Detection of anomalous seismicity as a stress change sensor

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1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 110,, doi: /2004jb003245, 2005 Detection of anomalous seismicity as a stress change sensor Yosihiko Ogata Institute of Statistical Mathematics, Tokyo, Japan Received 21 June 2004; revised 14 October 2004; accepted 7 December 2004; published 31 March [1] Anomalous seismicity such as quiescence and activation is defined by a systematic deviation of seismic activity from the predicted rate by the epidemic-type aftershock sequence (ETAS) model that represents the normal occurrence rate of earthquakes in a region indicating the empirical triggering effect by the previous events. The model is fitted to a data set of origin times and magnitudes of earthquakes or aftershocks during May August 2003 in and around northern Japan. The detected quiescence and activation relative to the predicted seismicity rate are consistent with the coseismic changes of Coulomb failure stress (CFS) in the corresponding regions, transferred from certain strong earthquakes. Few results in this paper agree with the claim that there should be a threshold value of DCFS capable of affecting seismic changes. Thus we expect that significant deviation of actual activity from the predicted rates is sensitive enough to detect a slight stress change. Furthermore, I offer a similar interpretation of the detected seismicity lowering relative to the modeled rates preceding the strong earthquakes, assuming some aseismic slips. Citation: Ogata, Y. (2005), Detection of anomalous seismicity as a stress change sensor, J. Geophys. Res., 110,, doi: /2004jb Introduction [2] Seismic quiescence has attracted much attention as one of the precursors to a large earthquake [Inouye, 1965; Utsu, 1968; Ohtake et al., 1997; Wyss and Burford, 1987; Kisslinger, 1988; Ogata, 1992, 1999]. Also, precursory activation has been studied under various names such as M8 [Keilis-Borok and Malinovskaya, 1964], precursory swarms [Sekiya, 1976; Evison, 1977] and accelerating seismic moment release [Sykes and Jaume, 1990] in addition to foreshock activity in the wider sense. On the other hand, that the stress changes due to a slip can explain the mechanism of triggering another event, has been getting more attention than ever [Reasenberg and Simpson, 1992; King et al., 1994; Stein, 1999; Toda et al., 2002]. More importantly, shear stress changes in a receiver fault system, transferred from a rupture or silent slip elsewhere, can cause seismic changes in the region [Harris and Simpson, 1998; Toda and Stein, 2002; Ogata et al., 2003; Ogata, 2004c, 2004d]. Specifically, the quiescence can be found in the shadow zone where Coulomb s failure stress (CFS; defined below) has a negative increment due to a seismic or aseismic slip nearby, especially well seen in such a region where the activity has been high, including aftershock activity itself. [3] In general, it has been difficult to recognize instances of quiescence or activation clearly in the presence of complex aftershock activity, especially in periods and areas where the activity is high. The most conventional device to avoid this sort of difficulty has been declustering algorithms Copyright 2005 by the American Geophysical Union /05/2004JB003245$09.00 that remove aftershocks and swarms from the original earthquake catalog. I am concerned, however, with the aftershocks themselves, which comprise a major portion of an earthquake catalog, and therefore should include rich information reflecting stress changes [Dieterich, 1994; Dieterich et al., 2000]. [4] On the other hand, since a sequence of aftershocks is triggered by complex mechanisms under fractal random media, it is difficult to precisely describe the transfer of stresses both within itself and to the near field. In other words, triggering mechanics within an aftershock sequence are too complex to calculate the effect of stress changes. Nevertheless, we can use statistical empirical laws as a practical solution to aftershock triggering. That is to say, fitting and extrapolating a suitable statistical model for normal seismic activity in a situation without exogenous stress changes provides us with an alternative method through which to see the seismicity changes explicitly. Thus one of the main objectives of the present paper is to show the possibility that the diagnostic analysis based on fitting the epidemictype aftershock sequence (ETAS) model fitting to regional seismicity can be helpful in detecting small exogenous stress changes. Indeed, these changes are so slight that even current state of the art methods and the geodetic records from the GPS network can barely recognize systematic anomalies in the time series of displacement records. 2. Methods [5] Consider a statistical point process model [e.g., Daley and Vere-Jones, 2003] representing the occurrence rate of 1of14

2 earthquakes l q (t) at time t that is defined by the occurrence probability of an event in such a way that ProbfNt; ð t þ DÞ ¼ 1 j occurrence historyg ¼l q ðþd t þ oðdþ for a small time unit interval D, where N(s, t) is the number of events occurring during the time interval (s, t). Rigorously, l q (t) is dependent not only on the elapsed time t (e.g., the modified Omori model), but also on the occurrence times and magnitudes of previous events in the past (e.g., ETAS model; see Appendix A). [6] Then, given a sequence of occurrence times associated with magnitudes {(t i, M i )} during an observed period [S, T], the characterizing parameters q are estimated by maximizing the log likelihood function [e.g., Daley and Vere-Jones, 2003] ln LðÞ¼ q X Z T ln l q ðt i Þ l q ðþdt: t S<t i<t S See Utsu and Ogata [1997] for the computational codes and for technical aspects. Thus we use the maximum likelihood estimate (MLE) q _ to predict the future occurrence rate l q _ (t). [7] We can see how well or poorly the estimated model is fitted to an earthquake sequence by comparing the cumulative number of earthquakes with the predicted rate offered by the estimated models. Suppose that a series of events {t 0, t 1,..., t N } is generated based on a statistical model l(t) that is the predicted occurrence rate of events per unit time (say day ). Then consider the integral LðS; tþ ¼ Z t S lðþdu u that is the theoretical cumulative number of events over the time interval (s, t). For example, L(S, t) =K{ln(t + c) ln(s + c)} in the case of the original Omori model l(t) = K(t + c) 1. See Ogata and Shimazaki [1984], Matsu ura [1986], Ogata [1988, 1992, 1999], and Utsu et al. [1995] for further examples. If we consider the time change t i = L(S, t i ) from t to t, then {t 1, t 2,..., t N } is transformed one to one to {t 1, t 2,..., t N }, which distribute uniformly random in the interval [0, L(S, T)]. [8] Therefore, if the seismicity rate l^q(t) estimated from the events in the interval [S, T] is a good approximation to the real seismicity, then we can expect not only that the function curve L(S, t) of time t and the empirical cumulative function N(S, t) of events are fairly overlapping to each other until time T, but also that the extrapolated cumulative function L(S, t) oft T offers a good prediction of the actual cumulative number of earthquakes in the period after time T. Similarly, the transformed data {^t 1, ^t 2,..., ^t N+M } from the real occurrence data are uniformly distributed on the interval [0, L(S, t)] where N =N(S, T) and M =N(T, t) if and only if the model is correct; namely, we see that the cumulative number (i.e., i) becomes linear function of the transformed time t i = ^L^q(S, t i ). Then, the cumulative curves of the transformed times of event {^t N+1, ^t N+2,..., ^t N+M } after the transformed time L(S, T) should behave as a ð1þ ð2þ ð3þ standard Brownian process with a linear trend of slope 1, from which we see that the 95% error bar, for example, is given by (t 2s, t +2s) at time t since L(S, T) where s = [t L(S, T) + {t L(S, T)} 2 /L(S, T)] 1/2, taking the model estimation error into consideration [Ogata, 1992, Appendix B]. These envelope curves of t will be plotted to show the error distribution of the cumulative curve. [9] Then, our concern is with the significant activation and lowering of the seismicity relative to that predicted by the model, which we explore by matching the pattern of Coulomb s stress changes due to a rupture or silent slip elsewhere. Changes in seismic activity rate are often reported to correlate with the calculated Coulomb stress change [e.g., Reasenberg and Simpson, 1992; Toda and Stein, 2002] DCFS ¼ Dðshear stressþ mdðnormal stressþ; ð4þ where m represents the apparent friction coefficient, and positive normal stress means the compression. Throughout the paper we set m = 0.4, so as to minimize the uncertainty of DCFS in m as discussed by King et al. [1994], with the results of DCFS patterns generally being stable against their perturbation, unless receiver faults are close to the ruptured fault. The Coulomb stress change in an elastic half-space [Okada, 1992] is calculated by assuming a shear modulus dyn cm 2 and a Poisson ratio of Positive values of DCFS promote failure and negative ones inhibit failure. 3. Data [10] The detection of earthquakes clearly depends on their magnitudes. Nearly all large shocks are detected, while smaller ones have lower detection rates. An earthquake s detection rate in a catalog may change not only with location, but also with time, due to the changing observational environments [Ringdal, 1975, 1976, 1986; von Seggern and Blandford, 1976; Cristoffersson, 1980; Lilwall, 1987; Ogata and Katsura, 1993]. Therefore seismic activity is usually studied using data of magnitudes of completely detected events. However, the portion of earthquakes smaller than the threshold magnitude for the complete data is usually substantial. Regarding effective use of data, this is quite wasteful in conducting statistical analysis of seismic activity. Since the objective in this paper is to detect changes in seismicity, I would like to use all earthquakes of determined magnitude, based on the following rationale: [11] When the magnitude-frequency distribution of detected earthquake data is time-invariant throughout a period within a given region, it can be utilized for investigation of seismic activity, even if the events are not completely detected. Also, we can ignore the varying detection rates from place to place since our objective is to see seismicity change in each local region. This time invariance is nearly satisfied by the hypocenter catalog of the Japan Metrological Agency (JMA) [Japan Meteorological Agency, 2003] during the periods where no detection rate change is specified by the JMA, with the exception of during the early periods of aftershock activities. The detection lowering of aftershocks takes place because the contamination by the seismic waves of inten- 2of14

3 Figure 1. Cumulative curves of aftershocks of 2003 Miyagi-Ken-Oki earthquake of M7.0, plotted against (left) ordinary time and (right) transformed time for respective magnitude thresholds M c, during the period of about 80 days up until 13 August 2004, and extracted from the JMA hypocenter catalog. The time is transformed by equation (3) with s = 0 for the main shock occurrence time, and l(s) is the modified Omori rate in equation (A1) estimated from the aftershock sequence with threshold M c = 3.0. See color version of this figure at back of this issue. sive activity prevents us from detecting arrivals of the waves of smaller aftershocks. [12] For example, Figure 1 includes the plot of the cumulative numbers of aftershocks of the 2003 Miyagi- Ken-Oki (Miyagi Prefecture offshore) earthquake of M7.0 with several threshold magnitudes plotted against the same transformed time defined in the previous section, Figure 1 shows that the linearity eventually holds in the cumulative number of aftershocks of each threshold magnitude, indicating that aftershocks of any size can be homogeneously detected in the corresponding period occurring sometime after the main shock, depending on the magnitude band. 4. Coseismic and Preseismic Quiescences and Activations Relative to the Predicted Seismicity [13] The results of the analysis shown in this section are based on the report [Ogata, 2004a] presented to the Earthquake Prediction Coordinating Committee in August Therefore the selected data sets here are related to the focal strong earthquakes that occurred during the period from May 2003 to that date, which attracted the attentions of the committee members present at the meeting. Two strong earthquakes occurred at close proximity during the period, in northern Japan, as shown in Figure 2. The first rupture of magnitude (M) 7.0 took place on 26 May beneath the offshore region of Miyagi Prefecture (called the 2003 Miyagi-Ken-Oki earthquake) at a depth ranging from 60 to 70 kilometers. This rupture is of thrust type due to downwardly dipping compression within the subducting slab of the Pacific plate. After this, a shallow crustal earthquake of M6.2 took place at 0713 LT (Japan time) on 26 July 2003 (38.40 N, E; 12 km depth) in the northern part of Miyagi Prefecture (Miyagi-Ken), Tohoku Figure 2. Seismicity epicenter map of earthquakes with M 2.0 down to the depth 150 km during May July 2003 in the northern Tohoku District and its vicinity and the projections to (longitude, depth) and (depth, latitude) planes. The two proximate conspicuous clusters (relatively deep A and shallow B) show the aftershocks of the 26 May Miyagi-Ken-Oki event of M7.0 and the July 26 northern Miyagi-Ken event of M6.2, respectively. The circles, inverted triangles, and diamonds in the epicenter map show that the earthquakes are in depth ranges of 0 30, 30 80, and km, respectively. 3of14

4 Table 1a. Hypocenter Locations and Source Parameters of the Strong Earthquakes a Earthquake Date Time, LT Latitude Longitude Depth, km Mag 2003 Miyagi-Ken-oki earthquake 26 May N E northern Miyagi-Ken 26 July N E earthquake (the first foreshock) 2003 northern Miyagi-Ken 26 July N E earthquake (the main shock) 2002 Miyagi-Ken-oki earthquake 3 Nov N E a Source is JMA Hypocenter Catalog. Time is Japanese local time. District, which is called the 2003 northern Miyagi-Ken earthquake. This latter event caused much more severe damage than did the previous event. Moreover, the northern Miyagi-Ken earthquake was preceded by many foreshocks that were led by the largest event of M5.5, which occurred seven hours ahead (0:13, Japan time), within the source of the main shock (38.43 N, E; 11 km depth). Their hypocenters and available fault solutions are summarized in Tables 1a and 1b. In the following paragraphs, I will describe the analyzed results concerning the regional seismicity and aftershock sequences in chronological order. [14] First of all, preceding the Miyagi-Ken-Oki earthquake, I found that clear quiescence emerged in and around the source according to Figure 3. Both Figures 3 (left) and 3 (right) of the different zones suggest that the quiescence appeared during about the same period, prior to the main shock. If we tentatively assume that a 10% aseismic slip as that of the Miyagi-Ken-Oki (offshore) main rupture took place, then the CFS should decrease by tens of millibars in the quiet volume around the source shown in Figure 3. Here we assume that the receiver fault planes are oriented according to that of the plate interface between the North American Plate and the subducting Pacific Plate, beneath the Tohoku District, i.e., (strike, dip, rake) = (180, 20, 90 ), which is not very sensitive to minor selection changes. Also, since the slip size is actually unknown, I have assumed a value of 10%, meaning that a different DCFS value is expected, scaled proportionally for different slip sizes. [15] From the quiescence in the diagrams in Figure 3, the following scenario was considered. In November 2002, approximately half a year before the Miyagi-Ken-Oki main rupture, we had the interplate event of M6.1 (see Tables 1a and 1b) in the offshore of Miyagi Prefecture, which was the largest in around the offshore area since the 1978 Miyagi- Ken-Oki earthquake of M7.5. Then, the GPS network observed coseismic and postseismic crustal movement in Tohoku inland due to the slips [e.g., Geographical Survey Institute, 2003]. I would speculate that this might also have triggered the precursory slip of the 2003 Miyagi-Ken-Oki (offshore) earthquake of M7.0 (with DCFS of about +50 mbar). Moreover, in turn, this preslip might inhibit the activity in the neighboring plate boundary region (with 20 5 mbar) as seen in Figure 3. Relevantly, the aftershock activity itself of the M6.1 event lowered substantially due to the similar stress shadow episodes [cf. Ogata, 2004b, Figure 9e]. [16] Figure 4 shows the coseismic CFS change in the shallow inland of Tohoku District by the Miyagi-Ken-Oki (offshore) event. Here, I have adopted the source model inverted by GPS geodetic displacement [Geographical Survey Institute, 2004] (see Tables 1a and 1b), and assume thrust type receivers with the optimally oriented dip angle (34.1 ) due to the apparent frictional coefficient m = 0.4 [King et al., 1994], under the east-west compressional stress field, which is due to differential movement between Eurasian and Pacific plates. Geomorphological and seismological evidence shows that the majorities of earthquake faults within the continental plate in the Tohoku inland region are of dip-slip type and strike approximately northsouth [e.g., Ichikawa, 1971]. As such the inland of Tohoku District is known to be tectonically homogeneous in the principal stress field. [17] In the Tohoku District shown in Figure 4, I am concerned with the seismicity in the inland rectangular region where the seismicity has been active and also the coseismic DCFS values of the Miyagi-Ken-Oki event are highest: the CFS there increased up to a range from 5 to 50 mbar. Thus I fitted the ETAS to the sequence of times and magnitudes of events that occurred in this region, during a period of about 8 months prior to the Miyagi- Ken-Oki earthquake, the occurrence time of which is Table 1b. Fault Solutions Earthquake Latitude Longitude Depth, km Length, km Width, km Strike Dip Rake Slip, cm Reference 2003 Miyagi-Ken-oki Kikuchi and Yamanaka [2003] earthquake 2003 Miyagi-Ken-oki N E Geographical Survey Institute [2004] earthquake 2003 northern Miyagi-Ken Kikuchi and Yamanaka [2003] earthquake (the first foreshock) 2003 northern Miyagi-Ken Kikuchi and Yamanaka [2003] earthquake (the main shock) 2003 northern Miyagi-Ken N E Geographical Survey Institute [2004] earthquake (the main shock) N E Miyagi-Ken-oki earthquake Kikuchi and Yamanaka [2003] 4of14

5 Figure 3. Seismic activity during January 1998 to about July 2003 around the plate boundary near the source of the 26 May 2003 Miyagi-Ken-Oki earthquake of M7.0. (a) Activities of interplate events, deeper than 70 km, beneath the Tohoku region. The solid curve in the geographical map shows the discrimination boundary of the interplate events on the interface between the North American and subducting Pacific plates and the intraplate events within the subducting Pacific Plate, respectively, around the depth of 70 km. The thick gray and thin black cumulative curves in Figure 3a (bottom) represents the earthquakes (M 1.7) from the whole gray colored zone and the small rectangular region of gray boundaries proximate to the rupture zone in Figure 3 (left top), respectively. (b) (bottom) Depth against time of earthquakes (M 2 in the old JMA magnitude) from the shaded rectangular region (38 40 N) shown in Figure 3b (top) in the depth range of km. Note that the aftershock volume is included in the zone in Figure 3b but not in Figure 3a. indicated by the right-hand side vertical dotted line. After the Miyagi-Ken-Oki event, the actual cumulative number of events conspicuously deviates upward from the predicted cumulative curve. The clear departure indicates that the seismicity in the region was stimulated by the event. It is confirmed that the b value increased significantly during the triggered duration of about a month in this region. This indicates that the portion of smaller earthquakes become large, which agrees with the fact that the cumulative number of earthquakes are significantly larger than the predicted by the ETAS due to the definition of the model [see Appendix A]. [18] The occurrence plot of the earthquakes in this region with respect to the transformed time in Figure 4 shows more detailed features of the seismicity after the triggered time. That is, the slope of the cumulative curve corresponds to the rate of the activity relative to that of the ETAS fitted to the events in the previous period. From this, we see in real time that the seismicity was activated not only immediately after the coseismic triggering by the Miyagi-Ken-Oki earthquake, but also during the period of the foreshock activity preceding the northern Miyagi-Ken earthquake, after which the rate of the aftershock sequence reverted back to the normal ETAS rates observed prior to the triggering onset by the Miyagi-Ken-Oki earthquake; that is, the actual and theoretical cumulative curves become parallel during the aftershock period. Thus the foreshocks and the main shock of the northern Miyagi- Ken earthquake seem to have been promoted by the Miyagi-Ken-Oki earthquake, since the mechanisms of the main shock of M6.2 and the foreshock of M5.5 [e.g., Kikuchi and Yamanaka, 2003] (see Tables 1a and 1b) are consistent with the angles of the receiver faults assumed in Figure 4. 5of14

6 Figure 4. Shallow earthquakes (H 35 km) in the yellow rectangular region during the period of August 2002 to about July 2003 before and after the Miyagi-Ken-Oki (offshore) earthquake of M7.0 (occurring at the vertical dotted line indicated by the time T J ). Epicenters (M 1.5), latitude and longitude versus time, and cumulative numbers and magnitude (top right) against the ordinary time and (bottom right) against the transformed time by the estimated ETAS model fitted to the target interval (T S, T e ) are shown. In the yellow rectangular region in the geographical map, DCFS values range mbar assuming the E-W compression thrust-type mechanism triggered by the 26 May Miyagi-Ken- Oki event of M7.0. The foreshock activity during the period from the first event of M5.5 up until the main shock of M6.2 (both occurred at 26 July 2003; i.e., T F T M ) was more active than the predicted rate by the ETAS fitted in the interval (T S, T e ). However, its aftershock activity (during T M T end in Figure 4 (right bottom) but overlapped in the right end boundary in Figure 4 (top right) seems similar to the predicted rate (i.e., similar slope in frequency-linearized time). The dotted parabola-like envelope curves show the two fold standard deviations (95% error bands) of the cumulative numbers of the transformed time: see text in section 2. See color version of this figure at back of this issue. 6of14

7 [19] The May 2004 Miyagi-Ken-Oki earthquake itself has been followed by very many aftershocks, to which the simple modified Omori formula fits nicely throughout the period. This indicates that the secondary aftershocks are not conspicuous, probably due to the deep focal volume. Indeed, once the maximum likelihood estimate (see equation (2)) of the modified Omori function has been obtained by fitting it to the events of M3.0 and larger, in the time span (0.03, 55) days after the main shock, the number of the aftershocks during the period and even after the 55th day is accurately predicted, as shown in Figure 5a. Here, the first 0.03 day period after the main shock is removed from the target interval of the analysis because of significant missing events during the (0, 0.03) day, which are due to the contamination of the seismic waves (see Figure 1). [20] Because of similar observational reasoning, complete detection of aftershocks with M1.5 and larger, holds only after about 20 days from the main shock, which is seen from Figure 1 and from the magnitude frequency distribution. Furthermore, the aftershocks for the entire range of magnitudes (M > 0) have been detected homogeneously in time, during the same period after the 20 days: the period of the homogeneous detection of events at each magnitude band can be seen from Figure 1 or from the more sophisticated method of modeling the evolution of magnitude frequency distributions with time [cf. Ogata and Katsura, 1993]. Therefore the modified Omori function is fitted to the occurrence data in the time span (20, 55) days after the main shock to predict the occurrence rate of aftershocks for the extended period. [21] According to Figure 5b, the actual cumulative numbers followed the predicted, up until the northern Miyagi-Ken earthquake of M6.4 occurred in 60.5 days since the Miyagi- Ken-Oki main shock (see Figure 2 for the locations). After the northern Miyagi-Ken event, however, the actual cumulative numbers deviate downward from the predicted, as shown in Figure 5b. One may suspect that the detection capability of earthquakes might have lowered due to observational difficulties in determining hypocenters of small events by the seismogram disturbance from the neighboring source. However, the network stations of the JMA, including those of universities and Hi-net, are dense enough to avoid such confusion. Indeed, in the magnified cumulative curve of the M >= 3 case in Figure 5a, the corresponding gap appears immediately after the northern Miyagi-Ken event but it remains within an error bounds. Furthermore, if we look at the cumulative numbers of almost all the detected aftershocks with M > 0 in Figure 6, the lowering already started several days before the northern Miyagi-Ken earthquake. Furthermore, the lowest frequency of the aftershocks per day (i.e., slope of the cumulative number) for both M >= 1.5 and M > 0 cases was not attained during the first day immediately after the main shock, as seen from in the magnified cumulative curve in Figures 5b and 6, respectively. It seems that the significance becomes clearer as the sample size increases. [22] The northern Miyagi-Ken ruptures (the first foreshock of M5.5 and the main shock of M6.2) coseismically decreased the CFS in and around the aftershock volume of the Miyagi-Ken-Oki earthquake by about 5 mbar, assuming that the majority of the aftershock focal mechanisms are similar to that of the Miyagi-Ken-Oki main shock. Here, both the slip fault models of the northern Miyagi-Ken and the Miyagi-Ken-Oki earthquakes rely on the solutions by the geodetic displacement data including GPS records [Geographical Survey Institute, 2004, see Table 1]. The other solutions due to Kikuchi and Yamanaka [2003, see Table 1] by seismic waveform inversion also imply the similar DCFS values. Moreover, the observed quiescence in Figure 6 preceding the northern Miyagi-Ken earthquake is likely triggered by a smaller CFS decrease than the coseismic one, if a preseismic slip had occurred within or around the main rupture zone. [23] The northern Miyagi-Ken earthquake of M6.2 took place at 0713 LT (Japan time) 26 July 2003 in the southeast corner of the rectangular region in Figure 4. Figure 7 shows the space-time plot of the foreshocks, the main shock and aftershocks. Incidentally, it should be noted that, due to the space-time plots, the immediate aftershocks are sparsely distributed in the middle part around N, where the slip size in the main fault is found to be the largest (i.e., the asperity) owing to the waveform inversion [e.g., Hikima and Koketsu., 2004]. [24] First, I implement analyses of the aftershock activity. Figure 8a show the goodness of fit of the Omori function, while Figure 8b shows that of the ETAS model. The Akaike s information criterion (AIC) [Akaike, 1974] indicates that the ETAS model offers a better fit than the Omori formula by a difference of 5.7, which is approximately equivalent to adopting a 99.5% confidence to reject the modified Omori fit by the log likelihood ratio (c 2 ) test. This demonstrates the fact that the aftershock sequence itself includes further clusters triggered by aftershocks as shown in the estimated intensity rate changes in Figure 8b. [25] Then, consider the foreshocks that are initiated by the first event of M5.5 that took place at 0:13am (Japan time) 26 July At first, these events were considered as aftershocks of the M5.5 event, and the JMA announced the probability forecast of large aftershocks using the modified Omori function. Figure 9a shows the ETAS model fitted to the events in the whole time span up until the main shock of M6.2, while Figure 9b assumes that the seismicity pattern changed at a time (actually, about 3 hours before the main shock). If a set of different models for the divided periods before and after the suspected point of time offer a significantly better fit than a single model throughout the whole period, then the time point at which the set of two models provides the best fit is called the change point [Ogata, 1992, 1999]. That is, I fit the ETAS model for the first period and the stationary Poisson model for the second period to search for the most likely time of the change point and also to examine the significance of the change. The modified AIC [cf. Ogata, 1992, 1999] indicates that the latter case of the twofold model offers a better fit, by a difference of 4.3, even taking into account the model complexity, including the location of the change point. [26] Thus, during the last 3 hours of this interval preceding the main shock, we had fewer events than predicted (extrapolated) by the ETAS model fitted for the first period, which we may call the relative quiescence. It is very likely that the M5.5 fore rupture promoted the M6.2 main event (DCFS = +400 mbar at the main shock s hypocenter) and 7of14

8 Figure 5. Analyzed results of the aftershock sequences with (a) M 3 and (b) M 1.5 of the 2003 Miyagi-Ken-Oki earthquake of M7.0. The aftershocks are applied by the modified Omori formula for respective target time intervals (T s, T e ) = (0.03, 55) days and (20, 55) from the main shock of the 28 July 2003 to extrapolate the theoretical (predicted) curves. Such dates are indicated by the vertical dotted lines. The time T J = 60.5 days indicate the occurrence time of the northern Miyagi-Ken earthquake of M6.2, and the triggered coseismic quiescence is seen after that in Figure 5b. The red smooth curves show the theoretical or predicted cumulative number of aftershocks calculated by the integration (see equation (3)) of the modified Omori function in (A1). The red curve for the M 1.5 case (Figure 5b) is shifted down to adjust the same value as the real cumulative number at the 20 days from the main shock. We see that the aftershocks have occurred as predicted after T e = 55 days. Figure 5 (middle) shows an equivalent view, in which the time is transformed by the predicted cumulative curve so that the transformed times appear uniform if the model is correct (see section 2). Figure 5 (bottom) shows the magnified corresponding parts in Figure 5 (middle); see Figure 4 for the dotted parabola-like envelope curves. See color version of this figure at back of this issue. 8of14

9 Figure 6. (left) Aftershock sequence (M > 0) of the 2003 Miyagi-Ken-Oki earthquake of M7.0. The modified Omori formula is applied to the aftershocks with M > 0 in the target interval (T s, T e ) = (20, 55) days from the main shock to extrapolate the theoretical (predicted) curves. The time T J = 60.5 days represents the occurrence of the northern Miyagi-Ken earthquake of M6.2, and the preseismic quiescence is suspected before the main shock. (right) Magnified corresponding parts in Figure 6 (left). See Figure 4 for the dotted parabola-like envelope curves. See color version of this figure at back of this issue. presumably also the precursory aseismic slip of the main M6.2 event. If we assume a precursory aseismic slip of 10% size of the main rupture, then, in turn, the CFS over the foreshocks area should decrease by several hundreds of millibars, based on the mechanisms by Kikuchi and Yamanaka [2003, see Table 1] assuming that the foreshock events have predominantly similar mechanism to the first foreshock event of M5.5. Then, such stress decrease may have depressed the natural decay of the aftershock (foreshock) activity of the M5.5 event. Indeed, from the space-time plot in Figure 7, the seismic gap before the time of and in the region around the main shock is conspicuous. 5. Discussion [27] In either case of the original or declustered catalog, the conventional seismicity quiescence of the occurrence data is tested against the uniformly randomness representing the normal background seismicity. This is nothing but the quiescence of the background activity relative to the stationary Poisson process. It has been shown that ordinary seismicity and even a single sequence of aftershocks is generally well represented by the ETAS model [e.g., Ogata, 1988; Guo and Ogata, 1997]. Therefore the relative quiescence should be more sensitive than the conventional quiescence in the sense that quiescence can be more clearly seen by using a better model of normal aftershock activity or general seismicity. On the other hand, we should be careful about the heterogeneity of the seismicity pattern and stress field in choosing a seismic region. Namely, when we apply the ETAS model to the data that includes distinctive seismicity patterns, especially from a wide region, the estimated ETAS parameters only provide some averaged values unless the models of spatially or temporally distinctive parameter values are applied [cf. Ogata, 2001b, 2004c]. Therefore the ETAS model can usually be applied to the aftershocks or swarms in a narrow region [e.g., Ogata, 2001a]. [28] Few results in the present manuscript agree with the claim that there should exist a threshold value of DCFS 9of14

10 Figure 7. (top) Epicenters of foreshocks, the main shock of M6.2 (the largest circle) and aftershocks in northern Miyagi-Ken (prefecture), and (bottom) latitude versus time plot during whole day of 26 July The first and second largest circles indicate the main shock and the first foreshock, respectively. It is shown that the main contribution of the relative quiescence in foreshocks relative to the predicted rate is in the gap around the epicenter of the main rupture. value capable of affecting seismic changes. Indeed, the activation may depend on how close the fault is to the critical point of failure prior to the main event. Also, quiescence may depend on how active the seismicity is before it falls into a stress shadow. [29] We have seen that a small size of CFS increment down to the order of millibars can trigger activation and lowering of microseismicity. This is also supported by the Dieterich s seismicity rate equation [Dieterich, 1994; Toda and Stein, 2002] Rt ðþ¼ r exp DCFF 1 As n exp t ; ð5þ þ 1 _t where A is a fault constitutive parameter, s n is the normal stress, and _t is shear stressing rate. For example, about 70% of seismicity reduction R(t)/r is expected during the first few years by a suitable selection of parameters such as DCFS = 5 mbar, As n = t a _t = 15 mbar and _t = 5 mbar yr 1, and t a (=3 years) is the aftershock duration. Thus we expect that aftershock and general seismic activity relative to the modeled rate can be sensitive enough to detect a slight stress change. [30] Compared to the relative quiescence, the relative activation is not very sensitive with regards to detection by the ETAS. This is because the earthquakes (or large aftershocks) triggered by the activation further increase the CFS, which locally surpasses the original CFS increment from the external source. Therefore the exogenous effect is hard to see in the transformed time, since the ETAS model takes account of the internal triggering of clustered events depending on the magnitude. However, if the b value of the Gutenberg-Richter s magnitude frequency significantly increases (i.e., increase of the portion of the smaller events), we can observe the relative activation, as has been shown in the coseismic triggering effect in the Tohoku inland by the 2003 Miyagi offshore earthquake (see paragraphs 16 18). Another reason for the reduced sensitivity in detection of relative activation is that the ratio of future to past seismicity rates R(t)/r in (5) for the positive Coulomb failure increment is less effective than the negative increment. This should become more conspicuous for smaller values of As [cf. Ogata, 2004e]. [31] The empirical plots of R/r due to the coseismic change are given by Reasenberg and Simpson [1992] and Toda et al. [1998] and are well correlated with the R/r curve predicted by Dieterich s equation for the case of positive DCFS, although the correlation is not clear for the negative DCFS case. This is because their data is mostly from background seismicity that has been low prior to the triggering events. Namely, an increase of R/r is easily seen when r is low, while a decrease of R/r is clearly seen when the past seismicity rate r is high enough. In particular, the relative quiescence can be sensitively observed in a high rate aftershock sequence. Thus we expect that aftershock and general seismic activity relative to the modeled rates is sensitive enough to measure a slight negative stress change. This also explains the fact that seismic activity before a large earthquake can be quiet not only in the seismic gap, but also in its wide neighborhood [Inouye, 1965; Ogata, 1992; Kato et al., 1997]. [32] The sequence of events before and after the northern Miyagi-Ken earthquake is a typical case where we should be concerned with predictive discrimination of foreshocks, or with the possibility of the so-called doublet earthquakes [Oike, 1980]. On the basis of the ETAS analyses of more than a hundred aftershock sequences in and around Japan, Ogata [2001a] derived the probability assessment of having a proximate earthquake of similar size to or larger than that of the preceding main shock. That is to say, the rate is several times higher in the case when the relative quiescence in the aftershock sequence had been observed as compared to the case when the aftershock sequence decays normally. [33] In this paper I have attributed some of the stress shadows to aseismic slip episodes. In order to reinforce this argument, there needs to be independent evidence presented that these aseismic slip episodes are actually happening. Very few report is seen regarding this argument, although such an example is given by Ogata [2004c], who discusses the seismic anomalies in relation to the aseismic slip beneath the Lake Hamana-Ko, Tokai district, Japan, which has been detected by GPS records [e.g., Geographical 10 of 14

11 Figure 8. Aftershocks (M 2.5) of the northern Miyagi-Ken earthquake of M6.2. Cumulative number and magnitude against the (top) ordinary time and (bottom) transformed time by the applied model. The modified Omori model (Figure 8a) and the ETAS model (Figure 8b) are applied, and the superimposed thin blue and red curves are theoretical intensity function of aftershocks and expected cumulative number, respectively. The better fit of the ETAS model indicates the existence of further clusters within the aftershock sequence. See color version of this figure at back of this issue. Survey Institute, 2004, pp ]. It will be a further research subject to quantify the link between the ETAS analysis and the stress changes based on the accumulation of the cases additionally using the available focal mechanisms of events, which might hopefully enhance the above mentioned probability of discrimination. [34] An earthquake prediction scenario from the implication of the relative quiescence can be based on the asperity hypothesis [Kanamori, 1981] in the sense that precursory slip around asperities applies more shear stress to the asperities which promotes the rupture of the main fault [e.g., Ogata et al., 1996]. On the other hand, aseismic slips in a particular region are not necessarily a precursor to the large event. Indeed, we have observed a number of aseismic slips, or silent earthquakes that are repeated in the same region, with no subsequent large events in the last decades. This is consistent with some empirical results suggesting that (relative) quiescence is not always followed by a large event. Therefore identification of an aseismic slip leading to the rupture of an asperity remains a further difficult research theme in earthquake prediction. At present, this issue can only be described in terms of probabilistic prediction as stated above, and we should enhance its efficiency by investigating stress changes for the identification of precursory slips. 6. Conclusion [35] The paper proposes a method of exploratory data analysis using the ETAS model, and provides examples of how this method might indicate changes in stress. The ETAS model represents the empirical regional occurrence rate of earthquakes as a function of previous origin times and magnitudes, enabling us to detect the period during 11 of 14

12 Figure 9. Foreshock sequence (M 1.5) for 7 hours duration till the main shock of M6.2 initiated by the earthquake of M5.5 occurred at the northern Miyagi-Ken (prefecture): their cumulative numbers and magnitudes against (top) ordinary time and (bottom) transformed time by the ETAS model. (a) Fit of the single ETAS model throughout the whole period of foreshocks and (b) best fit of the two models (ETAS for the former and stationary Poisson for the latter) for the two periods divided at the possible change point. The vertical dotted lines at the times T s, T e, and T c show that models are fitted to the events in the target period (T s, T e ) and that the time T c is the possible change point. In this case, the time T s is 0.01 day after the first event of M5.5, and T e is the occurrence time (about seven hours after the first event) of the main shock of M6.2. The case in Figure 9b is not negligible even taking account of the model complexity including the searched change point. We see the relative quiescence after about T c = 4 hours. The red solid curve and line in Figure 9b represent the theoretical cumulative curves due to the estimated ETAS model for the first period (T s, T c ); see Figure 4 for the dotted parabola-like envelope curves. See color version of this figure at back of this issue. which the actual occurrence rates deviate systematically from the modeled rates. [36] A number of focal examples from the seismic activities during May August 2003 in northern Japan have been shown. Then, the activation and lowering of the seismicity relative to the predicted rates by the model have been well matched with the patterns of the coseismic and preseismic Coulomb s stress changes due to the ruptures and possible aseismic slips, respectively. [37] These results have led us to a summarized observation that even a small size of the CFS changes of the order of millibars can trigger such lowering and activation, which is also supported by the seismicity rate equation of Dieterich [1994]. [38] Thus the anomaly in seismic activity, including the case of a single aftershock sequence relative to the model s rates, can sensitively reveal small stress changes caused by seismic or aseismic slips. Such a seismic anomaly could be a highly sensitive measure for exogenous stress changes in a wide region, comparable to, or possibly more sensitive than, various geodetic measurements. Thus such studies using the ETAS diagnostic method need to be carried out more comprehensively so as to quantify any link between the analysis and the stress changes, and eventually to 12 of 14

13 explore the difficult task of identifying and estimating such slips. Appendix A: Epidemic-Type Aftershock Sequence (ETAS) Model [39] The typical aftershock decay is represented by the modified Omori function [Utsu, 1961], l q ðþ¼ktþ t ð cþ p ; ðk; c; p; constantþ; ða1þ initiated by the main shock at the time origin t =0.In general, the inverse power trend holds for quite a long period in the order of some tens of years or more, depending on the background seismicity rate in the neighboring area [Utsu, 1968]. Utsu [1970] further found that in many cases, aftershock activity is multiple in such a way that l q ðþ¼ t X fm;t m<tg K m ðt t m Þ pm ; ða2þ where a particular sequence {t m } represents the occurrence times of triggering events of secondary aftershocks, and the sum is taken for the trigger event m which satisfy t m < t. See Ogata [1983], Ogata and Shimazaki [1984], Matsu ura [1986], and Ogata [2001b] on the procedure for the identification of triggering events {t m } and the estimation of the parameters in (A1) and (A2). [40] In case of general seismic activity, the trigger events, of course, include the main shocks. The restricted trigger model [Ogata, 1988, 2001b] is similar to the equation (A2) except for a constant l 0 added to the right hand side of the equation (A2) for the rate of background seismicity. In the original trigger model suggested by Vere-Jones and Davies [1966] an aftershock never triggers its own aftershock activity and magnitudes of individual events are not considered, so that the size of the aftershock sequence is not related to the main shock magnitude. Furthermore, it allows all possible choices of events for the triggering events, which leads to a difficulty in calculating the likelihood, due to combinatorial complexity. Therefore identification of the trigger events is inevitable for the maximum likelihood estimation procedure of the trigger models [cf. Ogata, 1988, 2001b]; otherwise the approximate spectral likelihood for the model is used instead [Hawkes and Adamopoulos, 1973]. [41] The epidemic-type aftershock sequence (ETAS) model [Ogata, 1988, 1989] extends these models to the case where any shocks j that occurred at time t j trigger their offspring events more or less, so that the seismicity rate at time t is given by the linear superposition of the aftershock effect in the past in such a way that l q ðþ¼l t 0 þ f X j;t j<t g p; K j t t j ða3þ where the sum is taken for all shocks j occurred before time t, and the coefficient K j for each shock j contributes to the size of the corresponding offspring, or aftershocks in wide sense. The constant l 0 (so-called the background seismic activity) represents the occurrence rate of the factor that cannot be explained as the aftershock effect from the past events whose record is available in the data. The crucial point of the present model is that the parameter K j is dependent on its magnitude M j as well as the cutoff magnitude M c of the data set, according to the following exponential function form K j ¼ K c e aðmj McÞ : ða4þ [42] One piece of evidence for the function form is the empirical formula obtained by Utsu and Seki [1955] on the linear relation between logarithm of aftershock area and magnitude M of the main shock. This relation suggests that the number of aftershocks is roughly estimated by the form in (A4). Also, see Utsu [1970] for further collateral evidence of the relation. Note that K c represents the standardized quantity that measures the productivity of the aftershock activity during a short period right after the main shock, used in forecasting the aftershock probability [cf. Reasenberg and Jones, 1989]. Yamanaka and Shimazaki [1990] discuss the distinction of the proportional constant in (A4), or K c, between intraplate and interplate earthquakes. See Utsu et al. [1995] for the summarized development of the models. [43] Acknowledgments. I have used the TSEIS visualization program package [Tsuruoka, 1996] for the study of hypocenter data and also used the PC program MICAP-G [Naito and Yoshikawa, 1996] for spatial visualization of Coulomb stress changes. Comments by Mark Bebbington, Karen Felzer, and Sandy Steasy were most useful in improving the original version of the paper. This study is partly supported by Grant-in- Aid for Scientific Research (B2), Ministry of Education, Science, Sports and Culture. References Akaike, H. (1974), A new look at the statistical model identification, IEEE Trans. Automat. Control., AC-19, Cristoffersson, A. (1980), Statistical models for seismic magnitude, Phys. Earth Planet. Inter., 21, Daley, D. J., and D. Vere-Jones (2003), An Introduction to the Theory of Point Processes, vol. 1, 2nd ed., Springer, New York. Dieterich, J. (1994), A constitutive law for the rate of earthquake production and its application to earthquake clustering, J. Geophys. Res., 99, Dieterich, J., V. Cayol, and P. Okubo (2000), The use of earthquake rate changes as a stress meter at Kilauea volcano, Nature, 408, Evison, F. F. (1977), The precursory earthquake swarm, Phys. Earth Planet. Inter., 15, Geographical Survey Institute (2003), Crustal movement in the Tohoku District, Rep. Coord. Comm. Earthquake Predict., 70, Geographical Survey Institute (2004), Crustal movement in the Tohoku District, Rep. Coord. Comm. Earthquake Predict., 71, Guo, Z., and Y. Ogata (1997), Statistical relations between the parameters of aftershocks in time, space and magnitude, J. Geophys. Res., 102, Harris, R. A., and R. W. Simpson (1998), Suppression of large earthquakes by stress shadows: A comparison of Coulomb and rate-state failure, J. Geophys. Res., 103, 24,439 24,451. Hawkes, A. G., and L. Adamopoulos (1973), Cluster models for earthquakes: Regional comparisons, Bull. Int. Stat. Inst., 45(3), Hikima, K., and K. Koketsu (2004), Source processes of the foreshock, mainshock and largest aftershock in the 2003 Miyagi-ken Hokubu, Japan earthquake sequence, Earth, Planets and Space, 56, Ichikawa, M. (1971), Reanalyses of mechanism of earthquakes which occurred in and near Japan, and statistical studies on the nodal plane solutions obtained, , Geophys. Mag., 35, Inouye, W. (1965), On the seismicity in the epicentral region and its neighborhood before the Niigata (in Japanese), Q. J. Seismol., 29, Japan Meteorological Agency (2003), The Annual Seismological Bulletin of Japan for 2003, Tokyo. 13 of 14

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