Spatial distribution of aftershocks and background seismicity in central California

PAGEOPH, Vol. 137, No. 1/2 ( 1 9 9 1 ) 0033-4553/91/020035-2751.50 +0,20/0 �9 1991 Birkh/iuser Verlag, Basel

Spatial Distribution of Aftershocks and Background Seismicity in Central California

MARIANA ENEVA 1'2 and GARY L. PAVLIS 3

Abstract --We examine the spatial distribution of earthquake hypocenters in four central California areas: the aftershock zones of the (1) 1984 Morgan Hill, (2) 1979 Coyote Lake, and (3) 1983 Coalinga earthquakes, as well as (4) the aseismically creeping area around Hollister. The basic tool we use to analyze these data are frequency distributions of interevent distances between earthquakes. These distributions are evaluated on the basis of their deviation from what would be expected if earthquakes occurred randomly in the study areas. We find that both background seismic activity and aftershocks in the study areas exhibit nonrandom spatial distribution. Two major spatial patterns, clustering at small distances and anomalies at larger distances, are observed depending on tectonic setting. While both patterns are seen in the strike-slip environments along the Calaveras fault (Morgan Hill, Coyote Lake, and Hollister), aftershocks of the Coalinga event (a thrust earthquake) seem to be characterized by clustering only. The spatial distribution of earthquakes in areas gradually decreasing in size does not seem to support the hypothesis of a self-similar distribution over the range of scales studied here, regardless of tectonic setting. Spatial distributions are independent of magnitude for the Coalinga aftershocks, but events in strike-slip environments show increasing clustering with increasing magnitude. Finally, earthquake spatial distributions vary in time showing different patterns before, during, and following the end of aftershock sequences.

Key words: Earthquakes, aftershocks, spatial distribution, central California, seismicity, patterns.

Introduction

Standard tools used for interpret ing the spatial d is t r ibut ion of ear thquakes are

maps, cross-sections, and stereo pair projections (GERMAN and JOHNSON, 1982) of

ear thquake hypocenters. Similarly, space-time plots are commonly used to examine

the dependence of seismicity on time. While these techniques are undoubted ly

useful, interpret ing data based on such graphical displays is highly subjective. Some

authors have recognized this problem and have developed schemes to quant ify

certain aspects of spatial seismicity pat terns (e.g., KAGAN and KNOPOFF, 1980;

NOAA/NGDC, 325 Broadway, Boulder, CO 80303, U.S.A. 2 Present address: Department of Physics/Geophysics, University of Toronto, 60 St. George Street,

Toronto, Ontario Canada M5S 1A7. 3 Department of Geological Sciences, Indiana University, Bloomington, IN 47405, U.S.A.

36 Mariana Eneva and Gary L. Pavlis PAGEOPH,

REASENBERG, 1985; OUCHI and UEKAWA, 1986; SADOVSKY et al., 1984, 1987; HIRATA, 1989; FROHLICH and DAVIS, 1990).

This paper builds on three related publications (ENEVA, 1984; ENEVA and PAVLIS, 1988; and ENEVA and HAMBURGER, 1989), hereafter collectively referred to as "our previous work." The purpose of this article is to use the methods we introduced earlier to compare and contrast spatial seismicity patterns observed in four areas of central California (Figure 1). Three of these areas were defined by the aftershock zones of three of the largest earthquakes Xhat have occurred in this region. These are the 1979 ML = 5.9 Coyote Lake earthquake (REASENBERG and ELLSWORTH, 1982; MENDOZA and HARTZELL, 1988), 1983 ML = 6.9 Coalinga earthquake (e.g., EATON, 1985; EBERHART-PHILLIPS, 1989; EBERHART-PHILLIPS and REASENBERO, 1989; MICHAEL, 1987), and 1984 M L = 6.2 Morgan Hill earthquake (CoCKERHAM and EATON, 1984; HARTZELL and HEATON, 1986; OPPEN- HEIMER et al., 1988). The fourth area was chosen as a quite different setting in the same region; the creeping section of the Calaveras fault near Hollister, CA (MAvKO, 1982). For the sake of brevity, these four areas will sometimes be referred to as CL, CO, MH, and HO respectively.

The following specific questions concerning the spatial distribution of earthquakes in central California are addressed:

1. We have previously found (ENEVA and PAVLIS, 1988) that there were significant deviations in the spatial distribution of earthquakes in the Morgan Hill area as compared to what would be expected from randomly distributed events in the same area. Is this true elsewhere in central California? If so, are there common patterns, or do earthquakes occurring on different types of faults show different patterns?

2. Is the spatial distribution of earthquakes self-similar and if so, at what scale does the self-similarity hold? ENEVA and HAMBURGER (1989) suggested that the spatial clustering of earthquakes may be self-invariant at scales of several hundreds of km, but smaller scales have not been examined in this respect.

3. Does the spatial distribution of earthquakes vary in time? If it does, are there systematic patterns in this variation or is it erratic?

4. Do spatial distributions of earthquakes depend upon magnitude? Before considering these questions we need to provide some details about the

data and techniques we have used in this study.

Data

The hypocentral locations we used for Morgan Hill are the same as those used by ENEVA and PAVLIS (1988). These data span the period January 1, 1978-March 31, 1986, and were relocated with the program HYPOELLIPSE (LAHR, 1984) using COCKERHAM and EATON'S (1984) velocity model and station corrections. Data for

Vol. 137, 1991 Spatial Distribution of Seismicity 37

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38 Mariana Eneva and Gary L. Pavlis PAGEOPH

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the remaining three areas (Coyote Lake, Hollister, and Coalinga) for the period 1969-1983 were provided by D. Oppenheimer from the U.S. Geological Survey. He has recently relocated these events using regionally dependent station corrections.

The seismicity for the MH, CL, and CO areas is dominated by the occurrence of the mainshock-aftershock sequences that were used to define these areas. The data were split into preshock and aftershock periods to allow comparison of preshock and aftershock spatial properties. We used preshock seismicity for six year periods prior to the mainshock in each of these areas. There were no events of magnitude larger than 4.5 in Hollister that occurred in the 1969-1983 period. All the available data were examined in this case, since significant aftershock sequences were not observed.

We examined the yearly magnitude-frequency distributions for each study area in order to determine lower magnitude cut-offs. A conservative measure of the completeness threshold for the events along the Calaveras fault (MH, CL, and HO) for the whole study period is ML = 1.5. For Coalinga, this level would be appropri- ate for the aftershock sequence, but until 1982, a threshold of ML -- 2.5 appears to be more suitable and we used it for the whole study period. The outer limits of the Hollister area were outlined on the basis of the standard geographic areas used by the U.S. Geol. Survey (F. KLEIN, personal communication). For the aftershock zones, we selected the events enclosed within the boundaries of each aftershock sequence suggested from epicentral maps and space-time plots. These choices are shown as polygons in Figure la and are labelled with the number 1 in Figures 1 b, d, f, and h. Table 1 summarizes general information about the data sets studied.

Techniques Used

The basic tool used in this paper is a technique we have previously referred to as "pair analysis" (ENEVA and PAVLIS, 1988; ENEVA and HAMBURGER, 1989). We measure the spatial separations between all events in a volume, and obtain the frequency distribution of these distances. The shape of the resulting curve, however,

Table 1

General description of the data

Per iod Magnitude Total Number Number of Number of Area Considered Threshold of Even ts Af te rshocks Preshocks

MH 1978-1986 1.5 632 316 157 CL 1973-1983 1.5 692 256 119 HO 1969-1983 1.5 673 -- -- CO 1977-1983 2.5 1492 1322 36


is dominated by the geometry of the study area. To correct for this, the concept of residual distribution is used. It is calculated by comparing the actual distribution derived from the data with the average distribution produced from a large number of simulations. Each simulated catalog consists of events randomly distributed inside the same volume from which the original data were selected. A uniform distribution is used for the random generations. That is, each simulated event can occur with equal probability anywhere within the specified volume. Each residual distribution is obtained by subtracting the average simulated distribution from the actual one. Nonzero values of the residual distributions indicate deviations of the actual distributions from the ones produced by random simulations. These deviations are used to quantitatively evaluate the degree of nonrandomness in earthquake spatial distribution. Because uniform random distribution is used for the simulations, ~ in this paper is understood as "nonuniformity" and/or "irregularity." See ENEVA and PAVLIS (1988) for more details on the pair analysis. Figures 3 -9 in this paper all show residual distributions. The vertical axes show the percentages of residual number of pairs. The horizontal axes represent interevent distances in km. The pair frequencies are counted with a step of 0.5 kin. The following concepts are required to interpret these plots.

1. Positive values indicate an excess of pairs compared to the number of pairs expected from a uniform distribution. Conversely, negative values indicate a deficiency in number of pairs.

2. The area between the residual curve and the distance axis measured over a particular distance range represents the percentage of anomalous pairs with interevent distances in this range. The percentage of anomalous pairs can be further used to quantify the percentage of events responsible for a large peak or trough in a residual distribution (equation (7) in ENEVA and PAVLIS, 1988), which we wilI refer later to as "the degree of nonuniformity (nonrandomness)." Stated in a simple way, the square root of the portion of residual pairs defining an anomaly over certain distance range is an approximate measure of the portion of the events involved in this anomaly.

3. Larger peak values and rapid oscillations in the residual distribution curves indicate a tendency toward greater nonrandomness. However, any peak value represents one particular measurement, which is usually only a part of the anomaly spanning a certain distance range. Furthermore, the peak values depend upon the step size used to count the pair frequencies. For this reason, peak values are less meaningful in a quantitative sense than the area measures described above.

4. To quantify the expected scatter in the residual distribution curves, we use tolerance limits (for example, look at Figures 4 and 6). At least 90% of the random trials used to produce the residual distribution curve, fall inside these limits with a 95% probability. The portions of the residual distribution curve that fall outside these limits are statistically significant. That is, they have a high probability of not being due to random fluctuation of the curve. On the other hand, residual values


remaining within the tolerance bands are not proven to be random fluctuations, but their significance is questionable.

This paper differs from our earlier work in two respects. We previously examined mainly epicentral distances between events whose epicenters were in rectangular zones. In the present work we use total spatial separation between events (i.e., depth is included) to obtain the observed distributions. Furthermore, polygons of arbitrary shape are used for generating uniformly distributed epicenters by applying the winding number algorithm (GoDKIN and PULLI, 1984). These polygons represent the surface projections of the volumes where the actual hypocenters are located. To simulate the depths associated with the simulated epicenters, we form upper and lower bounding surfaces (not necessarily planar) for the top and bottom of the volumes. This is done by representing each irregularly shaped volume by a collection of vertically oriented parallelepipeds. Their map projections cover the surface projection of the volume studied (that is, the associated polygon) and represent 3 km square cells for larger areas or 1 km square cells for smaller areas. In each of these cells, the original data were scanned to determine the maximum and minimum depth of the earthquakes whose epicenters occurred within that cell. The depth of a simulated event is generated as a random number falling between the maximum and minimum depth for the cell the respective simulated epicenter happened to fall in. Thus, expected distributions were calculated on the basis of points uniformly distributed within volumes of irregular shape.

Finally, to separate aftershocks and small clusters from the catalogs, we used the same approach as that used by ENEVA and HAMBURGER (1989). An example of applying this procedure to the data from Morgan Hill is shown in Figure 2. This approach allows us to separate the events in each region into a "clustered" and "declustered" set. The "clustered" events, in this context, are swarms and mainshock-aftershock sequences. The "declustered" data set, in contrast, can be thought of as representing the background seismic activity in the study area.

Selection of Subareas

In the introduction we raised the question of how earthquake spatial distributions change with scale and with location. To address this problem we subdivided each of the four main study areas into two distinct types of subareas as shown in Figure 1. Those labelled 1, 2, and 3 were chosen primarily to address the question of scale. That is, they represent a sequence of subareas of progressively smaller size. The objective was to look at areas of decreasing size which to the eye appeared to have an increasingly uniform distribution of earthquakes. The subareas labelled 4 to 8, on the other hand, were chosen primarily to study the stability of distributions within the main areas. The objective in this case was to choose areas of comparable size that had minimal overlap. These choices were guided by other

Vol. 137, 1991 spatial Distribution of Seismicity 43

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M L -> 1.5, 1978-1986; (b) declustered catalog; and (c) clusters derived from (a).


authors' analysis of geometric features of faulting in these areas (e.g., fault jogs) and/or apparent clusters of activity as seen from maps, cross-sections, or stereo projections (BAKUN, 1980; MAVKO, 1982; REASENBER6 and ELLSWORTH, 1982; COCKERHAM and EATON, 1984; EATON, 1985; HARTZELL and HEATON, 1986; MICHEAL, 1987; MENDOZA and HARTZELL, 1988; OPPENHEIMER et al., 1988; EBERHART-PHILLIPS, 1989; EBERHART-PHILLIPS and REASENBERG, 1989).

Types of Spatial Distributions

On the basis of this study and earlier work, the residual distribution curves can be classified into three different types (Figure 3). To facilitate the understanding of the subsequent plots, we will explain in detail the particular features suggested by the examples shown in this figure.

1. Type I distributions show an excess of pairs at relatively small distances, and a consistent deficiency of events at larger distance scales. In the particular example shown, the excess of pairs for distances 0-12 km indicates clustering. The peak value of 1.5% excess pairs occurs at 5 km. However, the total percentage of excess pairs over the full range is 20.5%, which is calculated from the area under the curve from 0 to 12 km (represented by the sum of all percentages measured in this range with a step of 0.5 kin). We use equation (7) of ENEVA and PAVLIS (1988), which is simply reduced here to taking a square root from 0.205 (the above 20.5%). Thus, we obtain that about 45% of the events in the data used for this particular example were responsible for the clustering observed. As Figure 3 shows, the clustering is compensated for by a deficiency in earthquake pairs at larger distances. This type of distribution can be explained by many randomly distributed clusters of events with no characteristic distance between the clusters.

2. Type II distributions are characterized by two distinct anomalies: clustering (as in Type I), and an excess of pairs at longer distances. We call the latter a

o.,

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alone.


"long-distance anomaly." A deficiency of pairs is present between the two positive anomalies. The example shown indicates clustering at distances of 1-3 kin, a

deficiency of pairs between 3 and 16 kin, and an excess of pairs between 16 and 25 km. The positive peaks occur at distances 15 and 23 km and are of size 1.3% and 2%, respectively. While these numbers are not very informative, we can calculate the total percentage of pairs associated with the two positive anomalies. They are 5% and t5% respectively, which implies that 22% of the earthquakes in the data set were responsible for the clustering and 39% for the long-distance anomaly. Note that the events forming these last percentages are not mutually exclusive, since the analysis is based on pairs. That is, a single event can contribute to different parts of the same curve. This type of distribution can be explained by the presence of two or more clusters of activity with a characteristic spacing.

3. Type III distributions have a shape similar to a negative sine function with a period equal to the maximum length scale for the area they are associated with. The example shown in Figure 3 indicates a deficiency of pairs of earthquakes separated by less than 1 km and an excess of earthquakes separated by distances of 1-2.5 kin. The total percentage of excess pairs is 22%, which translates into 47% events. The pattern associated with this type of residual curve only occurs in some of the smallest subareas we examine. It can be explained by events randomly distributed around the edges of a crustal block within which few, if any, earthquakes occur.

We note that the residual curve that would represent one single random simulation compared with the average of many such simulations, would deviate only very slightly from the 0 lines shown in Figure 3 (for an example, see Figure 3d in ENEVA and HAMBURGER, 1989). There was no distribution in the present study to suggest that such a uniformity exists in the reality.

Results

Universal Nonuniformity

A first-order observation is that the spatial distribution of earthquakes in the areas we examined is essentially never uniform (Figure 4). The distributions of both aftershocks and events in declustered catalogs consistently deviate from the distributions derived from randomly scattered events within the same volumes. Indeed, all residual curves in the figure fall outside the tolerance bounds.

Effect of Declustering

While aftershocks and events in declustered catalogs both exhibit nonuniform spatial distributions, declustering certainly has an effect on the observed patterns (Figure 4). The fluctuations in the residual distribution curves are smaller for the


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Distribution of hypocentral distances in MH, CL, HO and CO areas (shown in Figure la). Upper frames show residual curves for aftershoeks (subsets of the clustered catalogs) in MH, CL, and CO; and all events in HO. Lower frames show distributions from declustered catalogs for the following time periods: MH, 1978 1986; CL, 1973-1983; HO, 1969-1983; and CO, 1977-1983. All residual distribution curves are drawn with solid lines. Dotted lines indicated tolerance limits. Percentages (frequency of

pairs x I00%) are given along the vertical axes here and in all subsequent graphs of this type.

declustered catalogs than for the aftershocks in Morgan Hill and Coyote Lake, and the full catalog for Hollister (all of these areas are along the Calaveras fault). For example, in the Morgan Hill area 37% more aftershocks than expected were separated by distances of less than 7 kin, while in the declustered catalog this percentage drops to 26%. As before, these estimates use equation (7) of ENEVA and PAVLIS (1988) and are derived from the total percentages of pairs associated with the clustering anomalies shown in Figure 4. Similar changes are observed in the other areas. However, while in Coalinga the distribution of aftershocks looks very different from the distribution resulting from the declustered catalog, the latter contains only 50 events. The tolerance bands are therefore much wider, making the significance of this difference questionable.

Dependence on Scale

In our previous work we observed universal nonuniformity of earthquake spatial distribution over regions with maximum dimensions varying from 1500 to 30 km. In particular, clustering was found to be nearly universal. In this work, we examined areas of a smaller size that provide an opportunity to look at clustering within clusters.

Figure 5 shows three residual distribution curves for each of the four main areas. These curves are calculated from events falling inside the areas labelled 1, 2,

Voi. 137, 1991 Spatial Distribution of Seismicity 47

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curve. Vertical axes are as in Figure 4.

and 3 in Figures l b, d, f, and h. As discussed above, these areas were chosen by visual inspection of maps and cross sections with the idea that they appeared to have a progressively more uniform distribution of earthquakes as the size of the area decreased. These results show that visual perceptions of randomness can be misleading, as many of the curves in Figure 5 suggest the opposite. That is, instead of decreasing with scale, the degree of nonuniformity actually increases in most cases (note especially Hollister). This suggests that the spatial distribution of earthquakes in smaller areas tends to be less uniform than the one in larger areas.

The results of this analysis also bear on the hypothesis put forward by some authors that earthquake distribution in space is self-similar (KAGAN and KNOPOFF, 1980; SADOVSKY et al., 1984). While self-similarity is not specifically studied here, we have the following reasons to assume that our results do not support this hypothesis at the scales examined.

1. If self-similarity held, the type of residual distribution curve (Figure 3) should not change with the size of the area. This appears to be the case in Coalinga, but not in the other three areas (Figure 5). This simple criterion is therefore sufficient to suggest that the spatial distribution of earthquakes in the areas along


the Calaveras fault does not seem to agree with the self-similarity hypothesis. At Coalinga, the forms of the curves are, however, similar as all three have a zero crossing at approximately 1/3 of the maximum distance range for each subarea. If the distances were normalized by the maximum dimensions in each subarea (so that the horizontal axes ran from 0 to 1), the three curves from Coalinga might have significantly overlapped, thus suggesting self-similarity. However, this possibility is apparently rejected by the next criterion.

2. If the curves were to suggest spatial self-similarity, the percentages of events responsible for the clustering anomaly (i.e., excess events at short distance scales) should be constant within a given main area. These percentages, in fact, vary widely. Although the smallest, this variation exists even in Coalinga, with the events involved in clustering decreasing from 45% in the main area 1 to 36% in subarea 3. The largest variation is observed in Hollister. As the size of study area shrinks, clustering at distances smaller than 3 km increases from 22% of the events involved in that anomaly in area 1 to 45% in subarea 3. The spatial distributions of earthquakes in the other two areas along the Calaveras fault, as indicated above, show increasing degree of overall nonuniformity with decreasing size of area.

Thus, our results indicate that the spatial distribution of earthquakes along the Calaveras fault is not self-similar by either of the above criteria, and tends to become less random (or more nonuniform and irregular) as we go to shorter length scales. The result for Coalinga shows the opposite tendency, but no self-similarity can be suggested in this case either.

Dependence on Location

The results in Figure 5 indicate that seismicity in the areas we studied is nonuniform at all scales we could examine. A related question is whether the type and level of nonuniformity depends on location in space. This question can be addressed at two different levels. First, at a larger scale we examine seismicity in four different areas of comparable size within central California. Secondly, the subareas shown in Figures lc, e, g, and i define volumes of comparable size within

each of the four main areas. Dependence on tectonic setting. Three of the largest areas we examined contain

earthquakes associated with the Calaveras fault (MH, CL, and HO in Figure la), which is a major right-lateral, strike-slip fault. The fourth area, is quite different as the Coalinga earthquake was a thrust event. Furthermore, unlike the other three areas the Hollister area is in a section of the Calaveras fault that has not experienced any larger events. It is also an area where surface measurements of fault creep are well documented (e.g., MAVKO, 1982). We therefore consider how results from different areas depend on tectonic environment. The following can be noted in this regard:

1. Clustering (positive relative residual numbers of pairs at the shortest distances) is seen everywhere, regardless of setting (Figure 4). The degree of clustering


varies considerably. The percentage of events involved in clustering for the Hollis- ter, Morgan Hill, Coyote Lake, and Coalinga are 22%, 37%, 37%, and 45%, respectively. The distance scale over which the clustering anomalies are observed also varies, ranging from < 3 km for Hollister to < 12 km for Coalinga.

2. Some of the residual curves for areas (and subareas) along the Calaveras fault show long-distance anomalies (Type II distribution), as seen in Figures 4 to 7. The long-distance anomalies are associated with two or more discrete clusters of events separated by sites of lower activity. In Morgan Hill the long-distance anomalies are caused by concentrations of activity near San Felipe Valley and south of Anderson Reservoir (see Figures lb and 4). Similarly, concentrations of activity at both ends of the Coyote Lake (REASENBERG and ELLSWORTH, 1982) and Hollister (MAVKO, 1982) areas produce long-distance anomalies in residual distribution curves for these areas; see Figures ld, lf, and 4, as well as Figure 7 for Coyote Lake. While the ML -> 1.5 residual curve for the Coyote Lake aftershocks shown in Figure 4 does not exhibit any long-distance anomaly, such an anomaly is evident for larger events (ML -> 2.0 and ML -> 2.5 in Figure 7).

3. We may expect differences in the spatial distributions for Morgan Hill and Coyote Lake compared to that of the Hollister area, since the first two areas were sites of large events while the latter had no event with magnitude larger than 4.5 for the 1969-1983 period. It might be noted that the clustering anomaly is more compact for HO (distances smaller than 3 km) than for MH (<6 km) or CL ( < 9 kin), and the total percentage of events involved in the clustering is smaller for HO (22%) than the MH and CL aftershocks (37%). Furthermore, the long-distance anomaly at Hollister (Figure 4) is most prominent. However, all three areas exhibit the same type of spatial distribution, Type II, and the residual curves alone cannot be used to distinguish between aftershocks and the seismicity in Hollister.

Fine-scale variations. The other level at which we can search for similarities and differences among spatial distributions is for each main area to compare results from the subareas shown in Figures lc, e, g, and i labelled with numbers 4-8. These results are presented in Figure 6. For Morgan Hill, Coyote Lake, and Hollister there is essentially nothing consistent. For example, in the Morgan Hill area, subareas 4, 5, 6, and 7 are in the vicinity of two dilational fault jogs (see Figure 1 of ENEVA and PAVLIS, 1988), that mark areas of high activity. It is known from the results of OPPENHEIMER et al. (1988), that the mechanisms of the events in these subareas are predominantly strike-slip. Subarea 8, in contrast, is located near a compressional fault jog, and the events there are predominantly thrust events. Thus, one might expect the distributions from subareas 4, 5, 6, and 7 to be similar to each other and distinctly different from the distribution associated with subarea 8. However, in actuality there is nothing similar about the results from subareas 4, 5, 6, and 7 and, consequently, nothing that is clearly different about area 8. Similar statements can be made for Coyote Lake and Hollister. The general observation is that all types of distributions are observed in small subareas along the Calaveras


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Figure 6 Spatial distributions for small scale areas. Each graph shows a residual distribution curve for one of the subareas labelled 4-8 in Figures lc, e, g, and i. Results for different subareas are arranged in the following manner: the vertical columns show distributions from a common main area, with subarea 4 at the top and the highest numbered subarea at the bottom. Residual distribution curves are shown with solid lines, and the tolerance limits are shown with a pair of dotted lines. Vertical axes are as in

Figure 4.

fault zone. In contrast, all subareas of Coal inga show Type I distributions with

varying percentages of events associated with clustering. Patterns associated with

fine-scale variations of seismicity still cannot be identified. Pair analysis therefore

fails to provide any useful insight in this respect.

Dependence on Magnitude

ENEVA and PAVLIS (1988) noted that epicenters of Morgan Hill aftershocks

exhibited nonuni form spatial distributions with the degree o f clustering increasing

with magnitude. We extend this observation here with the results in Figure 7. The


Morgan Hill

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40

Figure 7 Dependence of hypocentral spatial distribution on magnitude. Shown are residual distribution curves for varying lower magnitude cutoffs indicated on the plots. The vertical bar symbols at the right of each

frame show the average width of the tolerance limits for each curve as in Figure 5.

same pattern occurs for the hypocentral distance distributions all along the Calav-

eras. That is, larger magnitude events within a given area tend to be progressively more clustered than smaller events. Associated percentages of events are shown in

Table 2. This result is unexpected from inspection of maps and cross sections. Indeed, one might be led to think that the smaller events are more clustered because

they are more numerous. To explain this observation one must recognize that the four main areas studied here (Figure la) were originally outlined by examining

Table 2

Dependence o f clustering on magnitude

Distance Area (kin) M L >- 1.5 M L >- 2.0 M L -> 2.5

MH < 7 37% 43% 59% CL <4 26% 35% 49% HO < 4 22% 25% 36%


maps of events with M L > 1.5. The dependence on magnitude is due to the fact that the larger events tend to occur in even more localized areas along the fault zone.

The Coalinga aftershocks, in contrast, show no dependence on magnitude. The two curves for Mc -> 2.5 and ML > 3.0 are virtually identical and the fluctuations in the ML >- 3.5 curve are due only to the small sample size. Note that events with magnitudes smaller than 2.5 were not examined because the catalog was found to be incomplete below this level (see Data).

Dependence on Time

ENEVA and HAMBURGER (1989) found that spatial distributions of earthquakes in Central Asia were essentially stable with time. However, much larger regions and longer periods of time were studied there than the ones examined in the present work. It is to be expected that this stability would not be observed in small areas. In particular, we can hypothesize that the spatial distribution of seismicity before large earthquakes is likely to be different from the distribution of aftershocks occurring in the same region.

The analysis we use to test this hypothesis is complicated by unequal time coverage and large differences in the background seismicity rate for each of the study areas. The Coyote Lake area permits the most complete coverage. That is, the data include seismicity prior to the mainshock (preshocks), aftershocks, and seismicity following cessation of aftershock activity (post aftershocks). In Morgan Hill and Coalinga, we could only study preshocks and aftershocks. However, in the Coalinga area there were very few (36) preshocks. To minimize problems caused by this variable coverage and different numbers of events in the data sets, we chose to consider groups of fixed size that covered variable time periods. We chose sample sizes of 70, 50, and 200 events in MH, CL, and CO (Figure la), respectively. This division yields the following: 2 groups of MH, 2 groups of CL, and 1 reduced (36 events compared to 200 in other time periods) group of CO preshocks; 4 groups of MH, 5 groups of CL, and 7 groups of CO aftershocks; and 2 groups of CL post aftershocks.

While these groups provide useful information on changes in earthquake spatial distribution in time, inconsistent detection and magnitude determinations have the potential to have influenced these results. HABERMANN and CRAIG (1988) found that in all three aftershock areas studied here, systematic decreases in magnitude determination took place after the mainshocks. Their conclusions were based on ML > 2.5 events, but it could be expected that magnitudes of the smaller events are also subject to changes. In this connection, when preshocks are compared with aftershocks, and we assume they span the same magnitude range, we may be unknowingly comparing lower magnitude data sets with higher magnitude data sets. This may not be that important in Coalinga, because the spatial distribution there does not seem to depend on magnitude. However, as already discussed, this


is not the case along the Calaveras fault, where higher degree of clustering is associated with larger events. At present, there is not much we can do about this problem except to be cautious about observations of changes in the degree of clustering of preshocks relative to aftershocks.

Selected results of this analysis are presented in Figure 8. We point out the following main observations concerning time dependence.

1. The spatial distribution of preshocks reveals some features that are of opposite polarity to features seen in the aftershock spatial distribution. For

6 - - All Aftershocks

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Figure 8 Dependence of spatial distributions on time. Different curves show residual distributions for data selected in varying time intervals. The vertical bar symbols at the right of each frame are as in Figure 5. For Morgan Hill, "Preshocks" are defined to be the events that occurred during a period of 35 months prior to the mainshock, "Earlier Preshocks" are the events in the period from 64 months to 36 months before the mainshock. The right frame for Morgan Hill shows results for various aftershock time periods. For Coyote Lake, "Preshocks" are the events that occurred during a period of 58 months before the mainshock, and "Post Aftershocks" are events that occurred between 17 and 31 months after the mainshocks. Aftershock time periods are indicated in the legend of the right frame. For Coalinga, "Preshocks" are all events that occurred from 1977 to the day of the mainshock. Aftershock time periods are denoted in the legend on the right. Durat ions of time periods are different because of the use of groups of fixed number of events (see text).


example, the 70 events immediately preceding the Morgan Hill mainshock (labelled "Preshocks" in Figure 8) are associated with a deficiency of pairs with interevent distances around 5 kin, which is replaced by a positive anomaly during the aftershock period. On the other hand, the preshock positive anomaly at distances around 25 km disappears in the aftershock distribution. Similar opposing features seem to exist in Coyote Lake and Coalinga. The Coalinga results, however, must be interpreted cautiously because the number of preshocks (36) is too small. Seismicity during earlier time periods before the mainshock may not always exhibit this opposing polarity pattern. We have only one sample to use as evidence to support this statement; the Morgan Hill curve labelled "Earlier preshocks" in Figure 8. Comparable results from Coyote Lake and Coalinga could not be presented because the number of preshocks is too small to reduce the tolerance limits to a usable level. These observations are tentative, but they may have some relevance to earthquake prediction.

2. The degree of nonuniformity quantified by the percentage of events involved in certain anomalies is higher for aftershocks than for preshocks for both the Morgan Hill and Coyote Lake events. In particular, 25% of Morgan Hill and 18% of Coyote Lake preshocks are involved in producing an excess of pairs at small distances. For aftershocks of both mainshocks, the percentage of events defining the clustering increase to 37%.

3. Temporal changes in spatial distributions can be also observed during aftershock sequences (Figure 8, right frames). First, some anomalies are evident only for a part of the sequence. For example, the Morgan Hill long-distance anomaly in the 15-20 km distance range is only present between 10 and 50 days after the mainshock. The earlier and the later aftershocks do not exhibit this feature. Second, spatial clustering of aftershocks varies during each sequence, but tends to show a decaying trend with time in all three aftershock sequences. For Morgan Hill, the percentage of aftershocks associated with clustering decreased from 42% to 25% by the end of the sequence; for Coyote Lake, aftershock clustering decreased from 41% to 26% in the post aftershock period; and for Coalinga aftershock clustering decreased from 55% to 35% in four months.

Finally, we note that we studied six groups of 100 consecutive events each in the Hollister area. The residual distribution curves are not shown because all were Type II curves which fluctuated randomly around the curve shown in Figure 4. This indicates that the spatial distribution of earthquakes in the Hollister area was relatively stable over the 1969-1983 period.

Dependence on Earthquake Location Errors

Another issue in evaluating our results is the influence of location errors. KAGAN and KNOPOFF (1980) analytically estimated the influence of the location precision on results using interevent distances. They concluded that this influence

Vol. 137, 1991

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.............. 0.50xO.50x2.00

1 2 3 4 5 6 Distance (km)

Figure 9

55

Effect of location errors on distribution curves. The example is from Morgan Hill subarea 6 (See Figure lc). The solid curve is the original distribution curve. The remaining curves result from catalogs with different random shifting of the hypocenters as specified in the legend and in the text. For example, the curve labelled 0.5 x 0.5 x 2.0 results from randomly shifting each hypocenter within _+0.5 km around

the original epicenter and + 2 km in depth. Vertical bar is as in Figure 5.

could be significant and can lead to highly unreliable results. We chose to use random simulations to evaluate how seriously the location errors might alter the residual distributions of earthquakes pairs. The basic idea was described previously (ENEVA and HAMBURGER, 1989). We compare residual distributions of earthquakes pairs obtained from the original catalogs and from catalogs with randomly shifted hypocenters within certain limits representing the average horizontal and vertical errors.

An example of the results of these calculations is shown in Figure 9 (similar results are found in other study areas). The curves shown were generated by random shifting of the hypocenters around their original locations within +0.25 km or _+0.5 km in the horizontal plane and _+ 1 km or +2 km along the vertical. These are reasonable estimates of typical location errors for the data used, since the pair analysis results depend only on relative, not absolute locations. It is evident that the spatial distribution is not dramatically affected by relative location errors of this size.

Discussion and Conclusions

1. Earthquakes are not randomly distributed in space. The present study combined with our previous work gives quantitative evidence that earthquakes are not


uniformly distributed in space at any scale. It may not be surprising to find nonrandomness at large scales, since maps and cross sections already show that most earthquakes occur along distinct fault zones. However, one may expect that it is possible to outline smaller areas inside which earthquakes would be randomly distributed. Our results show otherwise, and what is more, in most cases both background seismic activity and aftershocks are distributed in significantly nonrandom fashion. Observations of nonuniformity in the spatial distribution of seismic events have also been reported by VERE-JONES (1978) for microearthquakes in Japan, HABERMANN et al. (1986) for the seismicity along five convergent plate boundaries, and SADOVSKY et al. (1984, 1987) for two earthquake catalogs of local and world-wide scale. These observations are most likely related to the heterogene- ity of stress, material properties, and/or fault geometry that exists at any scale. Indeed, BAKUN et al. (1980), BAKUN (1980), SEGALL and POLALRD (1980), GIBSON (1986), and KING (1986) point out specific correlations between discontinuities of fault geometry and seismic activity, including the geometry of initiation and termination of earthquake rupture.

2. Earthquakes occur in specific patterns that are scale dependent. Some of these can be carried over from large to small scales. Clustering is the feature which seems to be persistent in all conditions. Long-distance anomalies, suggesting alternating of sites of relatively low and high seismic activities, are characteristic of seismicity in large zones (ENEVA and HAMBURGER, 1989) and small (<40 kin) areas in strike- slip environments like the Calaveras fault. While similarities in earthquake spatial distribution in small and large areas do exist, the calculated measures of the degree of nonrandomness from pair analysis are quantitatively different.

The concepts of fractals and self-similar processes have received a substantial amount of attention in geophysics in recent years (e.g., SADOVSKY and PISARENKO, 1989; TURCOTTE, 1989; RUNDLE, 1988). SADOVSKY et al. (1984) reported self-similarity in nonuniform earthquake spatial distributions, while KAGAN and KNOPOFF (1980) argued that earthquake spatial distribution is self-invariant and is statistically indistinguishable from a uniform distribution along vertical planes. In addi- tion, self-similarity of fault geometry was hypothesized by ANDREWS (1980), KAGAN (1982), and KING (1983) among others. The Gutenberg-Richter relationship for earthquake frequency distributions can also be explained by a self-similar faulting process (e.g., KING, 1983).

We would argue that self-similarity in the faulting process that would lead to self-similar earthquake distributions should only be expected when results are averaged over areas that are very large compared to the rupture areas of the largest events studied. This is definitely violated here, and if we had obtained erratically fluctuating residual curves we would not be able to imply anything about the self-similarity hypothesis. However, a greater degree of nonuniformity was detected in the smallest areas of several kilometers in size. ENEVA et al. (1991) made similar observations in aftershock zones of some moderate earthquakes in the Garm

Vol. 137, 199t Spatial Distribution of Seismicity 57

region of Central Asia, which suggests that this property is not peculiar to California. It has been suggested that self-similarity may break down at very small and very

large scales (e.g., ANDREWS, 1980; K~N6, 1983). AWLES et al. (1987) and OKUBO and AKI (1987) conducted analyses of fault segments forming the San Andreas fault. Fractal dimensions estimated by these authors imply greater fault complexity for smaller scales (0.5 and 2 km in their studies). Furthermore, AKI (1987) argues that the magnitude-frequency relationship departs from self-similarity for earthquakes with magnitude smaller than about 3.0. Some of our results support these previous observations because we find an increasing degree of spatial nonuniformity of earthquake distributions with decreasing size of study area along the Calaveras fault.

3. Earthquake spatial distribution depends on tectonic setting. Our results suggest the existence of differences between the two major types of tectonic setting studied here, strike-slip and thrust. In both cases, spatial clustering characterizes the earthquake distribution. However, long-distance anomalies are evident in the strike-slip environment along the Calaveras fault, but are absent in the thrust tectonic setting in Coalinga. These anomalies are associated with alternating zones of higher and lower seismicity. Epicentral maps and cross sections of aftershocks (REASENBERG and ELLSWORTH, 1982; COCKERHAM and EATON, 1984; MENDOZA and HARTZELL, 1988), as well as coseismic slip and cumulative seismic moment measurements (BAKUN, 1980; BAKUN et al., 1986) all suggest that the areas of lower seismic activity (asperities) are related to the rupture zones of the largest events that have occurred along the Calaveras fault. The average size of these asperities and the distance range (7-20 km) over which we observe long-distance anomalies may be related to the predominant fault segment length of 12km reported by BILHAM and KING (1989) for the San Andreas fault.

The absence of long-distance anomalies in the Coalinga aftershocks may be a general characteristic of earthquakes associated with fold-thrust environments as ENEVA et al. (1991) found similar distributions for aftershocks of events in the Garm region, Soviet Central Asia, which lie in an active fold-thrust belt. While small clusters constrained to a nearly two-dimensional surface can lead to the existence of long-distance anomalies like those we observed along the Calaveras, this is not the case in an active fold and thrust system like Coalinga or Garm. Coalinga aftershocks appear to lie on multiple, complicated, intersecting fault systems (EATON, 1985; EBERHART-PHILLIPS, 1989) that can naturally lead to Type I spatial distributions. That is, the seismicity can be thought of as a collection of many discrete clusters with no characteristic spacing.

Another important difference between the Calaveras areas and Coalinga is that Iarger events along the Calaveras cluster more in space than the smaller earthquakes. In contrast, no magnitude dependence is evident in Coalinga. ENEVA et al. (1991) observed similar behavior at Garm. One hypothesis to explain this difference is that nucleation sites for larger earthquakes are more limited in strike-slip zones than in a fold and thrust setting.


Finally, there is a clear difference between our study areas that is not reflected in the results from pair analysis. The Hollister area is well known for the surface fault creep that is observed there. However, our results do not indicate anything especially different in the Hollister area compared to the Morgan Hill and Coyote Lake areas. In contrast, KING and BAKUN (1987) found distinct differences in seismic slip in Morgan Hill compared to Hollister. These differences are apparently not reflected in the spatial distributions of earthquakes represented by pair analysis.

4. Earthquake spatial distribution in aftershock zones show systematic changes with time. In every case we examined there is a difference between the degree of nonuniformity of preshock and aftershock seismicity. For both Morgan Hill and Coyote Lake, the aftershock distribution was more nonuniform than the preshock seismicity, exhibiting a higher degree of clustering. If we assume that small earthquakes occur preferentially where the stress is higher, this would imply that the state of stress following the mainshock is more heterogeneous than during the period preceding the mainshock. If we continue on this line of reasoning, the results from Coyote Lake (Figure 8) suggest that the seismic activity, and hence the stress, returned to a more homogeneous state after the end of the aftershock sequence. This would imply that the aftershock period itself may result from a transitional, more heterogeneous stress state introduced by the mainshock rupture, and the aftershock sequence ends when the transitional stress is relaxed. However, such an explanation may be oversimplified since spatial variations in seismicity do not necessarily imply a spatial variation in stress (MICHAEL, 1987).

Another observation of a temporal dependency of seismicity is the tendency for distributions of preshocks and aftershocks in strike-slip environments to exhibit opposing patterns. This may be the specific way the pair analysis results reflect the lack of seismic slip on some sections of the Calaveras fault with subsequent accommodation by a mainshock-aftershock sequence (BAKUN, 1980; BAKUN et al., 1980, 1986). Some authors have pointed at the existence of identical spatial patterns of preshocks and aftershocks, associated with long-term geometric features of the seismogenic faults (e.g., L~NDH et aI., 1989). While our results do not contradict the existence of long-lived geometric features, only qualitatively can they be called "identical," since pair analysis shows temporal changes in earthquake spatial distribution before and after mainshocks. That is, the geometric features are there, but the relative intensities of seismic activity associated with them vary in time. Thus, our results point to some aspects of the short-term behavior of fault geometric features, which are otherwise of significant longevity.

There have been other studies that also reported changes in earthquake spatial distribution before main events: WARDLAW et al. (1989) used interevent distances to detect seismic quiescence before M > 7.2 events in some subduction zones; OUCHI and UEKAWA (1986) reported changes in fractal dimensions in earthquake spatial distribution before mainshocks; and ENEVA et al. (1991) observed changes in spatial distributions of earthquakes preceding two moderate events in the Garm


regions of Central Asia. A more formalized study may show whether it is possible to use pair analysis for reliable indentification of changes in earthquake spatial distribution before moderate to large events.

Acknowledgements

The present work has been funded through the National Earthquake Hazards Reduction Program under grant 14-08-001-G1533 from the U.S. Geological Survey, and was completed while M. E. held a National Research Council Research Associateship at NOAA. C. Frohlich and an anonymous reviewer helped us to significantly improve the paper. We are grateful for discussions we had at various times with the following colleagues: T. Habermann, M. Hamburger, M. Chinnary, S. Davis, L. Whiteside, F. Klein, A. Lindh, D. oppenheimer, and P. Reasenberg. M. E. is greatly indebted to N. Enev, M. Davis, M. Ertle, L. Whiteside, and F. Creamer for computer help. We thank J. Harste for typing the original manuscript, and R. Hill for his computerized drafting skills.

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(Received August 30, 1990, revised JuIy 16, 1991, accepted August 31, 1991)

Documents

Spatial distribution of aftershocks and background seismicity in central California