小地震も大地震も始まりは似ている
Nature ダイジェスト Vol. 16 No. 12 | doi : 10.1038/ndigest.2019.191236

原文：Nature (2019-09-05) | doi: 10.1038/d41586-019-02613-5 | Small and large earthquakes can have similar starts

Rachel E. Abercrombie

小さな地震と大きな地震の始まりは、よく似ているのか、あるいは異なっているのか、という問題は、地震学の長年の課題だ。日本周辺の地震を分析した結果、一部のケースでは、小さな地震と大きな地震の始まりはほぼ同一であることが分かった。

図1 2011年東北地方太平洋沖地震による被害
2011年3月11日、日本の近代地震観測史上最も強い地震が発生して津波を引き起こし、壊滅的な被害を与えた。井出は、大きな地震の始まりは、小さな地震の始まりとほぼ同一である場合があることを見いだした1。これは、地震の最終的な大きさの予測に関わる知見だ（写真は2011年3月21日、自宅の片付けをする男性。宮城県気仙沼市で）。 | 拡大する
CHRIS MCGRATH/GETTY

ある地震がどれだけ大きくなるのかが分かるのはどの時点だろうか？　1つの地震のマグニチュードは、その成長の始まりの状況とダイナミクスに左右されるのだろうか？　もし左右されるのであれば、初期の地震波の観測により、あるいは地震が起こるだろう地域の観測によっても、地震動の早期警報が可能になるかもしれない。一方、左右されないなら、そうした短期予測の可能性は低い。東京大学大学院理学系研究科の井出哲はこのほど、日本周辺で起こった数千回の大きな地震と、それらに近い震源を持つ小さな地震について、互いの始まりの地震波の波形を比較し、Nature 2019年9月5日号112ページに報告した1。井出は、今回分析した地震波の周波数範囲では、大きな地震の約20％の始まりの地震波は、それらと震源が近い小さな地震の始まりの地震波と区別がつかないことを見いだした。

Letter
Published: 04 September 2019
Frequent observations of identical onsets of large and small earthquakes
Satoshi Ide
Nature volume 573, pages112–116(2019)Cite this article

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Abstract
Every gigantic earthquake begins as a tiny rock failure at almost a point, followed by successive slip of the complex fault system, before radiating strong shaking from a vast rupture area extending over hundreds of kilometres. Whether the growth process of the rupture of a large earthquake is predictable and whether it produces observable signatures different from that of smaller events1,2,3,4,5 are fundamental questions related to the potential for earthquake early warning and probabilistic forecasting. Inspired by a recent discovery that large earthquakes might have seismic waves, and probably rupture processes, that are almost identical to those of smaller events6,7,8, we show that such similarity characterized by large cross-correlation is a common feature of earthquakes in the Tohoku–Hokkaido subduction zone, Japan. A systematic comparison of 15 years of high-sensitivity seismograph records for approximately 100,000 events reveals 80 extremely similar and 390 very similar pairs of large (moment magnitude M > 4.5) and small (M < 4.0) earthquakes, co-located within about 100 metres. An extremely high similarity is observed for pairs of subduction-type earthquakes (170 of 899 large events) separated by a long period of up to 15 years, whereas for pairs of other types of large earthquakes only the foreshocks and aftershocks are similar. This frequently occurring similarity between different-sized subduction-type earthquakes suggests repeated cascading rupture processes in a widespread hierarchical structure9,10,11,12 along the plate interface and indicates a specific but probabilistically limited predictability of the final size of the earthquake (that is, the location and a set of possible sizes of an earthquake are well predicted, but its final size is not at all well constrained).

Main
Earthquakes have complicated rupture processes and frequently occur along complex fault systems, such that they are generally considered unpredictable phenomena. However, their occurrence is not completely unpredictable. Good examples of predictable earthquakes are repeating earthquakes, or repeaters, which have been discovered in many seismogenic regions worldwide12,13,14,15,16. Repeaters are considered to represent the recurring rupture of a segment, or patch, of a reasonably mature fault system, such as the plate interface in a subduction zone. They occur at quasi-regular intervals and are approximately the same size, radiating almost identical seismic waves. Therefore, once rupture is initiated within a known repeater’s patch at the expected timing, we can predict its final size with high probability. However, repeaters are not the predominant seismic activity in seismogenic regions. For example, 105 repeaters of M > 4.5 were identified in the Tohoku–Hokkaido subduction zone, Japan, from June 2002 to February 201116, out of more than 600 similar-sized earthquakes occurring during the same period. Little is yet known about the predictability of events other than repeaters17.

The predictability of earthquake size is also important. To determine how different the earthquake rupture and radiated seismic waves of different-sized earthquakes are is a classic problem in earthquake seismology1,2,3,4,5. The initial waveforms of large earthquakes are complicated1,3, but the very beginnings can be similar to those of small events18. The initial slip patterns of large earthquakes are also sometimes similar to those of small earthquakes19,20. Although their high complexity makes a comprehensive comparison difficult, a recent study reported that the initial waveforms of earthquakes are statistically independent of magnitude5,6. As recently shown, the seismic waveforms of some specific combinations of M ≈ 3 and M ≈ 5 co-located earthquakes are found to be almost identical7, with similar rise, fall and fluctuations during the first 0.1 s. Since this first report investigated only five earthquakes of M ≈ 5, the generality of such an observation needs to be quantitatively confirmed over a much broader region. Here I use waveform cross-correlation analysis to conduct a systematic comparison of the initial seismic waveforms from different-sized earthquakes observed in the Tohoku–Hokkaido subduction zone. As demonstrated below, the analysis reveals that many pairs of co-located events of different sizes have high waveform similarity, especially for low-angle thrust earthquakes.

The study area covers a section of the Japan Trench around 1,100 km long that extends about 250 km landward (Fig. 1); and the study period is from 3 June 2002 to 21 April 2018. I extracted all of the M > 4.5 earthquakes that occurred at depths shallower than 70 km from the Japan Meteorological Agency (JMA) earthquake catalogue, and then selected events with focal mechanism information estimated by the National Research Institute for Earth Science and Disaster Resilience (NIED), thus yielding 2,518 earthquakes for analysis. These earthquakes were divided into 1,262 subduction-type earthquakes, similar to the 2011 Tohoku-Oki earthquake, and 1,256 other-type earthquakes, classified according to their moment tensor similarity (see Methods), as shown in Fig. 1.

Fig. 1: Distribution of large earthquakes (M > 4.5) considered in this study, showing their beachball focal mechanism solutions.
figure1
a, Subduction-type earthquakes. b, Other-type earthquakes. The study region is demarcated by a cyan line and the seismic stations are shown as green circles. The dashed lines are isodepth contours of the plate interface at depths of 20 km, 40 km and 70 km. The beachballs indicate events with CCmax > 0.9 (red), 0.8 < CCmax <0.9 (orange), CCmax < 0.8 (black), and insufficient data for cross-correlation analysis (grey).

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The initial waveform of each large earthquake was compared with the waveforms of earthquakes of 2 < M < 4 within 10 km horizontally and 5 km vertically of the hypocentre of the large event, taken from the JMA catalogue. This region is sufficiently large compared with the median error of events in the catalogue (about 1 km horizontally and vertically). Approximately 95,000 small events were selected for comparison with the 2,518 large events, yielding approximately 340,000 event pairs. In addition, 2,649 repeater pairs were analysed using the catalogue of ref. 16; these were extracted from the JMA catalogue on the basis of waveform similarity, to quantitatively compare the waveforms of repeater and non-repeater event pairs.

The data analysed primarily consist of ground velocity seismograms recorded by short-period sensors at 100 samples per second. The analysis considered only the event pairs that were detected by more than ten stations after quality control of the data (see Methods). This criterion reduces the number of available large events from 2,518 to 1,654, of which 899 were subduction-type events and 755 were other-type events. Many of the far offshore events were removed, suggesting that such a comparison is still difficult for these distant earthquakes (Fig. 1).

The similarity of earthquake onsets for event pairs was analysed via waveform cross-correlation for the initial 0.2 s (see Methods). The initial waveform is often too simple to evaluate the similarity, especially when the attenuation is large21. Nevertheless, the difference in amplitude and timing at many stations can be used to judge the similarity. Therefore, unlike ordinary cross-correlation approaches, the cross-correlation coefficients were first normalized according to the larger signals for each station, and a grid search was then performed to obtain the maximum of the average values of cross-correlation coefficients among the analysed stations, CCmax. Figure 2 shows examples of raw velocity and acceleration waveforms for M = 3.9 and M = 4.7 subduction-type events (CCmax = 0.975). These events are surrounded by many stations because they occurred beneath mainland Japan at a depth of 60 km. Although the overall amplitude of the waveform is naturally larger for the large event, the waveforms are almost identical during the initial 0.2 s, which is comparable to the typical duration of a M = 3.9 earthquake. These observations provide strong evidence that the two events have similar rupture processes, at least within the observation frequency range, which is limited by the instrument’s response (1 Hz), the path attenuation of seismic waves, and ambient noise. The difference of timing of less than 0.01 s ensures that they occurred within 100 m of each other, which is the typical source size of a M ≈ 2 event.

Fig. 2: Comparison between the seismograms of a large (black) and a small (red) earthquake.
figure2
The central map shows the seismic station locations (green triangles) and the epicentre of the large earthquake (red star). Unfiltered velocity waveforms (top) and acceleration waveforms (bottom) are shown, with the station code and the vertical scale (in micrometres per second for velocity and in micrometres per second per second for acceleration) provided in the top and bottom left-hand corners of each waveform plot, respectively. The origin of the time axis is aligned with the arrival time measured by JMA.

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Figure 3a, b shows the CCmax histograms for the subduction-type and other-type earthquakes, respectively. Subduction-type events generally have higher correlation coefficients than other-type events. Repeater pairs have very high CCmax values, with an average value of 0.85 (Fig. 3c), which is not surprising given that their waveforms are almost identical. These histograms suggest that many pairs of different-sized earthquakes have CCmax values that are comparable to those of repeaters. The CCmax > 0.9 and CCmax > 0.8 thresholds identify 78 pairs for 55 large events and 349 pairs for 170 large events (18.9%) among the 899 subduction-type earthquakes, respectively. The same two thresholds identify 2 pairs for 2 large events and 41 pairs for 30 large events (4.0%) among the 755 other-type earthquakes, respectively. The average of magnitude difference is 1.31 for all 390 pairs, which include 120 pairs of magnitude difference δM < 1.0, 127 pairs of 1.0≤δM<1.5, 90 pairs of 1.5≤δM<2.0 and 53 pairs of 2.0≤δM. The information for all earthquake pairs for which CCmax > 0.8 is summarized in Supplementary Tables 1 and 2. Some events appear several times in tables, suggesting that they are repeating, or at least partially repeating earthquakes, in a part of the fault that is often ruptured. The Supplementary Information compares the waveforms of the 80 pairs for which CCmax > 0.9. Although the beginnings of high-frequency acceleration seismograms are very similar, we can find some differences between two seismograms in velocity seismograms after a time of around half the duration of the small event has passed. For comparison, Extended Data Fig. 1 shows an example of waveforms with CCmax ≈ 0.6 for pairs for which the hypocenters were located within 200 m of each other by slip inversion7,8.

Fig. 3: CCmax histograms for different groups of events.
figure3
a, Subduction-type events. The dotted lines indicate the CCmax = 0.8 and CCmax = 0.9 thresholds discussed in the text. b, Other-type events. c, Repeater events. d, Distribution of inter-event times for three different periods: the entire time period (top), 1 week (middle), and 1 day (bottom).

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The location of these events shows that high CCmax values occurred along the coastline at depths greater than 40 km (Fig. 1). This may simply be due to the less attenuated waveforms at these stations from nearby deep events. By contrast, pair number 5 and pair number 70 in the Supplementary Information are examples of far-offshore events with attenuated waveforms, in which low-frequency signals are dominant but contaminated with large noise. Most far-offshore events have poor signal-to-noise ratio and small values of CCmax. Although the observation conditions are not much different between the subduction-type and other-type events, CCmax is generally small for the other-type events, even beneath mainland Japan. This is probably because the hypocentre locations are more distributed or focal mechanisms are more diverse for other-type events.

The inter-event times show another difference between subduction-type and other-type earthquakes. Figure 3d shows the inter-event times between the large and small events, for pairs with CCmax > 0.8. Only two M = 5.1 normal fault earthquakes have CCmax > 0.9 in the other-types group. One event (20130310051130) correlates well with a foreshock that preceded it by 3 min, and the other event (20110414073549) is quite similar to an aftershock that occurred about 6 months later. These small earthquakes were probably affected by the stress change related to these large earthquakes. The inter-event times in the group of other-type earthquakes are concentrated, 14 of 41 pairs and 12 of 30 events, within 1 week of the large earthquake for pairs with CCmax > 0.8. Furthermore, 7 of 14 small events within this 1-week range occurred as immediate foreshocks within 1 day of the large event. The mechanism of these foreshocks may be similar to that described in previous reports of immediate foreshocks near the mainshock hypocentre22,23. However, the inter-event times of subduction-type earthquakes are widely distributed and can be longer than ten years. The source of this difference is currently unknown, but the difference in loading conditions and fault maturity may play a part. The wide distribution of subduction-type earthquakes suggests that there is no direct relationship between the paired earthquakes, and each occurred owing to the long-term stress accumulation via plate subduction, which is similar to the mechanism suggested for repeaters. Therefore, we can assume that some long-term characteristic structure is present that is capable of repeatedly hosting both large and small earthquakes.

What kind of models explain the observations? An earthquake fault system is generally complex, such that one part of the system may slip more easily than another as a result of its geometry (Fig. 4). The complexity of a fault system can be observed at various scales and is often approximated as a fractal24,25,26,27. This allows the complex fault system to be simplified using a set of circular or elliptical patches with a fractal size distribution9,10,11. Such a hierarchical structure of patches has previously been proposed in the study region8,12. Given that the fracture energy of a patch is linearly dependent on the patch radius, the rupture of a small patch may trigger larger patches, with this cascading rupture potentially culminating in a very large earthquake. The cascade process is controlled by the spatial distribution of hierarchical patches and stress conditions, with the final size of the earthquake determined after the process is halted at some scale. The process of such a cascading rupture has previously been simulated using the rate-and-state friction law and two different-sized patches11, with the repeating occurrence of large and small earthquakes modelled for a wide variety of cascading rupture scenarios. The percentage of events with high CCmax, about 20% of all of the large earthquakes, is large, but may not be sufficient to assume that this mechanism operates for all seismogenic regions. Further investigation over much longer periods than the 15 years of data studied here is necessary to confirm the validity of this idea and to identify the distribution of patch structures.

Fig. 4: Schematic illustration of a hierarchical structure that produces almost identical initial waveforms, regardless of the size of the earthquake.
figure4
a, Generalized fault system with a complex and nested geometrical heterogeneity. Parts of the fault can be simplified at various scales. b, Simplified image of a complex fault system with three nested patches. c, Illustration of the cascading rupture of a hierarchical patch. d, Typical seismic waveforms from small, medium and large earthquakes occurring on the hierarchical structure.

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Initial onset may be related to the nucleation process, which is believed to be initiated before the dynamic rupture process in rocky materials28,29. The immediate foreshocks, which may occur during the nucleation process30,31, in the present study are observed primarily for the group of other-type earthquakes, implying some slow deformation process and related stress changes that are seismically undetectable. The rupture of a small patch did not cascade to a larger scale, with this nucleation process potentially triggering the rupture of the larger patch. The observations in this study cannot rule out such a possibility, because the comparison is limited by observation conditions, such as instrument response, structural attenuation and ambient noise. Nevertheless, similar initial seismic waves often found between different-sized earthquakes suggest that size-dependent nucleation processes are unlikely.

Instead, two similar processes may occur, with a slight difference in rupture conditions stopping one process and initiating the cascade-up of the other, and the final earthquake size unknown until the cascading rupture of the hierarchical structure is terminated (Fig. 4). If such processes repeat many times, we observe partially repeating earthquakes, which may also be called hierarchical repeaters. Factors controlling cascading rupture may include fluid diffusion, shear heating, microcracking and plastic deformation, for example, which cannot be measured via geophysical observations and cannot be predicted deterministically26,32. The probability of cascading should therefore be estimated theoretically or empirically and can then be employed to assess the predictability of future earthquakes with a more quantitative size estimation.

Methods
Earthquake classification
Subduction-type earthquakes are distinguished from other types using the similarity of the moment tensor M of each earthquake to that of a typical subduction earthquake Msub, as calculated from the double-couple solution of the 2011 Tohoku-Oki earthquake determined by NIED (strike 200°, dip 27°, rake 88°). The events with trace(M~M~sub)≥0.75 were grouped as subduction-type earthquakes, where M~ is a normalized moment tensor, which is a moment tensor divided by the seismic moment of the corresponding best double-couple solution.

Data handling
The analysed seismograms were downloaded from the NIED Hi-net server as ‘event data’, which is a set of seismograms for which manual phase picking was performed by JMA. Seismograms from 401 stations were used for the analysis. Each station is operated by NIED, JMA, Hokkaido University, Tohoku University, the University of Tokyo, Hirosaki University, Aomori Prefecture, Tokyo Metropolis, the Geospatial Information Authority of Japan, or the Japan Agency for Marine-Earth Science and Technology. The data are primarily ground velocity seismograms recorded by short-period (1-Hz) sensors at 100 samples per second. The highest frequency available is around 40 Hz, but this is practically limited by seismic attenuation depending on the source location. Only the vertical component around the P-wave is used because it is clearly observed, with the arrival time determined by JMA used as the reference time. Each original velocity record is differentiated to its corresponding acceleration record to emphasize the onset of each earthquake. The pre-signal noise, which is defined as the 1-s signal starting 1.1 s before the reference time, is compared with the 1-s signal starting 0.1 s before the reference time at each station for quality control. Data points were excluded from the analysis if the root-mean-square amplitude of the noise exceeds 10% of the root-mean-square signal. Furthermore, if the root-mean-square noise of one event in a pair is different from that of the other event by more than one order of magnitude, the station is excluded because of potential instrument issues.

Correlation measurement
For two discrete time series with zero mean, ui and vi (for i = 1, …, N), the cross-correlation coefficient CC is usually defined as:

CC(u,v)=�年i=1uivi�年i=1uiui�年i=1vivi−−−−−−−−−−−−−−−√
As I am comparing the similarity between the time series, including both the signal amplitude and shape of the time series, the normalizing factor in the denominator is changed to the root mean square of the larger signal, such that:

CCscaled(u,v)=�年i=1uivimax(�年i=1uiui,�年i=1vivi)
where CCscaled is the scaled cross-correlation coefficient. This value is small for similar waveforms with different amplitude, which are often observed when structural attenuation is so large that the complexities in source process are smeared out.

For a pair of events, the maximum of the averaged scaled cross-correlation coefficients at Nsta stations is defined as:

CCmax=1Nsta�破=1Nstamax(CCscaled(uj(tju+δtj),vj(tjv+δtj+δtc)))
where tju is the reference time for the large events, which is the P-arrival time determined by JMA. tjv=tju+Δtij is the reference time for the small events, where Δtij is the difference of the origin times between two events. δtc is the common time adjustment between two events shared by all stations. This is almost zero, but can be non-zero even for two co-located events because the catalogue information is not always correct. δtj determines the time window to be used at the jth station. This parameter enables me to capture a section of waveforms that maximize the similarity, which depends on the observation conditions such as attenuation and noise level. Here I use Nsta = 10. The grid search is carried out to maximize CCmax in the ranges −0.2s≤δtj≤0.1s and −0.1s≤δtc≤0.1s, for each sampling (0.01 s) interval. When many stations are available, the ten stations closest to the large event are selected. The number of samples is 20; that is, the initial 0.2 s of the P-wave signal is analysed (given that the reference time is the arrival time and δtj = δtc = 0); 0.2 s sufficiently covers most of the source duration of the small events.

Data availability
All waveform data are available from the NIED Hi-net server (http://www.hinet.bosai.go.jp).

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Acknowledgements
This work was supported by funding from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, under its Earthquake and Volcano Hazards Observation and Research Program, JSPS KAKENHI 16H02219 and MEXT KAKENHI 16H06477. All data were obtained from the NIED Hi-net data server. Figures were prepared using the Generic Mapping Tools.

Author information
Affiliations
Department of Earth and Planetary Science, The University of Tokyo, Tokyo, Japan
Satoshi Ide
Corresponding author
Correspondence to Satoshi Ide.

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Extended data figures and tables
Extended Data Fig. 1 Comparison between the seismograms of large (black trace) and small (red trace) earthquakes for dissimilar onsets.
CCmax ≈ 0.6. ‘Bad example’ indicates that compared to many pairs having CCmax above 0.8, this value of 0.6 is small. The acceleration record, scaled by the noise level (left) and amplitude of the small event (middle left), and the velocity record, scaled by the onset of the small event (middle right) and large event (right), are shown for each station, with the appropriate scales shown in the bottom left-hand corner of each waveform set (micrometre per second per second for acceleration; micrometre per second for velocity). The grey box in each acceleration plot shows the time window used to calculate CCmax. The value of CCmax for each station is shown below the station name in each acceleration plot. The takeoff angle and azimuth (degrees) from the source to each station are shown below the station name in each velocity plot.

Supplementary information
Supplementary Figures Comparison between the seismograms of large (black) and small (red) earthquakes. The 80 figures show details of the 80 earthquake pairs for which CCmax > 0.9 are presented. The information relating to the occurrence time (YYYYMMDDhhmmss), hypocentre locations, and magnitude of each event are provided in the upper left-hand corner of each page, along with the corresponding CCmax value. The acceleration record, scaled by the noise level (left) and amplitude of the small event (middle left), and the velocity record, scaled by the onset of the small event (middle right) and large event (right), are shown for each station, with the appropriate scales shown in the bottom left-hand corner of each waveform set (micrometre per second2 for acceleration; micrometre per second for velocity). The grey box in each acceleration plot shows the time window used to calculate CCmax. The value of CCmax for each station is shown below the station name in each acceleration plot. The takeoff angle and azimuth (degrees) from the source to each station are shown below the station name in each velocity plot
Supplementary Table 1
Earthquake pairs of the subduction type with CCmax >0.8.

Supplementary Table 2
Earthquake pairs of other type with CCmax>0.8.

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https://www.natureasia.com/ja-jp/ndigest/v16/n12/%E5%B0%8F%E5%9C%B0%E9%9C%87%E3%82%82%E5%A4%A7%E5%9C%B0%E9%9C%87%E3%82%82%E5%A7%8B%E3%81%BE%E3%82%8A%E3%81%AF%E4%BC%BC%E3%81%A6%E3%81%84%E3%82%8B/101251

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