Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan

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1 25 9 Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan Takashi Kumamoto 1 and Yukiko Hamada 1 Abstract When calculating the probability of future earthquake occurrence, it is common to apply stochastic models to paleoearthquake data collected from fault trenching surveys. The Headquarters of Earthquake Research Promotion (HERP, 2001) concluded that in terms of fiscal meaning, stability, and ease of comprehension, the best of the stochastic models is the Brownian Passage Time (BPT) model. This model requires two parameters: average recurrence interval and aperiodicity of the mean period between events (coefficient of variation). HERP (2001) derived a value of 0.24 for the common aperiodicity from four paleoearthquake data sets, which is roughly half the value of 0.50 derived by Ellsworth et al. (1999) from 37 worldwide earthquake records. The purposes of this study are (1) to construct a paleoearthquake database of active intraplate faults in Japan based on trenching results conducted after 1995 and (2) to evaluate aperiodicity using the BPT model and this database. Common aperiodicity ( C ), calculated from 23 paleoearthquake data sets in this study, is 0.49, approximately the same as the result of Ellsworth et al. (1999). This study shows no distinct relations between aperiodicity and active fault type, fault activity, recurrence interval derived from trench results, or distance between trench site and the center of the seismogenic fault system. There is a small positive correlation between the aperiodicities in this study and the number of neighboring faults within 30 km of trench sites. This might be consistent with the BPT model, in that aperiodicity of a given fault can be affected by seismic activity of nearby earthquakes, which alters the recurrence interval and future earthquake probability of the fault under consideration. Probabilistic seismic-hazard assessment evaluates the frequency and/or intensity of future earthquakes by applying statistical methods to past earthquake catalogues and active-fault data sets. This can provide probabilistic seismic-hazard maps, which can be used in the prediction and prevention of earthquake-related disasters. Three types of fault data are used in conducting probabilistic seismic hazard assessment: (1) location, (2) magnitude, and (3) occurrence probability of future earthquakes. Given that earthquakes that cause severe damage are generally of magnitude 7 or greater and are generally characterized by surface ruptures, the location of future large onshore earthquakes can be determined from an active-fault database that tabulates tectonic landforms created by repeated surface ruptures. Empirical relations between the length of active faults and earthquake magnitude and between intensity and attenuation are also included in such assessments. Calculating the probability of a future earthquake commonly involves application of stochastic processes to paleoearthquake results from trenching surveys [e.g., The Headquarters of Earthquake Research Promotion (HERP), 2001], in light of the fact that the recurrence interval of any given seismogenic fault is independent and follows a predictable distribution. Analysis of Japanese paleoearthquake data reveals that Graduate School of Natural Science and Technology, Okayama University

2 10 Takashi Kumamoto and Yukiko Hamada 2005 after the 1989 Loma Prieta earthquakes (WGCEP, 1990), eventually resulting in a new active-fault data set (WGCEP, 1995, 2003). In the case of Japan, Suzuki and Matsuo (1995) provided a probabilistic estimation of the Kuwana fault based on paleoearthquake results for the Tanna, Atera, and Atotsugawa faults and the method of Nishenko and Buland (1987). In the context of creating a long-term conditional (time-dependent) seismic-hazard map for intraplate earthquakes in Japan, Kumamoto (1999) showed that compiling paleoearthquake results yields data sets indicating a recurrence interval for each fault that is quasiperiodic rather than random. The resulting distributions of recurrence ratios provide a basis for determining the Weibull probability density function. This analysis suggests that the application of conditional estimates for specific Frequency histogram for T/T ave values. T is the time interval between events taken from median value of the bounding ages provided for each event. T ave is the averaged interval of T at each trench site in which more than two recurrences are known in trenching results. recurrence intervals of active faults have statistically significant periodicity. This study allows the recurrence period and average recurrence interval of an active fault, derived from a single trench, to be plotted as normalized ratios; thus, a fault with perfect periodicity would have a ratio of 1.0. The resulting values range from 0.28 to 1.93 (Figure 1) though do not have a uniform distribution. Therefore, earthquake recurrence is neither completely periodic nor random, the average recurrence interval and variance are statistically meaningful. Moreover, the probability of future earthquakes can be evaluated stochastically, if earthquake recurrence can be assumed to be based on time since the latest seismic event (renewal process). Nishenko and Buland (1987) provide an example of stochastic evaluation based on the earthquake renewal process. They made a probabilistic seismic-hazard map of peri-pacific interplate earthquakes using the Weibull model and normalized ratios between recurrence period and averaged recurrence for specific rupture areas. In the case of California, where many damaging earthquakes have occurred in the last century, the data used in constructing conditional seismic-hazard maps has a log-normal distribution [e.g., Working Group on California Earthquake Probabilities (WGCEP), 1988]. The results were later revised faults is preferable to assuming that recurrence intervals are random. A more detailed analysis of the stochastic model is provided by HERP (2001). In terms of stochastic models, this report uses the Poisson model, with Log-Normal, Gamma, Weibull, Double-Exponential, and Brownian Passage Time (BPT) renewal process models, and parameters for average recurrence interval and elapsed time since the latest event. The five stochastic models were applied, using these two parameters, to four paleoearthquake data sets using the Akaike Information Criteria (AIC) and resulted in no distinct differences among the five renewal processes. Among these stochastic models, however, HERP (2001) concluded that the BPT model gives the best results in terms of physical meaning, stability, and ease of comprehension. The BPT model uses two parameters: average recurrence interval ( ) and aperiodicity of the mean period between events (coefficient of variation, ). Using 37 earthquake data sets from around the world, Ellsworth et al. (1999) arrived at an estimated value of 0.5 for common aperiodicity in the BPT model. In contrast, HERP (2001) calculated a provisional value of 0.24 for the common aperiodicity, based on paleoearthquake data sets for four active faults, and demonstrated, using the AIC comparison, that this value of 0.24 is statistically more applicable to individual aperiodicity (the Atotsugawa fault, 0.165; the Atera fault, 0.293; the Tanna fault, 0.213; and the Nagano-bonchi seien fault, 0.250). All four of these active faults, however, are known to

3 25 Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan 11 have high slip rates (>1 mm/year; Research Group for Active Faults of Japan, 1991), and so this provisional common value of 0.24 may not be applicable to other active faults in Japan. The report by HERP (2001) leaves this issue as a problem awaiting solution. Thus, the objectives of this study are (1) to construct a paleoearthquake database for active intraplate faults in Japan, with special focus on trenching results conducted after 1995, and (2) to evaluate the aperiodicity for the BPT model using this database. Several surveying methods have been used in investigating earthquake occurrence histories of active faults, such as trench excavation, boring surveys, and seismic reflection surveys. In comparing the reliability of these methods, it is clear that trenching surveys provide the best data, because trench location is based on tectonic landforms, and the active-fault plane itself is obvious on the excavated surfaces. Many trench surveys have been conducted on active faults in Japan, especially in the time since the Hyogo-ken nambu earthquake, providing one of the highest-density and highest-quality trenching data sets in the world. At present, long-term probabilistic seismichazard assessment of active intraplate faults in Japan, which have recurrence intervals of thousands or tens of thousands years, is accomplished almost exclusively by use of trench survey results. Constructing a trench database is considered to be essential to probabilistic seismic-hazard assessment. The application of this data, however, must be undertaken with an understanding of the relative certainty of events and the error margins in calibrating radiocarbon dates. With this in mind, an active-fault trench database was compiled from 15 reports, listed below, published since 1995 (Kumamoto and Nakata, in preparation). 1. Geological Survey of Japan, 1996, Preliminary report on active fault researches in the 1995 fiscal year, Geological Survey of Japan Open-file Report, No. 259, 98p. (J) 2. Geological Survey of Japan, 1997, Preliminary report on active fault researches in the 1996 fiscal year, Geological Survey of Japan Open-file Report, No. 333, 140p. (J) 3. Geological Survey of Japan, 1998, Interim report on active fault and paleoearthquake researches in the 1997 fiscal year, Geological Survey of Japan Interim Report, No. EQ//98/1, 188p. (JE) 4. Geological Survey of Japan, 1999, Interim report on active fault and paleoearthquake researches in the 1998 fiscal year, Geological Survey of Japan Interim Report, No. EQ//99/3, 309p. (JE) 5. Geological Survey of Japan, 2000, Interim report on active fault and paleoearthquake researches in the 1999 fiscal year, Geological Survey of Japan Interim Report, No. EQ/00/2, 235p. (JE) 6. Geological Survey of Japan/AIST, 2001, Annual report on active fault and paleoearthquake researches, No.1, 380p. (JE) 7. Geological Survey of Japan/AIST, 2002, Annual report on active fault and paleoearthquake researches, No.2, 358p. (JE) 8. Geological Survey of Japan/AIST, 2003, Annual report on active fault and paleoearthquake researches, No.3, 364p. (JE) 9. Science and Technology Agency, 1997, Proceedings of the results of a grant-in-aid for active fault researches in the 1995 and 1996 fiscal year, 241p. (J) 10. Science and Technology Agency, 1998, 1st Proceedings of the results of active fault researches, 344p. (J) 11. Science and Technology Agency, 1999, 2nd Proceedings of the results of active fault researches, 356p. (J) 12. Science and Technology Agency, 2000, 3rd Proceedings of the results of active fault researches, 236p. (J) 13. Ministry of Education, Culture, Sports, Sciences and Technology, 2001, Proceedings of the results of active fault researches and subsurface structure under sedimentary plain researches in 2001, 269p. (J) 14. Ministry of Education, Culture, Sports, Sciences and Technology, 2002, Proceedings of the results of active fault researches and subsurface structure under sedimentary plain researches in 2002, 237p. (J) 15. Ministry of Education, Culture, Sports, Sciences and Technology, 2003, Proceedings of the results of active fault researches and subsurface structure under sedimentary plain researches in 2003, 276p. (J) Data compiled in the database follow those of Nagai and Ota (1999): fault system and fault name, excavation location, excavation year, event number, event age ( 14 C age and calibrated age), event certainty and standard of judgment, recurrence interval, slip rate, slip amount per event, slip type, and reference information. In order to develop a geographic information system database based on 1:25,000

4 12 Takashi Kumamoto and Yukiko Hamada /4/15). Calibrated ages were read where the 14 C dates plot on the INTCAL98 calibration curve for year B.P., with one standard deviation (expressed in italics in Table 1). Event ages beyond the calibration range of INTCAL98 were excluded from the analysis. In order to estimate the average recurrence interval ( ) and aperiodicity of the mean period between events ( ) for the BPT model, those trench records that include three or more paleoearthquake events were extracted from the trench database (Table 1). Paleoearthquake events of uncertain age (trench records such as the event occurred 1,200 years B.P. or later or the event occurred before 2,000 years B.P. ) were omitted from later calculations. Total 23 Map showing the distribution of active intraplate faults in Japan and trench excavation sites in 15 reports listed in the document (Kumamoto and Nakata, in preparation). scale topographic maps and the active-fault database (Nakata and Imaizumi eds., 2002), trench location (longitude and latitude) was determined from trench record figures (Figure 2). Errors in trench location are, therefore, a function of the scale and/or distinctness of the original figures, and so the precision of trench location is not uniform in the database. Data gathered in future trenching surveys should include global positioning system-based locations. One of the more difficult items to assess is the certainty of each event. Comparing faults depicted in trench record figures using the criteria of Watanabe (1996) was impossible due to the inconsistency of standards and figure scales among trench records. Instead, certainty is simply expressed as either high (A) or low (B), based on statements in the trenching records. In cases where certainty is not noted in the trenching records, it is assessed as A (high) for those cases where strata are shown to be cross-cut by faults in trench figures and B (low) in all other cases. Another problem in constructing the database is event age. Some trench records provide only 14 C dates, whereas others indicate calibrated ages, with or without original 14 C dates. If the uncalibrated dates were excluded, the database would be too small for statistical analysis to be meaningful, those 14 C dates were converted to calibrated ages using CALIB4.4 software, developed by the Quaternary Isotope Lab, University of Washington ( trench data sets, including the compilation by Kumamoto (1999), were used in calculating the parameters of the BPT model for intraplate earthquakes in this study. The calculation follows the method of HERP (2001), and the best parameters are derived using maximum-likelihood estimation. According to this procedure, the average recurrence interval ( ) and aperiodicity of the mean period between events ( ) of the BPT model are calculated as follows: E [T i ] 2 E [1/T] where T i is ith interval of an individual trench record, and the operator E[ ] denotes the arithmetic mean. When calculating T i from the trench database where event ages have some uncertainty, such as years B.P., the median value is used. The aperiodicity of the mean period between events ( ) ranges from 0.07 for the Okamura fault to 0.80 for the Agematsu fault (Figure 3). Next, the common aperiodicity ( C ) is calculated from individual aperiodicity ( i ) using a weighted average of the number of events in the ith trench record (Ni): c2 = ( 12 N N i2 N i ) / (N 1 + N N i ) 3 The common aperiodicity ( c ) for the 23 paleoearthquake data sets in this study is The individual aperiodicity ( i ) and the common

5 25 Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan 13 (2001) but approximately the same as the 0.50 value determined by Ellsworth et al. (1999) from 37 worldwide earthquake records. One of the possible reasons is that the activities (slip rates) of the four active faults used by HERP (2001) are high ( 1 mm/year), and fault length, except the Tanna fault is over 40 km. According to the fault evolution model of Wesnousky (1988), planes of active faults with long length and high slip rates are comparatively smooth as a result of repeated slippage and show characteristic earthquake recurrences. This might account for the low aperiodicity calculated by HERP (2001). In contrast, the data set of 23 trench in this study records from faults with a variety of lengths and slip rates includes faults at various stages of fault evolution, yielding a higher aperiodicity value. This difference in aperiodicity highlights the Frequency histogram for aperiodicity of the mean period between events ( ) for the BPT model derived from 23 trench results (Table 1). aperiodicity ( c ) are compared using the AIC procedure (HERP, 2001) to see which parameter best explains the data sets. The AIC for individual aperiodicity ( i ) is and for common aperiodicity ( c ) is This means that common aperiodicity ( c ) characterized the data sets slightly better, although the difference is not statistically meaningful. The common aperiodicity ( c ) of 0.49 in this study is almost twice as large as the 0.24 value calculated by HERP question of whether a single aperiodicity value, particularly one derived exclusively from active faults with long length and high slip rates, is appropriate for the construction of probabilistic seismic-hazard maps that include active faults with different length and slip rates. It implies that the parameters for seismic-hazard assessment should be based on individual active-fault characteristics, rather than on an average. Aperiodicity values of intraplate active faults in Japan (a) (b) Relation between fault length and aperiodicity ( ): (a) the segment scenario and (b) the maximum length scenario (Kumamoto, 1999).

6 14 Takashi Kumamoto and Yukiko Hamada 2005 Trench records that include three or more paleoearthquake events were extracted from the trench database for estimation of the average recurrence interval ( ) and aperiodicity of the mean period between events ( ) for the BPT model. Trench ID Fault system after ± before ± after ± before ± 1 Adera Hagiwara Nobi earthquake Nukumi Kiso-sanmyaku Agematsu seien Nobi earthquake Neodani Hinagu Hinagu (southern part) Miura-hanto kita Takeyama Ametaki- Ametaki Kamado Kamado Median Tectonic Okamura Line Median Tectonic Line 10 Median Tectonic Line Fault event ID. 14C y.b.p. Age of Paleoearthquake Cal.y.B.P. event time Naruto minami Mino Fujikawa Shibakawa Tonami heiya Horinji interval (Ti)

7 25 Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan 15 Trench ID average recurrence interval ( ) normalized (Ti/ ) aperiodicity ( ) Table 1 continued. segment maximum length(km) length(km) Activity Type Number of faults within 30km Reference A LL 108 Toda et al. (1996) A LL 113 Yoshioka et al. (2001) B RL 149 Shishikura et al. (2003) A LL 86 Awata et al. (1999) B RL 94 Shimokawa and Kinugasa (1999) A RL 34 Yokosuka city (1999) LL 17 Tottori prefecture (1999) A RL 21 Ehime prefecture (1999) A RL 70 Tokushima prefecture (1999) A RL 28 Tokushima prefecture (1999) A R 42 Iwata et al. (1997) B R Toyama prefecture (2000)

8 16 Takashi Kumamoto and Yukiko Hamada 2005 Trench ID Fault system Fault event ID. Table 1 continued. Age of Paleoearthquake 14C y.b.p. Cal.y.B.P. after ± before ± after ± before ± event time interval (Ti) 13 Kitaizu Tanna Itoigawa-Shizuoka Kamishiro Tectonic Line Itoigawa-Shizuoka Gofukuji Tectonic Line Itoigawa-Shizuoka Okaya Tectonic Line Itoigawa-Shizuoka Osawa Tectonic Line Adera Hagiwara Adera Owachi Adera Owachi Adera Owachi Adera Adera Nojima Nojima

9 25 Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan 17 Trench ID average recurrence interval ( ) normalized (Ti/ ) aperiodicity ( ) Table 1 continued. segment maximum length(km) length(km) Activity Type Number of faults within 30km Reference LL TFTG (1983), Hirano (1984) A R 92 Okumura et al. (1998) A LL 92 Okumura et al. (2000) LL 92 2nd OFTRG (1989) B LL 86 ISTLTRG (1988) A LL 108 Okada et al. (1988) A LL 86 Awata et al. (1986) A LL 86 Toda et al. (1995) A LL 86 GSJ (1988) A LL 141 Toda et al. (1994) B R 73 Nakata et al. (1996) 1.59

10 18 Takashi Kumamoto and Yukiko Hamada 2005 (a) (b) Relation between fault type with fault length and aperiodicity ( ): (a) the segment scenario and (b) the maximum length scenario (Kumamoto, 1999). derived using the BPT model range from 0.24, for four active faults with high slip rates (HERP, 2001), to 0.49, for faults with various slip rates enumerated in the 23 trench records of this study's database. If the nine trench records with four or more recurrence intervals are isolated from the 23 trench records (Table 1), the calculated aperiodicity becomes 0.52, which is slightly larger than the value for those faults with three or more intervals. The reason for this difference lies somewhere in the relation between fault aperiodicity and active-fault characteristics, which should be the subject of further study. The relation between fault length and aperiodicity is shown in Figure 4. Not every fault segment in the activefault database (Research Group for Active Faults of Japan, 1991; Nakata and Imaizumi eds., 2002) has produced an earthquake. In this context, grouping closely spaced faults into a long seismogenic fault system that is considered capable of producing very large earthquakes is called fault grouping, whereas fault segmentation involves estimating which segments of a long seismogenic fault system ( 30 km) will rupture during a future earthquake. The segmented rupture length is determined in accordance with the thickness of the seismogenic layer that underlies the Japanese islands and is considered an important criterion in earthquake size distribution (Shimazaki, 1986). This fault grouping/segmentation problem is common in active-fault research, because there are insufficient data to permit the proper analysis of how fault system segments interact when producing a huge earthquake [e.g., the 1891 Nobi earthquake; M=8, 80km]. There are two end-member scenarios (Kumamoto, 1999) for fault length in this study. One is the maximum length scenario, in which the entire length of a seismogenic fault system is assumed to rupture simultaneously. In this case, infrequent earthquakes of large magnitude are expected. The other is the segment scenario, in which long seismogenic fault systems are assumed to rupture separately, causing earthquakes that are small in magnitude but frequent. Figure 4 indicates the relation between aperiodicities and (a) the segment scenario or (b) the maximum length scenario, respectively, but no clear positive correlation is illustrated. Similarly, there are no distinct relations between aperiodicities and (1) the type of active fault (Figure 5), (2) fault activities (Figure 6), (3) the recurrence intervals derived from trench results (Figure 7), and (4) the distance between a given trench site and the center of a seismogenic fault system in which large displacement is expected to take place frequently (Figure 8). The relation between aperiodicity and the number of active faults within a 30-km radius of a trench site (Figure 9) should be considered in light of recent discussions about the dependency of seismicity rate and probability on stress

11 25 Examination of aperiodicity parameters for the Brownian Passage Time model using intraplate paleoearthquake data in Japan 19 (a) (b) Relation between fault activity with fault length and aperiodicity ( ): (a) the segment scenario and (b) the maximum length scenario (Kumamoto, 1999). ( ). Relation between average recurrence period and aperiodicity Relation between distance between a given trench site and the center of a seismogenic fault system and aperiodicity ( ). transfer from neighboring large earthquakes (e.g., Wyss and Wiemer, 2000). The 30-km distance used is based on the fault rupture lengths associated with surface rupture and earthquake magnitudes of approximately 7. A small positive correlation, with a coefficient of correlation of 0.5, means that the recurrence intervals of faults with many neighboring faults have high variance. This preliminary result is consistent with one of the reasons for adopting the BPT model: disturbances of a given fault segment caused by nearby seismic events change the recurrence interval of segment and its future earthquake probability (Ellsworth et al., 1999; HERP, 2001). These results yield a cumulative probability that ranges from 0.24 (solid line) to 0.49 (dashed line) for the BPT aperiodicity in cases in which the average recurrence interval changes every 1,000 years from 1,000 to 5,000 and

12 20 Takashi Kumamoto and Yukiko Hamada 2005 Relation between the number of active faults within a 30- km radius of a trench site and aperiodicity ( ). the elapsed time is between 0 and 5,000 years (Figure 10). The probabilities of aperiodicity value 0.49 in this study are higher than that of aperiodicity value 0.24 of HERP (2001) before the elapsed time reaches the average recurrence interval. A paleoearthquake database was constructed from 178 Japanese trench records published prior to 2004 fiscal year. Twenty-three trench records with three or more recurrence intervals were used in calculating aperiodicities using the BPT model. Aperiodicities range from 0.07 to 0.80, and the common aperiodicity of the weighted average is The common aperiodicity ( c ) of 0.49 in this study is approximately the same as the 0.50 value determined by Ellsworth et al. (1999) from 37 worldwide earthquake records but almost twice as large as the value of 0.24 calculated by HERP (2001) using the results of the Atotsugawa, Atera, Tanna, and Nagano-bonchi seien faults. One of the likely reasons for this discrepancy is that the four active faults used by HERP (2001) have long lengths and high activities, whereas the data set used in this study includes faults with a range of slip rates and fault lengths. There is no distinct relation between the aperiodicities in this study and the type of active fault, the activities, the recurrence intervals from trench results, or the distance Cumulative probability that ranges from 0.24 (solid line) to 0.49 (dashed line) for the BPT aperiodicity in cases in which the average recurrence interval changes every 1,000 years from 1,000 to 5,000 and the elapsed time is between 0 and 5,000 years. from trench site to the center of the seismogenic fault system. There is a small positive correlation between the aperiodicities derived in this study and the number of neighboring faults within 30 km of trench sites. This is consistent with the BPT model, which assumes that nearby seismic events can alter the recurrence interval and future earthquake probability of a fault. This study highlights several items that require improvement if the models and parameters used in longterm probabilistic seismic-hazard assessment are to be refined. Dating uncertainties must be reduced, and the data collected in the course of trenching studies, particularly that regarding event certainty, must be more uniform. Furthermore, the data sets used in calculating the BPT parameters in this study are mainly from active, strike-slip faults in central Japan and are not appropriate for analysis of the regionality of aperiodicities. Larger and better paleoearthquake databases are essential to the analysis of active-fault aperiodicity. Intensive trench surveys should be conducted, especially on active reverse faults in northern Japan, to clarify the recurrence history of reverse-fault activity. Reverse faults experience vertical displacement, and so documenting their past activity will require deeper trenches, for example by using geo-slicer (Nakata and Shimazaki, 1997), than those used in strike-slip fault

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