothesis is often interpreted to apply only to "plate boundary rupturing" or "gap-filling" events, which may be larger in some zones than in others. Unfortunately, neither KSO [1973] nor MNSK defined clearly what would qualify as such an event for each plate boundary segment. Thus, in applying this concept we would have to construct our own rules for data selection. Even if such rules were

based on the information in the work of MNSK the re-

quired personal involvement with the data would be in- appropriate in a statistical test. Thus, we are forced to take literally the selection criteria shown on the color map and the rules listed by MNSK [1979, pp. 1086- 088].

In Table I we lis• •hose shallow (depth 70 km or less) ear[hquakes wi[h Ms _) 7.0 in •he ckcum-Pacific region

since 1979 which fall into one of the MNSK [1979] area categories 1, 2, and 6. Therefore, many earthquakes, such as intraplate events or those occurring in areas of categories 3 to 5 are excluded from the table and the consequent analysis. Since the MNSK regionalization is expressed through a map, to compare these epicenters with the MNSK forecast, we produced epicenter maps on a scale and projection like the MNSK [1979, Fig- ure 1] map. We superimposed our maps over their map and counted the epicenters falling into each segment.

Several problems are encountered during event assignment. First, our maps do not overlay the MNSK [1979] map exactly, possibly due to paper deformation in printing. Therefore, to attribute a MNSK zone to each epicenter, we have attempted to match coast out- lines in the neighborhood of the event. Second, the scale of the MNSK map (about I ß 7 x 107) and print resolution make it sometimes difficult to decide in which zone

an epicenter belongs. The resolution accuracy on the color map is of the order of 1/4 to 1/2 mm, which cor- responds to 20-35 km possible assignment error. Since the map information is in analog form, some disagreement in event attribution is unavoidable.

For ease of comparison and discussion, we numbered zones counterclockwise starting with southern tip of South America. In this numbering scheme we considered any connected zone as one unit. In total we counted 17 "red" zones, 34 "orange" areas, and 36 "green" zones (Table 2). An affiliation of each epicenter is shown in the "MNSK" column of Table 1. In cases

where an epicenter lies on a boundary of two zones, we assigned it to both (see, for example, event 20 in Ta- ble 1).

Epicenters of events listed in Table 1 are shown in Figure 1, along with an artist's rendition of the MNSK [1979] color map. Note that we assigned earthquakes to zones using the original color map, not the artists's rendition of our Figure 1. Thus any minor discrepancies between our Figure 1 and that of MNSK did not affect zone assignment. Boldface italic numbers correspond to event indices of Table 1. Roman characters indicate

zone labels in the "zone" column of Table 1.

We prepared similar tables for three additional sets of earthquakes. The first of these sets is for events with Mo > 7.0 from the PDE hst of USDIG$ [1988]. This magnitude is usually Ms obtained from different sources [USDIGS, 1988]. The epicenter coordinates for this set are taken from the PDE hst [ USDIGS, 1988]; hence coordinates are the same as hsted in Table 1.

In two other sets we use magnitude M,0 calculated from the value of scalar seismic moment, M0 reported by the Harvard group [Dziewonski et al., 1989] and by the U.S. Geological Survey (USGS) [Sipkin and Need- ham, 1989]:

2

M,,, - •.[log•.o(Mo ) - 9.0],

21,422 KAOAN AND •JAC•_•gON: SEIglVIIC GA• HYPO•ESiS

+ + +

• R-6-•G_8/-0-1o

-!-

+ D+ _

G-5

+ • 56 + R-1

53

G-2

-I-

I 1 I I I •øw 105øw 90ow 75ow 60ow 45ow

A

- 30"N

- 15ON

-0

- 15"S

- 30"S

- 45"S

16oos 30øW

Fig. 1. Seismicity map of the circum-Pacific region for 1979-1988. All of the earthquakes with Ms > 7.0 in mp: Sout (b)

Bold italic numbers correspond to event indices of Table 1. Roman characters indicate zone labels in the "zone" column of Table 1. "R" indicates a red zone (highest seismic potential according to MNSK [1979]); "O" indicates an orange zone (intermediate seismic potential); and "G" indicates a green zone (lowest seismic potential). "Y," "C," and "B" denote yellow, cross-hatched, and blue zones of MNSK. Seismic potential of Y, C, and B zones was judged by MNSK to be uncertain, so we did not include them in our analysis.

where M0 is measured in Newton meters. These two

catalogs available to us cover the period from January 1, 1979, to February 29, 1988. In both cases we used centroid coordinates of moment release to better corre-

late with the regions of MNSK [1979], unlike epicentral coordinates which may correspond to accidental features of the rupture process. Like epicenter estimates, centroid locations might be subject to errors connected with lateral heterogeneities. Nevertheless, they provide a better estimate of the rupture zone's center. Further- more, they represent an independent estimate of earthquake location. Use of centroids in addition to epicenters gives a more stable estimate of the event count in each zone.

Many authors, including KSO [1973] and MNSK [1979], argue that only gap-filling earthquakes whose rupture zones fill whole gaps are forecast by the gap hypothesis. We consider epicenters and centfolds only, rather than the rupture surfaces, for the following reasons: (1) the rupture surface is poorly defined and less amenable to formal, objective testing; (2) according to the seismic gap hypothesis, rupture zones of large earthquakes tend to abut those of previous earthquakes, so a sufficiently large event may be assumed to fill a gap if its centroid is in the gap; (3) the seismic gap hypothesis becomes worthless if it applies only to very specific earthquakes, distinguishable from others only with spe- cialized seismological data; and (4) MNSK and KSO

I•OAN AND •ACK30N• SEISMIC GAP HYPOTHE3IS 21,423

G-19

' O-21

G-20

R'9 +

G-18

1-17

25 5O

O-19

+ + + + +

+ + + + +

+ + + + + + +

I I I I I 135øE 150øE 154øE 180' 165øW 150•W 135øW

,24 •.

-G-14 _ 60ON

45øN

O-18 '

/

R-7

30øN

B 15ON 120øW

© c I I I I ' I 60os

105øE 120øE 135øE 150øE 165øE 180øE

Fig. 1. (continued)

TABLE 1. PDE List of Earthquakes With Ms •_ 7.0 in Circum-Pacific B. egion Zone

Earth- Depth, quakes Date Coordinates km rnb Ms Mo KSO MNSK Weight

I Jan. 30, 1973 18.5øN -103.0øW 43 6.2 7.5 7.3 1• - - 2 Feb. 28, 1973 50.5øN 156.6øE 27 6.3 7.2 7.1 G - - 3 June 17, 1973 43.2øN 145.8øE 48 6.5 7.7 7.7 G - - 4 June 24, 1973 43.3øN 146.4øE 50 6.3 7.1 7.1 G - - 5 Aug. 18, 1974 -38.5øS -73.4øW 36 5.9 7.1 7.0 G - - 6 Oct. 3, 1974 -12.3øS -77.8øW 13 6.6 7.6 7.5 1• - - 7 Oct. 8, 1974 17.3øN -62.0øW 47 6.6 7.5 7.1 B. - - 8 Nov. 9, 1974 -12.5øS -77.8øW 6 6.0 7.2 6.2 B. - - 9 Feb. 2, 1975 53.1øN 173.5øE 10 6.1 7.6 7.5 G - -

10 May 10, 1975 -38.2øS -73.2øW 6 6.5 7.7 7.8 G - - 11 Jan. 21, 1976 44.9øN 149.1øE 41 6.3 7.0 6.4 G - - 12 March 23, 1978 44.9øN 148.4øE 33 6.4 7.5 7.3 G - - 13 March 24, 1978 44.2øN 148.9øE 33 6.5 7.6 7.5 G - - 14 June 12, 1978 38.2øN 142.0øE 44 6.8 7.7 7.5 1• - - 15 Aug. 23, 1978 10.2øN -85.2øW 56 5.7 7.0 7.2 G - - 16 Nov. 29, 1978 16.0øN -96.6øW 18 6.4 7.7 7.9 G/I• - - 17 Feb. 28, 1979 60.6øN -141.6øW 15 6.4 7.1 7.4 1• - - 18 March 14, 1979 17.8øN -101.3øW 49 6.5 7.6 7.6 G/I• (1-13 0.66 19 Oct. 23, 1979 -10.6øS 161.3øE 22 6.1 7.1 7.2 - (1-31 1.0 20 Dec. 12, 1979 1.6øN -79.4øW 24 6.4 7.7 7.7 B. (1-7/O-5 1.0 21 Feb. 23, 1980 43.5øN 146.8øE 44 6.3 7.0 7.1 G (1-19 1.0 22 July 8, 1980 -12.4øS 166.4øE 33 5.9 7.5 7.8 - (1-32 0.05 23 July 17, 1980 -12.5øS 165.9øE 33 5.8 7.9 8.0 - (1-32 1.0 24 Oct. 25, 1980 -21.9øS 169.9øE 33 5.8 7.2 7.1 - 0-34 1.0 25 Jan. 30, 1981 51.7øN 176.3øE 33 6.3 7.0 7.1 G (1-16 1.0 26 July 6, 1981 -22.3øS 171.7øE 33 6.9 7.0 7.0 - 0-34 1.0 27 July 15, 1981 -17.3øS 167.6øE 30 5.6 7.0 7.1 - 0-33 1.0 28 Oct. 16, 1981 -33.1øS -73.1øW 33 6.2 7.2 7.5 1• O-1 1.0 29 Oct. 25, 1981 18.0øN -102.1øW 33 6.2 7.3 7.4 B. O-17 1.0 30 Dec. 26, 1981 -29.9øS -177.7øW 33 6.1 7.1 6.6 - G-36 1.0 31 Jan. 11, 1982 13.8øN 124.4øE 46 6.0 7.1 7.4 - 0-26 1.0 32 June 7, 1982 16.6øN -98.4øW 34 6.3 7.0 6.9 G (1-12 1.0 33 Aug. 5, 1982 -12.6øS 165.9øE 31 6.2 7.1 7.5 - (1-32 1.0 34 Apr. 3, 1983 8.7øN -83.1øW 37 6.5 7.3 7.2 G/- O-13 1.0 35 Oct. 4, 1983 -26.5øS -70.6øW 15 6.4 7.3 7.4 G 0-2 1.0 36 Feb. 7, 1984 -10.0øS 160.5øE 18 6.6 7.5 7.7 - (1-31 1.0 37 March 24, 1984 44.1øN 148.2øE 44 6.1 7.0 6.7 G (1-19 1.0 38 Nov. 17, 1984 0.2øN 98.0øE 33 6.3 7.2 7.4 - 1•-13 1.0 39 Dec. 28, 1984 56.2øN 163.5øE 33 6.2 7.0 6.7 1• (1-17 1.0 40 March 3, 1985 -33.1øS -71.9øW 33 6.7 7.8 7.5 1:{. O-1 1.0 41 Apr. 9, 1985 -34.1øS -71.6øW 38 6.3 7.2 7.5 1• O-1 0.08 42 May 10, 1985 -5.6øS 151.0øE 27 6.3 7.1 7.3 - O-31 1.0 43 July 3, 1985 -4.4øS 152.8øE 33 6.3 7.2 7.4 - 0-32 1.0 44 Sep. 19, 1985 18.2øN -102.5øW 28 6.8 8.1 7.9 1• O-17 1.0 45 Sep. 21, 1985 17.8øN -101.6øW 31 6.3 7.6 7.5 G/I• (1-13 0 46 Nov. 28, 1985 -14.0øS 166.2øE 33 6.0 7.0 7.2 - G-33/- 0 47 Nov. 28, 1985 -14.0øS 166.2øE 33 6.3 7.1 7.6 - G-33/- 1.0 48 Dec. 21, 1985 -14.0øS 166.5øE 43 6.0 7.3 7.6 - (1-33/- 0 49 Apr. 30, 1986 18.4øN -103.0øW 27 6.2 7.0 6.9 1• O-17 0.28 50 May 7, 1986 51.5øN -174.8øW 33 6.4 7.7 7.9 G (1-16 1.0 51 Nov. 14, 1986 23.9øN 121.6øE 34 6.3 7.8 7.5 - B.-11 1.0 52 Feb. 8, 1987 -6.1øS 147.7øE 55 - 7.4 7.3 - (1-29/- 1.0 53 March 5, 1987 -24.4øS -70.2øW 62 6.5 7.3 7.1 G G-4/B.-1 1.0 54 Oct. 16, 1987 -6.3øS 149.1øE 48 5.9 7.4 7.3 - 0-30 0.88 55 Feb. 24, 1988 13.4øN 124.6øE 21 6.0 7.0 7.1 - 0-26 1.0 56 Apr. 12, 1988 -17.3øS -72.4øW 54 6.1 7.0 6.8 1• P,-1 1.0

Time limits are from January 1, 1973, to June 24, 1988. Latitude limits are from 67øN to 60øS. Longitude limits are from 30øW to 90øE. Depth limits are from zero to 70 km. Only earthquakes which fall into one of zones defined by K$O [1973] or MNSK [1979] are listed. In the column "zone" epicenters are assigned to "red" (1•), "orange" (O), or "green" (G) zones. If an epicenter happens to be on a boundary of two zones, the assignment is made through slash, "G-1/1•-1." A dash in the column of zone means that the epicenter is outside of P,, O, or G zones. Therefore, "G-33/-" means that we count this earthquake as a half event.

KAOAN AND JACKSON: SEISMIC GAP HYPOTHESIS 21,425

TABLE 2. Number of Earthquake Epicenters in Different MNSK [1979] Regions.

Zones • Number PDE Ms PDE Mo tIarvard • Sipkin' Average Ratio

of Zones E Z E Z E Z E Z E Z E Z

119. 17 3.5 3.0 2.5 2.5 5.0 3.5 3.0 3.0 3.5 3.0 0.21 0.18 20 34 16.5 10.5 18.0 11.0 22.0 14.0 15.0 12.0 17.9 11.9 0.53 0.32 6G 36 17.0 9.5 20.0 10.0 23.0 12.0 14.5 10.5 18.6 10.5 0.52 0.29

E is the number of earthquakes. Z is the number of zones filled by earthquakes. • abbreviations as follows: 11{, "red" zones (category 1) of MNSK; 20, "orange" zones (category 2) of MNSK; and 6G,

"green" zones (category 6) of MNSK. • From Dziewonski et al. [1989]. ' From Sipkin and Needham [1989].

specifically mention that their forecast applies to shallow events with M _> 7.0. Recent forecasts by Nishenko [1991] continue the reference to M >_ 7.0 events. If the seismic gap theory really applies to specific earthquakes only, the proponents must provide objective criteria for recognizing these events.

Having compiled tables like Table 1 for all subcat- alogs, we calculate the number of events occurring in each regional set as well as the number of zones filled by earthquakes. In these calculations, if an epicenter is situated on a boundary of two zones, we assign the weight 0.5 to each zone. Our results are summarized in Table 2. The values in the last two columns cor-

respond to the ratio of the number of earthquakes or the number of zones filled by earthquakes to the total number of zones (column 2 in Table 2). The red zones seem to exhibit less seismic activity than the other two types of zones, whereas the earthquake potential of the green and orange zones is clearly indistinguishable. We interpret the MNSK [1979, p. 1082] discussion on seismic potential of various zones in the following way: the probabilities of an earthquake occurrence in these zones should be related as

and

We test here whether the above mentioned disagreement between the observations and the seismic gap hypothesis as formulated above is statistically significant. For simplicity, we test pairwise (red versus orange, and orange versus green).

Let H0 be the hypothesis that zones of all categories have the same probability of having earthquake(s),

(3)

and let H• be the hypothesis that these probabilities satisfy relation (2). The number of zones filled by earthquakes should be distributed according to the binomial distribution. If H0 is true, the likelihood ratio equals [Wilks, 1962, exercise 13.5]

- I - , (4)

where n• and n•. are the numbers of zones in each category to be compared, n - n• + n2, rnx and rn2 are the numbers of zones filled by earthquakes, m- rnx + rn2. The quantity -2 log • is distributed for large n according to the X •' distribution with one degree of freedom. In our tests the total number of zones is not especially large, but we use this statistical test to gauge the validity of the seismic gap model.

Calculating ,• for red and orange zones and for red and green areas, as shown in the "average" column of Table 2, we obtain ,•- 0.45 and • - 0.65, respectively. Both of these values indicate that Ho cannot be rejected on the basis of results from Table 2 [Kendall and Stu- art, 1977]. However, the statistical test results might still be consistent with the seismic gap hypothesis H•, if the probabilities on the right side of formula (2) are only slightly higher (a few percent) than those on the left side. Although MNSK [1979] do not give quantitative relations between the probabilities in (2), the gap hypothesis cannot be meaningful unless the red zones have a substantially greater earthquake potential. Aki [1989], for example, suggests that the seismic gap hypothesis should yield an order of magnitude probability gain in predicting large earthquakes. Let us assume, for example, that

and

or

P,a-

The value 0.3 in (Sa) is an approximate value of "•atio" in Table 2 that is common to orange and green zones; it •ep•esents the p•obability that a zone of a given colo• would experience an M > 7 earthquake in 10 years.


Under H• the probability that three or fewer of the 17 red zones would be rifled by earthquakes equals

P(r _< P,:,• I- P•,• . (6) i=0

We calculate that for case (Sb) such probability equals 0.018, and for case (5c) the probability is 0.00045. These low values indicate that the seismic gap hypothesis as given by (5) should be rejected with a high confidence level.

As another test of significance we may compare the numbers of earthquakes in different zones. We assume that the number of earthquakes in zones obeys the Pois- son distribution. Again, for the likelihood ratio we obtain [Wilks, 1962, exercise 13.10]

¾ , where n has the same meaning as in (4), and m is the number of earthquakes. The quantity -2 log • is again distributed for large n according to the X •' distribution with one degree of freedom. Calculations using the values in the column of averages of Table 2 yield • - 0.21 when comparing red and orange zones, and • - 0.22 for red and green zones. These values are now small enough to be significant at confidence levels of 92.5% and 92%, respectively. Thus the null hypothesis

els in favor of the antithesis of H•. That is, the data imply that

< (8,0 and

As we mentioned earner, the equa•ty

satisfies any statistical test. Equations 8a and 8b also mean that out of 100 random assignments of •one categories, more than 90 rea•ations should perform better than the seismic potential map proposed by MNSK

Using a different statistical procedure for comparing two intensifies for Poisson processes described by Co• and gewis [1966, chapter 9.2] similar tests yield almost the same v•ues for significance levels to reject the H0 hypothesis in favor of (8): 7.9% for comparison of red and green •ones, and 7.6% for comparison of red and orange •ones. If we again make an assumption similar to that of (5),

or

- (oa)

where • is the Poisson rate of events in a •one, then the MNSK [1979] hypothesis is rejected at confidence levels better than 98.8% and 99.7%, respectively. Suppose

we want to know what putative difference between the rates of orange and green areas is still consistent with the data. Simple calculations show [Coz and Lewis, 1966] that/zo•,•ye = 1.5/zy•e•,• is not rejected, whereas lZo•,nye = 2.01zyreen is rejected at 97.2%. confidence level.

Differences in earthquake occurrence are not the result of different zone sizes. Assuming an average width of 100 km, the average areas of red, orange, and green zones are about 29,000, 29,000, and 32,000 km 2, respectively. The 10% greater area does not explain why green zones had about 150% more earthquakes than the red zones.

We have not tried to update the MNSK [1979] seismic maps according to the criteria proposed by MNSK for two reasons: (1) we wanted to test the original forecast, and (2) it is not clear whether we should use only 30 and 100 years elapsed time criteria, or whether should we also review a subdivision of the seismic belt into segments. For example, Nishenko [1991] proposes a subdivision significantly different from that of MNSK. As shown in Table 1, there are three event sequences which occurred in the same orange segment and are therefore candidates for relabeling: 28 and 40; 29, 44, and 49; and 31 and 55. If we had relabeled these segments each time into green zones after occurrence of the first shock in the sequence, the numbers of earthquakes in green zones would increase. Of course, some green segments may be converted into orange, and orange zones may be converted into red due to the 10 years since the MNSK publication. However, the difference between seismicity levels in red and green or orange zones is such that these adjustments would not change our conclusions.

Finally, we test whether an increased earthquake activity in some zones may be explained by the presence of foreshocks and aftershocks. Test (4) does not depend on presence of the aftershocks in data, so we need to reeval- uate the results of test (7). For Table 1 in the weight column, we collected probabilities of each earthquake occurring independently; we estimated these probabilities using the maximum likelihood procedure similar to that described by Kayan and Knopoff [1987]. These probabilities are used as weights for each event; hence an event dependent on another earthquake should con- tribute little or nothing to our score. New calculations yield 3.5 events in the red zones, 14.74 earthquakes in the orange areas, and 13.71 shocks in the green segments (compare Ms columns in Table 2). These values are statistically compatible with (3); however, hypothesis (9) is again rejected with confidence levels of 96.15% and 98.2%, respectively.

Nishenko and McCann [1981] and Nishenko [1985] of- feted some corrections to the MNSK [1979] forecast. Al- though posterior modification of a forecast is inadmissi- ble for statistical validation, let us discuss these corrections. Nishenko and McCann [1981] propose changing the magnitude cutoff to M _• 7.15. This change greatly


reduces the number of earthquakes, so all the statistical tests would be inconclusive. If we count only those events with M _• 7.5 in Table 1, we find one event in the red category, 2.5 earthquakes in the orange •.ones, and 5.5 events in the green areas. Comparing these with the results in Table 2, we see that the new values are less statistically significant but still suggest the same conclu- sion as the values obtained with a magnitude cutoff of 7.0. Nishenko and McCann [1981] and Nishenko [1985] suggested also that earthquakes in the red zones should be much stronger (M• • 9.0) than events in other areas. This suggestion is not supported by Table I either. The mean Ms magnitudes are 7.33, 7.29, and 7.30 for red, orange, and green areas, respectively.

KSO [1973] FORECAST

There are several difficulties in analyzing KSO [1973] forecasts: (1) The forecasts are expressed through two sets of maps: large-scale maps for a general overview and detailed maps of specific regions. These maps sometimes disagree. For example, there are five gaps shown in Latin America [KSO, 1973, Figure 15], but six gaps are presented in the summary plot ([KSO, 1973, Fig- ures 1 and 2]). (2) In the detailed maps which represent, according to the authors, a final result, the zones are show • as line segments; the width of the zones is not clearly s;ated, and projection of the segments on the seismic belt cannot be made unambiguously. (3) Only one catalog, the PDE list [USDIGS, 1988] is available for testing in this time period. Because of these circum- stances, test results for KSO [1973] are more tentative than those for MNSK [1979].

To improve the stability of statistical testing, we ac- cept as dangerous all zones where KSO [1973] find that no strong earthquakes have occurred during the last 30 years (filled areas in their Figure 2b). We take the other zones studied by KSO to be nondangerous. Thus, we disregard any further distinction between the dangerous zones as shown in their overview Figure 1. In Table 1 we show a list of shallow events since 1973 with

Ms •_ 7.0 in the circum-Pacific belt with each earthquake assigned to a dangerous ("R") or a nondangerous ("G") zone. Again, when it is not clear whether an epicenter belongs to one or the other •.one, we treat it as a half event in each. In total 16.5 events fall into R •.ones and 19 events fall into G areas. We estimate the total

length of both sets of •.ones: for R •.ones it is 10,500- 11,500 kin, and for G •.ones the length is 9000-9500 kin. Therefore, nondangerous •.ones are on the average 1.3- 1.4 times more likely to have a strong earthquake per unit of length than are dangerous •.ones. Applying a statistical test similar to the one described above [Coz and Lewis, 1966, equation 9.2.3], we find that the difference in seismicity rates between dangerous and nondangerous zones is not statistically significant. The difference has the sign opposite to that predicted by the seismic

gap model. Again, if we assume that the seismicity rates in dangerous zones should be higher by 50%, such a hypothesis is rejected with the confidence level of more than 97%.

DISCUSSION

Assigning events to specific gaps is not so straight- forward as one might wish. We have indicated in the previous sections that we forego the use of more detailed discussions in the work of MNSK [1979] or KSO [1973], and we use only final maps in our assignment. Even with these maps some ambiguities still exist. Since MNSK and KSO do not provide exact coordinates of their •.ones, and they do not specify which magnitudes are to be used in comparison, certain disagreement and possible errors in event attribution are unavoidable. It is important that all earthquakes be processed according to the same criteria. We believe that the results reported in Tables 1 and 2 are robust with regard to possible alternative assignments of events.

Nishenko [1989] reported that several recent events have occurred in previously identified gaps, thus lend- ing support to the gap hypothesis. In Table 3, we list all those events reported by Nishenko as being within gaps, giving our •.one assignments as well. Of these 15 events, seven are not suitable for testing either the KSO [1973] or the MNSK [1979] forecasts: five events ore- date both forecasts, and two events (12 and 15) do not occur in red, orange, or green •.ones of either forecast. Of the relevant events, only three can be counted as successfully forecast by MNSK: the Valparaiso and Mi- choacan events were in orange zones, and the Tumaco earthquake occurred on the border of an orange and a green •.one. The events in Table 3 provide somewhat better support for the earlier KSO forecast, with five events in red •.ones and two events straddling red and green zenes. However, it is inadequate to validate a hy- pothesi• by considering "successes" only. A reasonable test requires a consideration of all relevant events. Fi- nally, Nishenko [1989] implies that each event in his list supports the gap model by fulfilling one or more of several published forecasts. This raises an important issue: how should an evolving theory be evaluated? Does each published version supercede previous versions? Should each version of the model be evaluated on its own mer-

its, regardless of subsequent publications by the same authors? Available statistical methods are appropriate for judging a single hypothesis against a null hypothesis, but it is not clear how to judge a composite hypothesis expressed in several, partly contradictory publications.

To test the robustness of our conclusions, we carried out a numerical experiment designed to favor the gap hypothesis H•. In this experiment each event which occurred near the boundary of two •.ones (marked by a slash in Table 1), was assigned to the "redder" of the two •.ones. We use only the MNSK [1979] regionali•.a- tion and Ms magnitude in this test. The result was


TABLE 3. Comparison of Table 1 Results With Arishenko's [1989] Table I

Earthquakes • Coordinates Zone

No. T1 Ni Date PDE Ms KSO MNSK Location

1 - 1 1944,6 33, 34øN 133,137øE - • • Nankai, Japan 2 - 2 1968 40.9øN 143.4øE - • • Tokachi, Japan 3 - 3 Aug. 11, 1969 43.5øN 147.4øE 7.8 • • Southern Kuriles 4 - 4 Dec. 15, 1971 56.0øN 163.3øE 7.8 # # Central Kamchatka 5 - 5 July 30, 1972 56.8øN -135.7øW 7.6 # # Sitka, Alaska 6 I 8 Jan. 30, 1973 18.5øN -103.0øW 7.5 R e • Colima, Mexico 7 3 6 June 17, 1973 43.2øN 145.8øE 7.7 G • Nemuro-Old, Japan 8 6 9 Oct. 3, 1974 -12.3øS -77.8øW 7.6 R • • Lima, Peru 9 16 13 Nov. 29, 1978 16.0øN -96.6øW 7.7 G/R e # Oaxaca, Mexico

10 18 14 Mar. 14, 1979 17.8øN -101.3øW 7.6 G/R e G-13 Petarian, Mexico 11 20 15 Dec. 12, 1979 1.6øN -79.4øW 7.7 R • G-7/O-5 Tumaco, Colombia 12 - 16 Dec. 19, 1982 -24.1øS -175.9øW 7.7 - .e Southern Tonga 13 40 17 Mar. 3, 1985 -33.1øS -71.9øW 7.8 R • O-1 Valparaiso, Chile 14 44 18 Sep. 19, 1985 18.2øN -102.5øW 8.1 R e O-17 Michoacan, Mexico 15 - 21 Oct. 20, 1986 -28.1øS -176.4øW 8.1 - *e Northern Kermedec

• The first column (No) are the sequential numbers; the second column (T1) are the numbers in Table 1; the third column (Ni) lists numbers in the work of Nishenko [1989].

b In zone columns, the pound sign signifies an earthquake predating the forecastl the asterisk signifies an earthquake in a zone other than red, orange, or green; and dash signifies an earthquake outside of the forecast map.

e According to Nishenko [1989] this is a successful forecast by K$O [1973]. a According to Nishenko [1989] this is a successful forecast by Kelleher [1972], the paper which can be considered as a

predecessor to that of K$O [1973]. • According to Nishenko [1989] this is a successful forecast by MNSK [1979].

that 14 events occurred in seven of the 36 green zones (compare Table 2), 17 events occurred in 11 of 34 orange zones, and four events occurred in three of 17 red zones. For the Ms count of events (Table 2, columns 3 and 4) the calculations using (7) yield • = 0.28 for comparison of red and orange zones, and • - 0.31 for comparison of red and green zones. For the numbers quoted above, these values are • - 0.35 and • -- 0.65, respectively. In all these cases, the likelihood ratio fa- vors the hypothesis H0 (• _< 1.0), as compared to Hi, although not so strongly that it implies (8). Therefore, our basic conclusions would not change as a result of such reassignment.

The MNSK [1979] and other papers published in the 1970s represent a preliminary version of the seismic gap hypothesis. Is it fair to test an early model when so much has been learned since about variable recurrence

times and characteristic earthquakes for specific gaps [cf. Nishenko, 1991]? There is, at present, no choice. One must test a hypothesis with data independent of those used to formulate the hypothesis, so that newer versions cannot be tested yet. Recent formulations of the seismic gap model require knowledge of the mean recurrence time, a need which poses a fundamental problem. Two estimates of the recurrence time for a partic- ular zone are commonly used: (1) the sample mean of known interevent times and (2) the ratio of characteristic earthquake displacement to the slip rate. Both are

subject to large uncertainties, because evaluating mean recurrence time over relatively short time intervals requires (1) nearly periodic earthquake occurrence (the very hypothesis to be tested) and (2) the characteristic earthquake assumption (that stress is relieved primarily by earthquakes of the same size). Hence, seismic gaps are being frequently redefined, and hypothesis testing is becoming more difficult. Elsewhere (Y. Y. Kagan and D. D. Jackson, unpublished manuscript, 1991) we discuss in detail the difficulties which we anticipate in testing the new modifications of the seismic gap or characteristic earthquake predictions.

Even in the future it will be difficult to test new, long- term predictions statistically. For example, the Work- ing Group on California Earthquake Probabilities [1988] offers a forecast for California in the next 30 years, based on a new seismic gap model which accounts for variable recurrence times on different fault segments as well as variable forecasted earthquake magnitude. The total number of forecasted strong earthquakes is 4.6 [Working Group on California Earthquake Probabilities, 1988, Table 2], whereas the Poisson rate is easily estimated from the same table to be 3.9. Clearly, even if the model is correct and the number of earthquakes will be as expected, after 30 years there will not be enough events for statistical testing. Actually, if differences between rates of occurrence will be similar to that of the

Working Group on California Earthquake Probabilities


[1988, Table 2], we would need either about 3000 years of observation in California or observations of 100 re-

gions for 30 years to obtain a result significant at better than a 95% confidence level.

If our results in testing the MNSK [1979] and KSO [1973] forecasts were positive but not positive enough to be statistically significant, one could expect that with better methods the performance of the model could be improved. However, in both cases considered here, seismicity rates in dangerous zones are found to be lower than those in safe zones. Moreover, the difference between seismicity levels in red and green zones is so large that even adjustments in selection of events based on different interpretations of the MNSK text and detailed maps (see above) do not change our conclusions.

In our opinion, the seismic gap hypothesis has a fundamental problem: it assumes that strong earthquakes are periodic or quasi-periodic, whereas seismicity of all earthquakes is clustered. Elsewhere [Kagar• arid Jacksor•, 1991] we review additional evidence that the time-space clustering of earthquakes is a universal phenomenon having two genera: (1) short-term, strong clustering of shallow earthquakes responsible for foreshock-main shock-aftershock sequences and (2) long-term, weak clustering for all earthquakes (shallow, intermediate, and deep). If the clustering assumption is true, no improvement or modification of the seismic gap hypothesis will help, as long as the hypothesis expects lowered seismicity in the wake of a strong earthquake.

The contradiction between the observed clustering and the more intuitive quasi-periodicity is often explained as follows: in some regions the earthquakes are clustered, whereas in other regions they are quasi- periodic (see, for example, Cror•e arid Orndahl [1988]). To be credible, this explanation should always include a formal definition of these zones with a control test

performed in regions not used for developing the definition. Otherwise, one may argue that a series of random tosses of a symmetrical coin can also exhibit patterns of quasi-periodicity. The fallacy of such statements is obvious.

Our results or comments certainly do not imply that the extensive geological and geophysical review and syn- thesis of data conducted by KSO [1973], MNSK [1979], and other researchers are unimportant or unnecessary. Quite to the contrary, we believe that such investiga- tions are very much needed for understanding long-term properties of an earthquake occurrence and seismic hazard assessment. The reasons we have chosen KSO and MNSK for our analysis is because these papers specify testable forecasts of seismic activity and do it in a clear, unambiguous manner. In this respect, these papers are favorably compared to many other publications in this field. The main point of this paper is the use of this information for predictive purposes' on the basis of the statistical analysis of the MNSK and KSO forecasts, we conclude that the almost universal belief among the geophysical community (see references in the introduction)

about the success of the seismic gap model in evaluating future seismicity is not supported by the history of strong earthquakes during the last 10 to 15 years.

We emphasize that the statistical tests described in this work have been applied to forecasts of future seismicity made by just two influential papers, those of MNSK [1979] and KSO [1973]. These tests indicate that the maps published in these two papers fail to forecast future M >_ 7 activity. However, we did not analyze in detail here the major assumptions of the seismic gap model in all its modifications; nor did we try to answer the question of whether seismic gap methodology can be modified or specified in a way to make it really predictive. In principle it is possible that more specific indica- tions of sizes, focal mechanisms, and other quantitative features of future earthquakes would make the predictions formally testable and would lead to acceptance of statistical validity and an understanding of limits to the new seismic gap hypothesis. To make it possible, we urge involved researchers to produce as formal, quantitative, and therefore statistically testable predictions as possible. Meaningful and testable forecasts should include unambiguous definitions of the zones (for example, latitudes and longitudes of zone corners) and a clear definition of applicable events (including any zone specific criteria such as characteristic magnitude). Else- where (Y. Y. Kagan and D. D. Jackson, unpublished manuscript• 1991) we review in detail the requirements for any predictions to be testable.

CONCLUSIONS

On the basis of statistical tests of seismic gap fore- c•ts of two well-known papers, we draw the following conclusions:

1. The estimates of earthquake potential summarized in the maps by MNSK [1979] and KSO [1973] did not forec•t well (that is better than random) the occurrence of the large subsequent earthquakes.

2. The hypothesis that the red gaps of MNSK [1979] are significantly more likely (for example, by a factor of 2) to experience strong earthquakes compared to the green "safe" zones can be rejected with more than 95% confidence.

3. During the last decade, strong earthquakes have occurred preferentially near the sites of previous, recent large events, and most plate boundary segments unruptured in the previous century remained unruptured. This suggests that earthquakes occur in clusters, rather than quasi-periodically.

4. Although it is possible that new, revised versions of the hypothesis formulated in the 1980s will forecast earthquakes better, our results reported here and elsewhere cast serious doubts on such a possibility. Many published applications of the new hypothesis cannot be statistically tested for many years due to the small sizes of seismic regions and insignificant differences between the forecasts of the hypothesis and the Poisson estimates.


TABLE 4.

Earth-

quakes Depth,

Date Coordinates km Ms Mo

Zone

MNSK

55

56

57

58

59

60

61

62

63

64

65

66

Feb. 24, 1988 13.5øN 124.6øE 21 Apr. 12, 1988 -17.2øS -72.3øW 54

Aug. 10, 1988 -10.4øS 160.8øE 34 Oct. 18, 1989 37.0øN -121.9øW 19 Oct. 27, 1989 -11.0øS 162.4øE 25 Nov. 1, 1989 39.8øN 142.8øE 29 Dec. 15, 1989 8.3øN 126.7øE 24 March 5, 1990 -18.3øS 168.1øE 20 March 25, 1990 9.9øN -84.8øW 22 June 14, 1990 11.8øN 121.9øE 18 July 16, 1990 15.7øN 121.2øE 25 Apr. 22, 1991 9.7øN -83.1øW 10

6.0

6.1

6.1

6.5

6.1

6.4

6.2

5.6

6.2

6.0

6.5

6.6

7.0

7.0

7.4

7.1

7.0

7.4

7.3

7.0

7.0

7.1

7.8

7.5

7.0

6.7

7.3

6.9

7.3

7.2

6.9

6.8

6.8

7.4

7.4

O-26

P,-1

G-31

O-18

G-31

O-21

O-26

O-33

G-9

O-26

O-26

O-6

Time limits are from January 1, 1988, to August 19, 1991.

Note added in proof. In Table 4 (addition to Table 1) we list earthquakes from the PDE catalogue which occured during the period 1988-1991. Events 55 and 56 in Table 1 were taken from a preliminary catalog; here they are listed in final form. No additional events occur in the MNSK [1979] red regions, hence our results are strengthened by these data. Although more events (total of 7) fall into orange than in green zones (total of 3) according to the MNSK regionalization, this new information does not change our conclusions. Similar results are obtained for the Harvard catalog: there is 1 event in a red zone, 7 events in orange zones and 5.5 events in green zones in the time interval from January 1, 1988, to July 1, 1991. Again, these new data agree with our conclusions.

Acknowledgments. We appreciate support from the Na- tions1 Science Foundation through grant EAR 88-04883, and from NSF Cooperative Agreement EAR-8920136 and USGS Cooperative Agreement 14-08-0001-A0899 to the Southern California Earthquake Center (SCEC). The authors thank G. Resgot and J. Dunphy of the U.S. Geological Survey for providing us with earthquake catalogs in a computer- readable form, as well as F. Leader of UCLA for his help in analysis of catalogs and seismicity plotting. Publication 3607, Institute of Geophysics and Planetary Physics, Uni- versity of California, Los Angeles. Publication 1, Southern California Earthquake Center.

REFERENCES

Aid, K., Ideal probabilistic earthquake prediction, Tectono- physics, 169, 197-198, 1989.

Bak, P., and C. Tang, Earthquakes as a self-organized critical phenomenon, J. Geophys. Res., 9g, 15,635-15,637, 1989.

Bakun, W. H., and A. G. Lindh, The Parkfield, California, earthquake prediction experiment, Science, •89, 619-624, 1985.

Cox, D. R., and P. A. W. Lewis, The Statistical Analysis of Series of Events, 285 pp., Methuen, London, 1966.

Crone, A. J., and E. M. Omdahl (Eds.), Proceedings of Con- ference XXXIX; directions in paleoseismology, U.S. Geol. Surv., Open File Rep., 87-673, 456 pp., 1988.

Dziewonsid, A.M., G. Ekstroem, J. H. Woodhouse, and G. Zwart, Centtold-moment tensor solutions for October- December 1988, Phys. Earth Planet. Inter., 57, 179-191, 1989.

Gilbert, G. K., Earthquake forecasts, Science, 89, 121-138, 1•09.

Kayart, Y. Y., and D. D. Jackson, Long-term earthquake clustering, Geophys. J. Intern., 104, 117-133, 1991.

Kayart, Y. Y., and L. Knopoff, Statistical short-term earthquake prediction, Science, 836, 1563-1567, 1987.

Kelleher, J. A., Rupture zones of large South American earthquakes and some predictions, J. Geophys. Res., 77, 2087-2103, 1972.

Kelleher, J. A., L. 1:[. Sykes, and J. Oliver, Possible criteria for predicting earthquake locations and their applications to major plate boundaries of the Pacific and Caribbean, J. Geophys. Res., 78, 2547-2585, 1973.

Kendall, M. G., and A. Stuart, The Advanced Theory of Statistics, 4th ed., vol. 1, Distribution Theory, C. Griffin, London, 1977.

McCann, W. 1:[., S. P. Nishenko, L. 1:[. Sykes, and J. Krause, Seismic gaps and plate tectonics: Seismic potential for major boundaries, Pure Appl. Geophys., 117, 1082-1147, 1979.

Nishenko, S. P., Seismic potential for large and intermediate earthquakes along the Chilean and southern Peruvian margins of South America: Quantitative reappraisal, J. Geophys. Res., 90, 3589-3615, 1985.

Nishenko, S. P., Circum-Pacific earthquake potential: An overview (abstract), Eos Trans. A GU, 69, 1299, 1988.

Nishenko, S. P., Earthquakes: Hazards and predictions, in: The Encyclopedia of Solid Earth Geophysics, edited by D. E. James, pp. 260-268, Van NosStand Reinhold, New York, 1989.

Nishenko, S. P., Circum-Pacific seismic potential - 1989- 1999, Pure Appl. Geophys., 135, 169-259, 1991.

Nishenko, S. P., and W. 1:[. McCann, Seismic potential for the world's major plate boundaries: 1981, in Earthquake Prediction: An International Review, Maurice Ewing Set.

I"[•kOAN AND JACKSON: SEISMIC GAP HYPOTHF•IS 21,431

Vol. •(, edited by D. W. Simpson and P. G. Richards, pp. 20-28, AGU, Washington, D.C., 1981.

Oppenheimer, D. H., W. H. Bakun, and A. G. Lindh, Slip partitioning of the Calaveras fault, California, and prospects for future earthquakes, Y. Geophys. Res., 95, 8483-8498, 1990.

Reid, H. F., Elastic rebound theory, Univ. Calif. Publ. Bull. Dept. Geol. Sci., 6, 92-120, 1910.

Rundle, J. B., A physical model for earthquakes, 1, Fluctu- ations and interactions, J. Geophys. Res., 93, 6237-6254, 1988.

Science Citation Indez, vols. 1-21, Inst. Scicnt. Inform. Inc., Philadelphia, 93,804 pp., 1988.

Shimazaki, K., and T. Nakata, Time-predictable recurrence model for large earthquakes, Geophys. Res. Lett., 7, 279- 282, 1980.

Sieh, K., M. Stuiver, and D. Brillinger, A more precise chronology of earthquakes produced by the San Andreas fault in southern California, J. Geophys. Res., 9•4, 603- 623, 1989.

Sipkin, S. A., and R. E. Needham, Moment-tensor solutions estimated using optimal filter theory: Global seismicity, 1984-1987, Phys. Earth Planet. Inter., 57, 233-259, 1989.

Sykes, L. R., Aftershock zones of great earthquakes, seismicity gaps, and earthquake prediction for Alaska and the Aleutians, J. Geophys. Res., 76, 8021-8041, 1971.

Sykes, L. R., and S. P. Nishenko, Probabilities of occurrence of large plate rupturing earthquakes for the San Andreas, San Jacinto, and Imperial faults, California, 1983-2003, J. Geophys. Res., 89, 5905-5927, 1984.

Thatcher, W., Earthquake recurrence and risk assessment in circum-Pacific seismic gaps, Nature, 3gl, 432-434, 1989.

Wilks, S.S., Mathematical Statistics, 644 pp., John Wiley, New York, 1962.

Working Group on California Earthquake Probabilities, Probabilities of large earthquakes occurring in California on the San Andreas fault, U.S. Geol. Surv., Open File Rep., 88-398, 62 pp., 1988.

U.S. Department of the Interior/Geological Survey, Prelim- inary Determination of Epicenters (PDE), Monthly List- ings, National Earthquake Information Center, Denver CO, January 1988.

D. D. Jackson, Department of Earth and Space Sciences, University of California, 3806 Geology Building, Los Ange- les, CA 90024.

Y. Y. Kagan, Institute of Geophysics and Planetary Phys- ics, University of California, Los Angeles, CA 90024-1567.

(Received August 2, 1990; revised August 9, 1991;

accepted August 23, 1991.)

seismic gap hypothesis: ten years after - uclamoho.ess.ucla.edu/~kagan/jgr_1991_after.pdf ·...

Documents