Decade-scale decrease inb value prior to the M9-class 2011 Tohoku and 2004 Sumatra quakes



[1] The Gutenberg-Richter frequency-magnitude distribution of earthquakes has become well established in seismology. The slope of the relation between frequency and magnitude (b value) is typically 1, but it often shows variations around 1. Based on an analysis of seismicity prior to the 2011 Tohoku and 2004 Sumatra earthquakes (both in magnitude (M) 9 class), we show that the pronounced decade-scale decrease inbvalue was a common precursor to both mega-quakes around their hypocenters. This is the first report onM9-class quakes to confirm a change inb value, which has been predicted based on the results of laboratory experiments. We propose that the b value is an important indicator of an impending great earthquake, and has great potential in terms of predicting a future large quake off the Pacific coast of Hokkaido, Japan.

1. Introduction

[2] The cumulative number (N) of earthquakes with magnitude (M) larger than or equal to a given value is well approximated by the Gutenberg-Richter (GR) law [Gutenberg and Richter, 1944], as follows: logN = A-bM, where the constant A characterizes seismic activity or earthquake productivity of a region and the constant b is used to describe the relative occurrence of large and small events (i.e., a high b value indicates a larger proportion of small earthquakes, and vice versa). Because Mis proportional to the logarithm of energy, the GR size-distribution of earthquakes obeys a power-law.

[3] Spatial and temporal changes in b are known to reflect stress state in the Earth's crust [Suyehiro et al., 1964; Smith, 1981; Schorlemmer et al., 2005; Narteau et al., 2009] and to be influenced by asperities and frictional properties [Hirose et al., 2002; Yabe, 2003; Schorlemmer and Wiemer, 2005] and by interface locking along subduction zones [e.g., Sobiesiak et al., 2007; Ghosh et al., 2008]. The results of laboratory experiments indicate a systematic decrease in the b value approaching the time of the entire fracture [Mogi, 1963; Scholz, 1968; Lei, 2003]. In this context, a decrease in the bvalue has been reported for the period leading up to moderate-size earthquakes [Suyehiro et al., 1964]. However, it has remained uncertain whether this is ubiquitous, because observations of seismicity prior to other moderate-size earthquakes have shown an increase in theb value [Smith, 1981]. This discrepancy may indicate that the prediction based on laboratory experiments is inapplicable to all moderate-size earthquakes because such events are not large enough to be considered as the entire fracture.

[4] Here, we investigated spatial and temporal trends in b values prior to the 11 March 2011 Mw9.0 Tohoku earthquake [Hirose et al., 2011] and 26 December 2004 Mw9.1 Sumatra earthquake [Lay et al., 2005], both considered as the upper size limit of subduction-zone earthquakes, indicating that their preparatory process may be weakly dependent on the characteristics of the subduction zones.

2. Method and Data

[5] To estimate bvalues consistently over space and time, we employed EMR (Entire-Magnitude-Range) technique [Woessner and Wiemer, 2005], which also simultaneously calculates the completeness magnitude Mc, above which all events consider to be detected by a seismic network. EMR applies the maximum-likelihood method in computing theb value to events with a magnitude above Mc. The insets in Figures 1a and 2b show a good fit of the GR law to observations in the present cases.

Figure 1.

Plot of b values as a function of time relative to M9-class earthquakes (vertical solid line) that occurred in (a) Tohoku and (b) Sumatra, and relative to (c) theM8.0 Tokachi earthquake (vertical dashed line). Diamonds for Figures 1a–1c indicate the b value obtained from seismicity occurring after the earthquake. The uncertainty estimates are according to Shi and Bolt [1982]. Grey shading indicates the period before 1965. Horizontal dashed line indicates b = 1.0. Arrows indicate events with M ≥ 7.3 (Figure 1a), M ≥ 7.1 (Figure 1b), and M ≥ 7.4 (Figure 1c). The b value for 1923–1964 (square) was included in A. The inset in Ashows the cumulative frequency-magnitude distributions of earthquakes, highlighted by green and red. The time interval, labeled “D” in Figure 1a, corresponds to that used for the map ofb values shown in Figure 1d. (d) Map of b values obtained from events from January 1990 to immediately before the Tohoku earthquake (the star indicating the epicenter of this event). Epicenters with M ≥ 7.3 are indicated by circles. The rectangles labeled “A” and “C” denote regions for which data are shown in Figures 1a and 1c, respectively.

Figure 2.

(a) Map of bvalues obtained from seismicity after 1 January 2006. The contours represent co-seismic slip during the Tohoku earthquake (;, whose epicenter is indicated by a star. The square shows the region considered in Figure 2b. Epicenters with M = 7.2 and M ≥ 7.3 are indicated by small and large circles, respectively. (b) Plot of b values (circles) as a function of time, as obtained from seismicity data for period from 2000 until the Tohoku earthquake. The uncertainty estimates are according to Shi and Bolt [1982]. The inset shows the cumulative frequency-magnitude distributions of earthquakes in the datasets (of the corresponding color) in the main panel. Events withM ≥ 7.2 in and around the study region are indicated by arrows. The time interval at the bottom of the main panel, labeled “A” is dealt with in Figure 2a.

[6] For the Tohoku earthquake, we used a dataset from the Japan Meteorological Agency (JMA) earthquake catalog dating back to 1923. For the dataset concerning long-term seismicity withM ≥ 5, we used a depth range of 0–100 km, wider than that covered by recent observations (down to about 60 km), to allow for data from the 1960s and 1970s with poorly constrained depth determination. This dataset covers seismicity from 1965 onward, because earlier events have yet to be relocated and old magnitude scales have yet to be converted to current standards [Japan Meteorological Agency, 2003]. After 1965, the seismic networks employed to maintain the JMA catalog have gradually been modernized. In view of these network updates, the setting of a minimum magnitude at M = 5 ensures the homogeneity of recording since 1965 [Nanjo et al., 2010]. We truncated the catalog at this magnitude to discard in advance all data that may be inhomogeneous.

[7] For the second dataset concerning short-term seismicity since 2000, we used a depth range of 0–60 km. An improvement in event detectability arising from a large increase in the number of borehole seismic stations [Obara et al., 2005] enables a reduction of the minimum magnitude at M = 2.5 for catalog homogeneity [Nanjo et al., 2010].

[8] For the Sumatra case, we used the ANSS catalog and analyzed M ≥ 4.5 seismicity since 1965 within a depth range of 0–100 km (Figure S1 of the auxiliary material). We set a lower threshold at M = 4.5 to ensure an adequate number of events for b-value analysis. Application of the EMR method to the truncated catalog allowsMc to be higher by about 0.4–0.6 than the threshold magnitude.

3. Results

[9] Our approach considers not only on the largest foreshock related to the Tohoku earthquake, a M7.3 event on 9 March 2011 [Hirose et al., 2011], but also longer-term trends in seismicity that precede this foreshock (Figure 1). We examined the region that covers the locations of aftershocks occurring in the first 20 days post-quake (rectangle A inFigure 1d), in which the source areas defined from seismic data [Ide et al., 2011; Simons et al., 2011] and geodetic data [Ozawa et al., 2011] (; are included. In creating Figure 1a, which shows a time series of b values, we used a moving window approach, whereby the window covered 150 events. The b values (circles) for the Tohoku earthquake were mostly above 1.2 until 15 years ago. Since 10 years ago, the b values have shown a rapid decrease over time, to values below 1.0. The foreshocks contributed to most recent values in this decreasing trend in b values. A comparison with the b value calculated for aftershocks from immediately after the Tohoku earthquake until 26 April 2011 (b = 1.13, diamond in Figure 1a) shows that a transition to normal levels has occurred. By way of reference, we applied the same procedure to events in 1923–1964, and obtained b values typically in b = 1.0–1.4 (mean, 1.195). A map view that shows data for the period from 1990 until immediately before the Tohoku earthquake (Figure 1d) shows a zone of low b values around the future hypocenter. To create Figure 1d, we calculated b values for events falling in a cylindrical volume with radius r = 150 km, centered at each node on a 0.1° × 0.1° grid and plotted a b value at the corresponding node only if at least 50 events in the cylinder yielded a good fit to the GR law. A comparison with a previous period 1965–1989 (Figure S2 of the auxiliary material) shows that the decrease in b value is pronounced in this zone (see also Figure S3 of the auxiliary material).

[10] A similar analysis was performed for the Sumatra earthquake. In constructing Figure 1b, we employed the same plotting procedure as for Figure 1a. The b values started falling below b = 1.2 since 1988. The seismicity from immediately after the Sumatra earthquake till 30 June 2011 shows a return to normal levels (b = 1.23, diamond).

[11] The data for both the Tohoku and Sumatra earthquakes show that a decrease in bvalues during the 10–20 years preceding each event, followed by a return to normal levels, is common between the mega-quakes. We similarly investigated other fourM9-class quakes, using the ANSS catalog (see Text S1 and Table S1 of theauxiliary material). The number of earthquakes analyzed for each M9-class event was inadequate, although the results are consistent with those reported above for the Tohoku and Sumatra events.

[12] To show that analyses of b values leading up to the Tohoku earthquake would have enabled an estimate of the magnitude of this event, we correlated the areas of low bwith areas of large co-seismic displacements. For this purpose, we used another JMA dataset concerningM ≥ 2.5 seismicity since 2000. A map view of b values (Figure 2a), based on seismicity over a period from 2006 till immediately before the Tohoku earthquake, reveals a zone of low b values (b = 0.5–0.6) near the eventual hypocenter, where the mapping procedure was the same as that for Figure 1d, except for a smaller node spacing (0.05° × 0.05°), a shorter cylinder length (60 km), and a smaller sampling radius (r = 60 km). This feature is not sensitive to the mapping parameters (Figure S4 of the auxiliary material). The characteristic dimension of unusually low b values in an approximately 1° × 1° area near the hypocenter of the Tohoku earthquake, is ≈100 km, indicating a M8-class event or larger. Lowb values are also seen in two areas farther to the south, near the Japan Trench. For earthquakes in the region indicated by the rectangle in Figure 2a, there is a clear decrease in b values to as low as b = 0.5–0.6 (Figure 2b), where we employed the same moving window procedure as for Figure 1a, but using a 200-event window. The final values are remarkably similar to those immediately before the entire fracture, as obtained in a previous laboratory experiment [Lei, 2003]. The result is not induced by a sampling bias (Figure S5 of the auxiliary material) and does not depend on depth (Figure S6 of the auxiliary material).

4. Discussions and Conclusion

[13] We compared the distribution of areas with low b values and the slip distribution (; based on combined GPS crustal deformation data on land [Ozawa et al., 2011] ( and ocean bottom displacement data measured on site [Sato et al., 2011]. Two of the three zones of extremely low bvalues coincide remarkably with locations of extremely large co-seismic slip (>48 m, >8 m). Little co-seismic slip was observed near the zone of lowb values located farther south, but large afterslip ( is currently taking place in this region.

[14] Figures 1c and 1dshow the high likelihood of a mega-quake off the Pacific coast of Hokkaido. In creatingFigure 1c, the same plotting procedure as that used in Figure 1a was applied to M ≥ 5 seismicity in the depth range 0–100 km for the region indicated by the rectangular region labeled “C” in Figure 1d. Figure 1c shows a decrease in b values starting around 20 years ago. However, in contrast to the Tohoku and Sumatra cases, the 26 September 2003 M8.0 Tokachi earthquake (vertical dashed line in Figure 1c) does not show a transition of b values to values above 1. Additional analysis using the JMA dataset concerning M ≥ 2.5 seismicity (Figure S7 of the auxiliary material) again indicates that the characteristic dimension of the zone of low b values is again ≈100 km, which is not indicative of a M7-class or smaller event in future. Our results, combined with the GPS observations (, show that this area of low b values occurs immediately west of and partly overlapping with an area of strong plate coupling. Overall, these results are remarkably similar to the Tohoku case. These findings, combined with the history of regional seismicity [Harada et al., 2011], fault models [Satake et al., 2008], and with global perspective of great earthquakes [McCaffrey, 2007], indicate the high likelihood of a future mega-quake along the Kuril Trench.

[15] We succeeded in detecting a b value precursor to two M9-class quakes, at a lead time of 10–20 years. This result provides the first confirmation of predictions based on laboratory experiment [Mogi, 1963; Scholz, 1968; Lei, 2003] for M9-class earthquakes. Out future research includes a detailed analysis in terms of the change in shape of the size-distribution of earthquakes before a mega-quake, predicted based on the critical point theory [e.g.,Amitrano et al., 2005; Girard et al., 2010; Amitrano, 2012].

[16] As shown for the Tohoku earthquake, assessments of earthquake hazards are markedly improved with the construction of a densely distributed high-sensitivity seismic network that yields improved event-detectability. The analysis ofbvalues calculated from the earthquake catalog of such networks helps to constrain the timing and location of future giant earthquakes, as well as their magnitude. It would be worthwhile to monitor the spatio-temporal distribution ofb values along the Kuril Trench.


[17] We thank the Editor (A. Newman) and two anonymous referees for their comments and the JMA and ANSS for the earthquake catalogs. This study was supported by the Special Project for Earthquake Disaster Mitigation in the Tokyo Metropolitan Area and by the Observation and Research Program for Prediction of Earthquakes and Volcanic Eruptions.

[18] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.