Contrasting Decay Patterns of the Proximate Large Earthquakes in Southern California Yosihiko Ogata Institute of Statistical Mathematics, Tokyo, Japan

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. B6, 2318, doi:10.1029/2002JB002009, 2003

When and where the aftershock activity was depressed: Contrasting decay patterns of the proximate large earthquakes in southern California Yosihiko Ogata Institute of Statistical Mathematics, Tokyo, Japan

Lucile M. Jones U.S. Geological Survey, Pasadena, California, USA

Shinji Toda Geological Survey of Japan, National Institute of Advanced Industrial Science and Technology, Tsukuba, Japan Received 4 June 2002; revised 16 February 2003; accepted 14 March 2003; published 25 June 2003.

[1] Seismic quiescence has attracted attention as a possible precursor to a large earthquake. However, sensitive detection of quiescence requires accurate modeling of normal aftershock activity. We apply the epidemic-type aftershock sequence (ETAS) model that is a natural extension of the modified Omori formula for aftershock decay, allowing further clusters (secondary aftershocks) within an aftershock sequence. The Hector Mine aftershock activity has been normal, relative to the decay predicted by the ETAS model during the 14 months of available data. In contrast, although the aftershock sequence of the 1992 Landers earthquake (M = 7.3), including the 1992 Big Bear earthquake (M = 6.4) and its aftershocks, fits very well to the ETAS up until about 6 months after the main shock, the activity showed clear lowering relative to the modeled rate (relative quiescence) and lasted nearly 7 years, leading up to the Hector Mine earthquake (M = 7.1) in 1999. Specifically, the relative quiescence occurred only in the shallow aftershock activity, down to depths of 5–6 km. The sequence of deeper events showed clear, normal aftershock activity well fitted to the ETAS throughout the whole period. We argue several physical explanations for these results. Among them, we strongly suspect aseismic slips within the Hector Mine rupture source that could inhibit the crustal relaxation process within ‘‘shadow zones’’ of the Coulomb’s failure stress change. Furthermore, the aftershock activity of the 1992 Joshua Tree earthquake (M = 6.1) sharply lowered in the same day of the main shock, which can be explained by a similar scenario. INDEX TERMS: 7223 Seismology: Seismic hazard assessment and prediction; 7230 Seismology: Seismicity and seismotectonics; 8164 Tectonophysics: Stresses—crust and lithosphere; KEYWORDS: aseismic slip, anomalous aftershock decay, Coulomb stress shadow, ETAS model, modified Omori formula, spatial pattern of aftershock decay Citation: Ogata, Y., L. M. Jones, and S. Toda, When and where the aftershock activity was depressed: Contrasting decay patterns of the proximate large earthquakes in southern California, J. Geophys. Res., 108(B6), 2318, doi:10.1029/2002JB002009, 2003.

1. Introduction events and their aftershocks are described by Hauksson et al. [1993]. The proximity of these earthquakes has led to a [2] The 16 October 1999 M = 7.1 Hector Mine earth- number of studies suggesting possible physical mechanisms quake occurred about 20 km northeast of the Landers [King et al., 1994], especially with regard to the question of earthquake (M = 7.3) which occurred on 28 June 1992 in whether the time of the Hector Mine earthquake was southern California. The 28 June 1992 Big Bear earthquake advanced by the stress changes caused by the Landers event of M = 6.4 followed the Landers main shock by three hours, [U.S. Geological Survey, 2000; Parsons and Dreger, 2000; about 35 km west of the Landers epicenter. Also, the 22 Gomberg et al., 2001; Freed and Lin, 2001]. April 1992 Joshua Tree earthquake preceded the Landers [3] However, there have been only a few seismicity event near the southern end of the future Landers aftershock studies on the relationship, based on their well-recorded zones (Figure 1). Detailed seismicity observations of these aftershock sequences. For example, change of seismicity patterns due to the Landers earthquake is argued by Wyss Copyright 2003 by the American Geophysical Union. and Wiemer [2000] based upon the declustered data set that 0148-0227/03/2002JB002009$09.00 removes aftershocks and swarms from the original catalog.

ESE 6 - 1 ESE 6 - 2 OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY

physical features of aftershocks, reflecting heterogeneity and complexity of fault zones including geothermal envi- ronment. For example, Wiemer and Katsumata [1999] present a spatial variability of decay rate for the Landers aftershocks, assuming that the p value of the modified Omori formula depends on location but is invariant with time, since they are concerned with nontransient, environ- mental features of the crust, such as heat flow and viscoelastic properties, in the different subregions. [5] In contrast, we are concerned with the detailed complex features of aftershocks such as interactively triggered aftershocks including those among off-fault regions within the wide aftershock regions of the Landers earthquake, as discussed by Felzer et al. [2002]. We will then analyze whether the model can be the same throughout the whole period or if the model needs to be modified to incorporate different parameter values after some time during the period, before we examine the regional patterns. That is to say, in this paper, we seek to apply good fitting models for normal aftershock occurrences to the Landers aftershock sequence, so as to examine whether an anomalous change to the aftershock decay rate took place or not. If such a change occurred, then perhaps the seismic change is somehow related to changes in stress in the crust, as described in Dieterich et al. [2000]. We also investigate the aftershock sequence of the 1992 M = 6.1 Joshua Tree earthquake leading up to the Landers earthquake.

2. Data

[6] We use the earthquake catalog that has been relocated with a three-dimensional velocity model [Hauksson, 2000] based on data from the Southern California Seismic Net- work (SCSN) and the new TriNet stations [Mori et al., 1998]. Thus the depths and locations of the earthquakes in Figure 1. Locations of the Joshua Tree, Landers, and our analyses are very well constrained. For the study of the Hector Mine aftershocks of M2.5 and greater. The study Hector Mine aftershocks, we use the available data for the region is in southern California (red box in inset). The color period from the main shock through to 23 December 2000. of the circles indicate the time of occurrence of the events The locations of these aftershocks are indicated in Figure 1 with dark blue for April to 27 June 1992, light green for 28 by red circles. For the study of the Landers aftershocks, June to 31 December 1992, light blue for 1993 to 15 indicated by light green and blue disks, we use events for October 1999 and red for 16 October 1999 to 2000. the period until the occurrence of the 1999 Hector Mine Epicenters of Landers, Joshua Tree, Big Bear, and Hector earthquake. Note here that this sequence includes the 28 Mine are shown by stars in region C, in region D, in region June 1992 Big Bear earthquake of M = 6.4 which followed E, and adjacent to region F, respectively. The Hector Mine the main shock by three hours on the same day. These aftershock area includes the cluster of activity during 1992 aftershocks can be considered as off-fault secondary after- (light green) triggered by the Landers event, and two other shocks of the Landers earthquake, as well as the aftershocks clusters (blue circles) during 1994 and 1996, respectively in the Barstow region (region A). The Joshua Tree after- (see text). shocks before the Landers rupture are given by dark blue disks in region D, which are overlaid on the Landers We are concerned, however, with aftershocks themselves, aftershocks. which comprise a major portion of an earthquake catalog, and therefore should include rich information concerning 3. Model Fitting to the Aftershock Sequences stress changes [Dieterich, 1994]. 3.1. ETAS Model [4] The observed relaxation properties of aftershock [7] The typical aftershock decay is represented by the sequences are considered to be the result of some complex Modified Omori function, and not well defined combination of processes and physical properties [Mogi, 1967; Kisslinger and Jones, 1991; Guo nðÞ¼t KtðÞþ c Àp; ðÞK; c; p; parameters ; and Ogata, 1997]. Extensive reviews on their possible mechanisms are given by Utsu [1970] and Kisslinger initiated by the main shock at time origin t = 0. This formula [1996]. In particular, the aftershock decay parameter p of was proposed by Utsu [1961] from fits to many data sets as the modified Omori formula has been estimated to explore a modification of the Omori law [Omori, 1894]. This OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY ESE 6 - 3 formula remains the most widely used model for typical is useful to compare the goodness of fit of the competing aftershock rate decay. To estimate the coefficients, Ogata models to a given data set. The model with a smaller AIC [1983] proposes the method which maximizes the log value shows a better fit (see also Akaike [1987] for relation likelihood function to the likelihood ratio statistics). For example, Guo and Ogata [1997] compared the goodness of fit between the Z XN T modified Omori formula (three parameters) and the ETAS ln LKðÞ¼; c; p; S; T ln nðÞÀti nðÞt dt; ð1Þ model (four or five parameters) applied to 34 aftershock i¼1 S sequences of the latest 20 years in the last century, in Japan and its vicinity. The results were that for two thirds of the with respect to K, c, and p, where {ti, i =1,2,..., N}isa sequences, the ETAS model fitted better than the modified series of occurrence times of aftershocks in the time interval Omori formula. In such a case, the p value of the modified (S, T ). Typically, equation (1) holds for quite a long period Omori formula is usually smaller than the p value of the in the order of some tens of years or more, depending on the ETAS model. This shows a heavier tailed decay in trend, background seismicity rate in the neighboring area. See owing to the effect of further clusters within the sequence. Utsu et al. [1995] and Ogata and Shimazaki [1984]. For the remaining one third of the sequences where the [8] As we consider small aftershocks, however, clustering modified Omori model is a (slightly) better fit than the within the sequence becomes apparent. Thus aftershock ETAS, its p value almost coincided with that of the ETAS. activity is not always best predicted by the single modified In general, the ETAS tends to fit better as the cutoff Omori function [Guo and Ogata, 1997], especially when it magnitude of the sequence lowers, as the clusters within it includes remarkable secondary aftershock activities of large become apparent. This demonstrates that ETAS is a natural aftershocks. Therefore we assume that every aftershock can extension of the modified Omori model for studying various trigger its further aftershocks or remote events, and that the types of aftershock sequences, including nonvolcanic occurrence rate at time t is given by a (weighted) superpo- swarms [Utsu et al., 1995]. sition of the modified Omori functions shifted in time [10] In order to examine whether or not the temporal X aftershock pattern changed at a suspected time t on a time afgMjÀMc lqðÞ¼t m þ e n t À tj ; interval (S, T) in a given data set, we consider a two-stage j ETAS model applied to the occurrence data sets on the separated subintervals (S, t) and (t, T ), respectively, to where m represents the rate of the background seismicity, calculate the corresponding AICs: and the summation is taken over every jth aftershock occurred before time t, including the main shock at time AIC1 ¼ÀðÞ2 maxq1 ln LðÞþq1; S; t 2dimfgq1 origin t0 = 0. The weighted size of its aftershocks is made as the exponential function of its magnitude Mj in accordance with the study by Utsu [1970], where M c AIC2 ¼ÀðÞ2 maxq ln LðÞþq2; t; T 2dimfgq2 ; represents the cutoff magnitude of the fitted data. We call 2 this the epidemic-type aftershock sequence (ETAS) model and search t that minimize AIC +AIC where, as noted in [Ogata, 1988], which was originally proposed for the 1 2 paragraph (8), L(q1; S, t) and L(q2; t, T) include the event general seismic activity in a region. For a single aftershock data not only in the time span (S, t) and (t, T) but also those sequence, we usually expect very low background seismic in the former time span (0, S) and (0, t), respectively, for the rate (i.e., m = 0) relative to the aftershock rate. For a history of occurrence times and magnitudes since the main sequence of occurrence times associated with magnitudes, shock. Then, to validate the significance of the change we can estimate the parameters q =(m, K, c, a, p)ofthe point, the single ETAS model is applied to the whole data ETAS model that are common to all i, by maximizing the for the period (S, T ), so as to examine whether log likelihood function of q, which is of the same form as the one in equation (1) with the exception that the Modified AIC ¼ÀðÞ2 max ln LðÞþq ; S; T 2dimfgq Omori intensity function n (t) is replaced by the ETAS 0 q 2 intensity lq(t). Here we note that in contrast to the Modified is greater than AIC1 +AIC2 +2q(N). If it is not greater, then Omori intensity function, calculation of the log likelihood it is not significant and we deem there to be no change in has to take account of the fact that the ETAS intensity lq(t)is activity. Here the function q(N) of the number of events in conditional on the past history of occurrence since the main the interval (S, T) is a further penalty value in the search for shock, in the sense that the intensity includes the events’ minimizing t: see Ogata [1999] for the explicit form of occurrence times and associated magnitudes in the time span q(N). The criterions for this comparison take account of the [0, t]. See Utsu and Ogata [1997] for computational codes overfitting bias due to the greater complexity of the two- and useful manuals and Helmstetter and Sornette [2002], stage models, and also the freedom in searching for a for example, for some discussions of statistical features of change point [Ogata, 1992, 1999]. the ETAS model. 3.3. Graphical Examination by the Time 3.2. Model Comparison and Change Point Analysis Transformation [9] The Akaike information criterion [Akaike, 1974] [11] The AIC is useful in the comparison of competing

AIC ¼ÀðÞ2 maxqfglog likehood models. However, having obtained the best model among proposed ones, there is still the possibility of the existence þ 2fg number of adjusted parameters of a better model. We can see precisely how well or poorly ESE 6 - 4 OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY

Table 1. Estimated Parameters for Hector Mine Aftershocks M 3.0a Models Fitted Period, days mˆ, events dÀ1 Kˆ , events dÀ1 cˆ, days aˆ , magnitudeÀ1 pˆ AIC À2q(N) M-Omori (0.25, 409.2) – 103.84 0.1344 – 1.18 À1466.6 – ETAS (0.25, 409.2) – 60.74 0.00087 2.44 1.13 À1526.1 À6.30 aThe penalty for change point significance q(N) is calculated from the equation of Ogata [1999, section 4.2], where N is the number of events in the fitted interval. the estimated model is fitted to an aftershock sequence by Thus it can be seen from Figure 2 that the aftershock rate of inspecting the cumulative number of aftershocks with the Hector Mine earthquake has decayed as predicted by the respect to the transformed time, using the estimated model models. The linearity of the cumulative functions holds for [Ogata, 1988]. Suppose that a series of events {t0, t1, ..., all the shown threshold magnitudes. This indicates that the tN} are simulated based on the model l(t), say the modified ratio of small to large aftershocks is almost the same at any Omori, ETAS or other. Then consider the integral time except for the first period immediately after the main Z shock, which indicates the same b value in Gutenberg- t Ritcher’s magnitude frequency in time [Utsu, 1962]. ÃðÞ¼t lðÞs ds; 0 4.2. Landers Aftershock Sequence which is the theoretical cumulative function. For example, [15] The clustering feature within the Landers aftershock Ã(t)=K{ln(t + c) À ln c} in the case of the original Omori sequence is conspicuous. This is not only because it model (p = 1.0). See Ogata and Shimazaki [1984] and includes the Big Bear aftershocks but also because of the Ogata [1988] for further examples. If we consider the time clusters due to the large aftershocks. For example, the kinks in the plots of the cumulative curve in Figure 3a are due to change ti = Ã(ti) from t to t, then {t0, t1, ..., tN}is the M5.3 and M 5.4 event of 27 November and 4 December transformed one-to-one to {t0, t1, ..., tN}. It is well known w 1992, respectively, in the Big Bear region (region E in that {t0, t1, ..., tN} distributes according to the stationary Poisson process with unit rate. Therefore, if the estimated Figure 1). Table 2 shows that the ETAS model (ETAS0) is a far better fit than the Modified Omori model (M-Omori0), intensity Ã^q(t) is a good approximation to the true with the AIC difference being 1087.2 for the whole period seismicity, then the transformed data {t^0, t^1, ..., t^N} from the real occurrence data is expected to behave like the until the 1999 Hector Mine event. Here, the background effect m is added to the Modified Omori intensity function. stationary Poisson process. Namely, {t^0, t^1, ..., t^N}are uniformly distributed on the interval [Ã(S), Ã(T)]; equiva- [16] The plot of the cumulative number of Landers after- lently, we see a linear alignment of the plots of cumulative shocks (M 3) against the transformed time by the ETAS ^ model for the whole period, deviates systematically from a number (i.e., i) against transformed time ti = Ã^q(ti). straight line (Figure 3b). This indicates that the observed aftershocks are not well modeled by the single ETAS model 4. Analysis of the Aftershock Sequences (Figure 3a). To examine this anomaly, we hypothesize that 4.1. Hector Mine Aftershock Sequence the aftershock activity pattern changed at some point during [12] From the cumulative curve, we see no conspicuous the period. Indeed, in Figure 3b, the cumulative function clusters in the Hector Mine sequence (M 3.0), probably appears to have a break in the straight line. owing to the lack of large aftershocks in the sequence. The [17] We therefore applied the change point analysis as statistical analysis, however, shows significant clustering described in paragraph [10]. The most likely time for within the sequence. Table 1 summarizes the comparison of the candidate of the change point is sought by minimizing the goodness of fit between the modified Omori formula AIC1 +AIC2 of the two-stage ETAS model for the sub- and the ETAS model fitted to the aftershocks of the Hector intervals divided at the time. Further, to validate this as the Mine earthquake. This shows that the ETAS model is a far change point, it is necessary to confirm whether the two- better fit with regards to the AIC. The difference between stage ETAS model on the subintervals divided at a sus- the AIC values is about 60, which is substantially signifi- pected change point, fits significantly better than the single cant when taking into account the likelihood ratio statistic ETAS model on the whole interval. Table 2 indicates that with only one parameter difference (relative to the chi- the two-stage ETAS model (ETAS1 + ETAS2) with the square distribution with one degree of freedom). most likely change point (190.59 days), fits significantly [13] Further analysis for the significant change point was better than the single ETAS model (ETAS0) used in Figures made through comparison of AIC1 +AIC2 with AIC0 À 2 3a and 3b, with an AIC difference of 15.3. q(N). The result was that the smallest value of the former [18] Consequently, we see that the ETAS model (ETAS1) among the two-stage models for each t, was larger than the can be fitted quite accurately to the Landers aftershock latter, indicating that no significant change point exists. sequence, including its conspicuous clusters, up until the [14] Figure 2 shows that the aftershocks of the 1999 change point for the first 6 months. Indeed, we have Hector Mine earthquake have a linear cumulative function confirmed no further significant change point in the se- during the interval up to December 2000, with the exception quence for the period of (0.75, 190.59) days. Namely, the of the initial short period immediately after the main shock smallest AIC value among the two-stage ETAS models was where the small events were incompletely detected. In larger than the AIC value of the single ETAS model addition, though not shown here, the theoretical cumulative (ETAS1). Incidentally, ETAS1 is a far better fit than the curve is very similar to that of the modified Omori model. M-Omori1, with an AIC difference of 1719.0. OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY ESE 6 - 5

Figure 2. Cumulative numbers of aftershocks of the Hector Mine earthquake with various cutoff magnitudes (Mc) for a period up until 23 December 2000 after the main event in (left) the ordinary time in months and (right) the frequency-linearized time. The thicker and longer time marks in the frequency- linearized time axis show a minute, an hour, a day, a month, and a year. The thinner and shorter time marks show 3, 6, 12 hours; 3, 7, 10, 20 days; and 2, 3, ..., 11 months. Here the concave part of the cumulative curves in Figure 2 (right) illustrates substantial undercounting of small events at the beginning of the aftershock sequence.

[19] Thus we eventually obtained Figures 3c and 3d between 4 and 8 km depth. The depth of 5.5 km was chosen which clearly show that aftershock activity changed around mainly to provide the same cumulative number of after- 190.6 days after the main shock occurrence. There, in shocks at the time of change point. particular, we extrapolated the theoretical cumulative num- [21] We also note that only some parts of the aftershock ber Ã^q(t) using the parameter estimates of ETAS1 in the zone clearly reflect the relative quiescence. Figure 5 shows Table 2. The predicted theoretical cumulative curve for the the cumulative numbers of aftershocks in each of five remaining interval of nearly 7 years leading up to the Hector subregions of the aftershock zone as shown in Figure 1, Mine rupture, however, shows substantially fewer events for the same transformation of time as in Figure 3d, using than expected. We call this lowered activity the relative the estimated ETAS coefficients (ETAS1) in Table 1. We quiescence. Here one may question whether the longer find that the shallow regions B, D and E (the Emerson, period of the quiescence can be considered following only Joshua Tree, and Big Bear segments) show relative quies- half a year of normal activity. However, we should note that cence, while the regions A and C (the Barstow and Landers though the first period has a shorter duration in this case, it regions) do not. There is a further suggestion that the accounts for more than 80% of all the aftershocks. More- shallow parts of A and C turn off at a later time, around over, as we will see in the next section, only some spatial 1996, as indicated by upward arrows. subsets of the aftershocks deviate from the first rate. [22] There are not many M5 class large aftershocks of the Landers earthquake besides the Big Bear event of M = 6.4, 5. Spatial Pattern of the Landers Aftershock which occurred mostly in the regions D and E. The Big Bear region (region E) has M5.3 and M5.2 (Mw5.4) shallow Decay (3–4 km depth) events that occurred on 27 November and 4 [20] The depths of events of the relocated catalog [Hauks- December 1992, respectively, in the same concentrated son, 2000] are very well constrained, with the Landers cluster around the northern boundary of region E. These aftershocks ranging from 0 to 15 km in depth. To examine are located before and after the steep rise of the cumulative the spatial distribution of the relative quiescence in more function in Figure 5, region E, respectively. detail, the cumulative curve of the Landers aftershocks is [23] The Landers earthquake also triggered three shallow separated into two cumulative curves for the events, above clusters of events (M 2.5) within the source region of the and below a depth of 5.5 km (Figure 4). From these curves, Hector Mine rupture (Figure 1). First, the Landers rupture we clearly see that the lowering (relative quiescence) took triggered a cluster of events, including an M5.4 event near place in the shallower part, while the deeper part follows the the Hector Mine epicenter (compare region F in Figure 1, decay pattern set in the first 6 months. The boundary in Figure 11 of Hauksson et al. [1993], and Figure 12 of King depth between the two behaviors is not sharp. A difference et al. [1994]. This activity (M 2.5) ceased after 4 months, in behavior can be seen by dividing the seismicity anywhere following which the relative quiescence of the Landers ESE 6 - 6 OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY

Figure 3. Goodness of fit of models to the Landers aftershock sequence (M 3). The time period considered is up to the 1999 Hector Mine event. (a) and (b) A single ETAS model applied to the whole period and (c) and (d) a two-stage ETAS model applied separately to two subperiods, divided at the change point (190.6 day, vertical solid grey lines). Figures 3a and 3c plot cumulative number versus ordinary time in days, whereas Figures 3b and 3d plot cumulative number against the respective frequency-linearized times. Pluses on the cumulative curves indicate 0.75 days from the main shock, which is the start of the period used to fit the ETAS model avoiding a bias owing to incomplete detection of events (M 3). The smooth grey curve in Figure 3a and the dotted straight line in Figure 3b correspond to the same theoretical cumulative numbers in the different timescales. The smooth grey curve in Figure 3c and the dotted straight line in Figure 3d indicate the theoretical cumulative number estimated from the data in the first period, with these extrapolations to the second period showing substantially fewer aftershocks than the expected. aftershock activity began. This quiescence lasted until the the northern off-fault region of the Hector Mine rupture Hector Mine rupture (see M-T plot in Figure 5). This (another cluster of blue disks in Figure 1). phenomenon led us to a speculation about possible precur- [24] The summarized space-time features of the Landers sory aseismic slip on the Hector Mine fault around asper- aftershocks are (1) the lowering of the Landers aftershock ities, which will be discussed in the next section. The activity in the specified shallow volumes B, D, and E but second cluster (blue disks over the star, Figure 1, around not lowering in A and C; (2) turnoff of the shallow the main shock epicenter) took place during 1994 at almost seismicity in regions A and C after 1996 up until the 1999 the same site as the Hector Mine epicenter (east of the first Hector Mine rupture, (3) the termination of the triggered cluster). The third cluster took place during 1996, located in activity in the western neighboring spot F of the Hector

Table 2. Estimated Parameters for Landers Aftershocks, Including Big Bear Secondary Aftershocks M 3.0 Models Fitted Period, days mˆ, events dÀ1 Kˆ , events dÀ1 cˆ, days aˆ , magnitudeÀ1 pˆ AIC À2q(N) M-Omori0 (0.75, 2649.0) 0.0441 324.98 0.4194 – 1.16 À1184.4 – ETAS0 (0.75, 2649.0) 0.0115 108.63 0.00751 2.32 1.10 À2271.6 À6.60 M-Omori1 (0.75, 190.59) 0.6332 243.72 0.0455 – 1.10 À2211.4 – ETAS1 (0.75, 190.59) 0.0 91.58 0.00637 2.20 1.05 À3930.2 À6.52 ETAS2 (190.59, 2649.0) 0.0500 129.94 0.00605 2.60 1.19 1636.7 – OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY ESE 6 - 7

Figure 4. Cumulative curves of the aftershocks (M 3) of the Landers event shallower (thin black) and deeper (thick gray) than 5.5 km depth, plotted against the ordinary and transformed occurrence times. The time marks in the axis of the transformed time are the same as in Figure 2. Note that the shallower and deeper parts of the fault produced about the same number of aftershocks in the first 6 months but that the shallower part shows a much slower rate of aftershocks after 1992.

Figure 5. Cumulative numbers of aftershocks (M 3) in subregions A–E and magnitudes of events (M 2.5) in region F, plotted against the frequency-linearized times. Thin black and thick gray lines represent shallow (= 5.5 km) and deep events, respectively. The lowering of shallow aftershock activity after about 6 months from the Landers event is seen in regions B, D, and E, and continues the 7 years up to the Hector Mine event. The activity in region F stopped at about the same time as this decrease in aftershock activity began. In regions A and C, in contrast, the rate is unchanged through 1992–1997 but does go down about 2 years before the Hector Mine rupture (see upward arrows). The numbers within each frame show total cumulative numbers of the corresponding curves. ESE 6 - 8 OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY

Mine main shock; (4) the activation of the other two months before the two events is clearly seen in both the clusters in the Hector Mine source during the period of shallow and the deep regions in the sequence of region E the Landers aftershock quiescence (see Figure 1); and (5) (e.g., see Figure 5). Incidentally, the focal mechanism of the the normal decay of the aftershocks in deep layer for all December event is a reverse fault type which can influence subregions A–E. the change in deep seismicity more strongly than the strike- slip type does. This is consistent with the fact that the slope of the cumulative curve of deep events following the change 6. Discussions point in region E, lowers a little relative to the one before 6.1. Possible Mechanisms for the Features of Landers the change point. Aftershocks [28] With regards to aftershocks in the Joshua Tree region [25] Wiemer and Katsumata [1999] showed that different (region D), on the other hand, we could not find any M5 parts of aftershock sequences in the Landers case, in class events that could affect the broken-line-shaped cumu- particular, decayed in different ways. They interpreted this lative curve of shallow events in Figure 5. Most of the M5 phenomenon as possible mechanical differences in the class events there occurred within several days following source subvolumes. Namely, near absence of stress in the the main shock, with no conspicuously large aftershock shallow part, or the inability of the shallow part to build up occurring around the first knot of the broken-line-shaped and maintain significant stress, leads to a situation in which cumulative function. the pockets of stress created by the main shock are quickly [29] Our last possible scenario for the mechanism is eliminated by aftershocks, thus shallow aftershock activity motivated by the sharp turning off of the seismicity at about stops essentially after 6 months. In contrast, the stress level the same time as the onset of the relative quiescence in in the deeper parts is higher; thus, aftershock activity can region F, as shown in Figure 5. This led us to the continue for a longer time. The idea that aftershocks may be speculation of a quiet slip within the Hector Mine Fault. controlled by fluid flow could be discussed in this context; Figure 6 shows this change in Coulomb’s failure stress special conditions of stress level or fluid flow could give around the Landers and Hector Mine aftershock regions, rise to normal Omori decays in the two shallow volumes from an assumed 10 cm aseismic slip in the southern where this exception is observed. shallow parts of the Hector Mine rupture source. The similar [26] The regions B and D of relative quiescence in this stress pattern can be produced by assuming the slip occurs paper correspond roughly to the regions of high p values in only in the two small subareas where the shallow after- the Landers fault if the modified Omori formula is applied shocks (M 2.0) are sparse along the above assumed fault to each region. Nevertheless, we need to apply the ETAS segment. The receiver fault orientation is followed by King model to analyze the complex, interactively triggered after- et al. [1994]. Majority of the Landers aftershocks are shocks among the subregions, rather than applying the consistently distributed with this orientation [Hardebeck et differently modified Omori functions to separated regions. al., 1998]. The M5.4 event in region F has consistent focal Indeed, the goodness of fit of the ETAS model was mechanism with the orientation [Hauksson et al., 1993], substantially better than the set of the differently modified which we assume adopt the similar mechanism to the Omori functions applied to corresponding divided data sets. clustered events in region F. Therefore, if such a slip Also, the identified change point of the Landers aftershock occurred at the end of 1992, the spatial pattern of the sequence is sharp in the sense that even the cumulative resulting stress changes almost explains the summarized function for the whole period clearly shows two broken line items described in paragraph [24]. In particular, the stress segments as given in Figure 3b. This feature is hard to see change effect could decay rapidly with depth relative to the from the cumulative function of the transformed time with one with horizontal directions, because the assumed slip the estimated modified Omori functions because the devi- was strike-type in the shallow crust, and perhaps stronger ation of such a function should be gradual. Similarly, confining pressure in the deep crust might further weaken viscoelastic rebound effects from lower crust and upper the effect of the stress change there. mantle should exhibit a sort of gradual effect, making it [30] Furthermore, if we assume a secondary aseismic slip difficult to explain the sudden stress change in the upper within part of the northern fault segment (the west side one) crust [cf. Freed and Lin, 2001]. from the future Hector Mine epicenter, this produces stress [27] Another possible mechanism for the relative quies- shadows in regions A and C, which could turn off the cence would be the stress changes resulting from the two activities about two years before the main rupture (cf., large aftershocks mentioned in paragraph [15]. The two arrows in Figure 5, regions A and C). The relative quies- significant (shallow, 3–4 km depth) earthquakes in the Big cence in the Big Bear region (subvolume E) is not easily Bear region (region E) occurred at 27 November and 4 explained by a precursory slip model, because the changes December 1992 that are about the time of the change point. in the Coulomb failure stress (CFS) owing to the assumed The lowering of the shallow events in regions E and C could slips in Figure 6 are neutral in that region. The change in be changes in the Coulomb failure stress (CFS) resulting this region may be better explained by what is described in from the mechanisms, which can be calculated by the first- paragraph [27]. motion mechanisms of these events listed in Table 2 of [31] Compared to the relative quiescence, the relative Hauksson et al. [1993]. For example, Harvard centroid activation is insensitive to the transformed time. This is moment tensor (CMT) solution for the December event because the times of triggered clusters are transformed into corresponds to a 32 cm thrust slip in the 2–5 km depth, with frequency-linearlized time which is due to the ETAS model, a 6 km length and (strike, dip, rake) = (120, 54, 112). unless the b value of the G-R magnitude frequency signifi- Interestingly, the quiescence (M 3.0) lasting for about 2 cantly increases (i.e., increase of the portion of the smaller OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY ESE 6 - 9

events). Also, equations (12) and (13) of Dieterich [1994] show that R/r (ratio of future to past seismicity rates) is nonlinearly increasing with t (change of shear stress, or the Coulomb failure increment) in a convex manner [Toda et al., 1998]. Therefore relative decreases of R due to t <0 should be more sensitive than the increases due to t > 0 for the same absolute increment. This should become more conspicuous for smaller values of As, where s is the normal stress and A is a fault constitutive parameter. The empirical evidence of the R/r curve is seen, for example, in the studies by Reasenberg and Simpson [1992] and Toda et al [1998] for the case t > 0, but is not clearly seen for the case t <0. This is because their data is mostly from background seismicity and therefore the decrease of R/r is seen only when the seismicity rate r is high enough, while an increase of R/r is easily seen, whether r is large or small, by simply counting the earthquakes. On the other hand, aftershock activity usually occurs at a high rate, so that the relative quiescence can be sensitively observed.

6.2. Anomaly of Joshua Tree Aftershock Sequence and its Mechanisms [32] First, we note that the change in the lowering of the decaying rate of aftershocks is conspicuously seen regard- less of threshold magnitude at the same time during the day of the Joshua tree main shock (compare arrow in Figure 7). This makes the determination of which part of the sequence should be considered ‘‘normal’’ more problematic, although it is clear that a change happened. To model this change, we first speculate that aseismic slip in the southern fault segment of future Landers aftershock zone, including the Eureka Peak Fault, might be triggered by the Joshua Tree rupture. The stress changes as shown in Figure 9 of King et al. [1994] and Figure 7 of Hauksson et al. [1993] support the possibility of such triggering. Indeed, Behr et al. [1994] observed aseismic afterslip of the Landers event in the Eureka Peak Fault, and suggested that the slip was triggered by the Joshua Tree earthquake. [33] With this model, say, a 10 cm aseismic slip in the shallow fraction given in Figure 8 could, in turn, inhibit the Joshua Tree aftershock activity. This is because most of Figure 6. Calculated changes in the Coulomb failure the Joshua Tree aftershocks, including off-fault ones, had stress at the depth of 3 km resulting from the assumed right-lateral focal mechanisms with nodal planes either shallow slip down to 5 km in some portion of the Hector subparallel to the main shock plane, or auxiliary nodal Mine source (white strips). We compute the Coulomb stress planes striking at high angles [Hauksson et al., 1993]. change for the depth of 3 km in an elastic half-space [Okada, 1992] by assuming a shear modulus of 20 GPa and 6.3. Is the Relative Quiescence Precursor to Another a Poisson’s ratio of 0.25 with the apparent friction rate m = Large Event? 0.4. The circles are events (M 3) after January 1993. A [34] Precursory seismic quiescences have been reported star is used to indicate the Hector Mine epicenter. Here we before a large earthquake (see Ohtake [1980] for a summa- assume that say, a 10 cm aseismic slip occurred as shown by ry). The quiescence has been observed from seismic activity black strips for cases throughout the southern fault segment itself or has been statistically examined in the ‘background from the main shock. Similar patterns can be obtained by seismicity’ based on a declustered catalog [e.g., Kisslinger, slips in the two sections where the shallow aftershocks (M 1996]. On the other hand, the relative quiescence is detected 2.0) are sparse along the black strips of the fault. in comparison to the normal activity predicted by the ETAS Resulting regions of positive Coulomb stress changes are model. The ‘conventional’ quiescence is therefore equiva- shown in light gray, negative changes are in dark gray, and lent to the relative quiescence when the background seis- the border between the two is given by white contour lines. micity data is tested against the stationary Poisson model The friction coefficient is assumed to be 0.4. Receiver faults instead of the ETAS model. Therefore we think the relative for the majority of aftershocks are assumed to have the quiescence includes the conventional quiescence in the sense orientation N30W with right-lateral strike-slip, and N40E that quiescence can be more clearly seen by using a better with left-lateral strike-slip. model of normal aftershock activity or general seismicity. ESE 6 - 10 OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY

Figure 7. Cumulative numbers of aftershocks of the Joshua Tree earthquake with various cutoff magnitudes (Mc) for the period until the end of April 1992, after the main event, in ordinary time in days. The downward arrow indicates the apparent change point of aftershock decay rate for every cumulative curve. After that time, the substantial lowering of the decay rate can be clearly seen.

[35] There are a number of hypotheses of precursory cence was not always followed by a large event [e.g., Wyss quiescence to a large earthquake based on the heteroge- and Wiemer, 1999; Ogata, 2001]. Therefore distinguishing neous strength (e.g., friction coefficients) of subfaults and whether or not an aseismic slip leads to the rupture of heterogeneous stresses within a fault, which include a asperity remains a further difficult research point in earth- bimodal asperity model [Kanamori, 1981], stress weaken- quake prediction. ing owing to a creep [Wyss et al., 1981], slip weakening [38] At present, this issue can only be described in terms [Cao and Aki, 1985] and others. Also, there are justifica- of probabilistic prediction. For example, the statistical tions for these hypotheses using computer simulations results from Japan [Ogata, 2001] suggest that the probabil- [Mikumo and Miyatake, 1983; Hainzl et al., 2000]. ity of another large earthquake becomes greater if the [36] On the other hand, it is reported that seismic activity aftershock activity of the first event shows the relative before a large earthquake can be quiet, not only in the quiescence. Specifically, the occurrence rate within a range seismic gap, but also in its wide neighborhood [Inouye, of 200 km is several times higher during the six years’ 1965; Ogata, 1992]. Moreover, even a short-term relative quiescence than would be the case if the aftershock activity quiescence within an aftershock sequence is occasionally continued normally. observed before a large aftershock whose rupture extends [39] Nevertheless, one of the major issues in this paper is beyond the source of the main event [Matsu’ura, 1986]. As to analyze seismicity using the ETAS which could provide a relevant mechanism, Kato et al. [1997] discuss a model sensitive detection of the stress changes in the analyzed for the quiescence in an extended wider area using the region, including the inhibition of the crustal relaxation simulation based on rate and state friction law, which also process due to a silent slip. We have been concerned with provides a useful scenario of geodetic changes in predicting the lowering activity of aftershocks themselves which interplate great earthquakes. comprise a major portion of an earthquake catalog, and [37] One of our scenarios for the relative quiescence in therefore should include valuable information concerning the present paper is similar to this and based on the asperity stress changes [Dieterich, 1994; Dieterich et al., 2000]. model in the sense that precursory slip around asperities applies more shear stress to the asperities, which in turn promotes the rupture of the main fault. However, on the 7. Conclusions other hand, aseismic slips in some region is not necessarily [40] On the basis of the ETAS model, we have shown that the direct precursor to a large event. Indeed, by the the Hector Mine aftershock activity has been normal relative inversion analysis [e.g., Hirose et al., 2000] based on the to the modeled decay. In contrast, although the aftershock records of strain and tilt meters or GPS time series in Japan, sequence of the 1992 Landers earthquake (M = 7.3), includ- we have observed a number of aseismic slips (silent earth- ing the 1992 Big Bear earthquake (M = 6.4) and its after- quakes; sometimes repeated in the same region) with no shocks, normally decayed up until about 6 months (the subsequent larger events in the last decades. This is consis- change point) after the main shock, the sequence showed tent with some empirical results that the (relative) quies- clear relative quiescence during the rest of the period until the OGATA ET AL.: DEPRESSED AFTERSHOCK ACTIVITY ESE 6 - 11

[41] Several possible mechanisms for the anomalous aftershock activity and the space-time features have been discussed. Among these, we are particularly concerned with the phenomenon that the substantial activity (including M5.4 event) near the Hector Mine epicenter that was triggered by the Landers event, which ceased closely before the onset of the relative quiescence of the Landers aftershocks. This could suggest inhibition of the crustal relaxation process presumably owing to an aseismic slip on the Hector Mine fault. Thus the speculative matching between the quiet volumes and the Coulomb stress shadows is applied to the aftershock activities of the Landers and Joshua Tree earthquakes by adjusting aseismic slip within the future rupture fault. The speculative slip ultimately needs to be confirmed by some geodetic records or more accumulation of matched examples elsewhere as examined in this paper.

[42] Acknowledgments. We would like to thank to Tokuji Utsu, David Vere-Jones, Takaki Iwata, Masakazu Ohtake, and Yoshihisa Iio for their useful discussions and comments. We have used the TSEIS visualization program package [Tsuruoka, 1996] for the study of hypocenter data and also the PC program MICAP-G [Naito and Yoshikawa, 1996] for spatial visualization of Coulomb stress changes. Comments by Massimo Cocco and an anonymous referee were most useful in the clarification of this paper. This study is partly supported by Grant-in-Aid 14380218 for Scientific Research (B)(2), Ministry of Education, Science, Sports and Culture.

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