地震津波研究部

Research on rapid estimation of the parameters for large earthquakes along trenches

BY

Seismology and Tsunami Research Department

気象研究所技術報告 第 77 号

海溝沿い巨大地震の地震像の即時的把握に関する研究

地震津波研究部

気象研究所

METEOROLOGICAL RESEARCH INSTITUTE, JAPAN March 2017

Director-General: Dr. Kiyoharu Takano Senior Director for Research Affairs: Dr. Kazuo Saito Senior Director for Research Coordination: Mr. Yoshiaki Takeuchi

Forecast Research Department Director: Mr. Ko Koizumi Climate Research Department Director: Dr. Tomoaki Ose Typhoon Research Department Director: Mr. Isao Takano Atmospheric Environment and

Applied Meteorology Research Department Director: Dr. Izuru Takayabu Meteorological Satellite and

Observation System Research Department Director: Mr. Osamu Suzuki Seismology and Tsunami Research Department Director: Dr. Kenji Maeda Volcanology Research Department Director: Dr. Hitoshi Yamasato Oceanography and Geochemistry Research Department Director: Dr. Tsurane Kuragano

1-1 Nagamine, Tsukuba, Ibaraki, 305-0052 Japan

TECHNICAL REPORTS OF THE METEOROLOGICAL RESEARCH INSTITUTE Editor-in-chief: Tomoaki Ose

Editors: Wataru Mashiko Masayoshi Ishii Masahiro Sawada Yuji Kitamura Hanako Inoue Hiroaki Tsushima Shinya Onizawa Norihisa Usui

Managing Editors: Rai Okabe, Miyuki Kawamata

The Technical Reports of the Meteorological Research Institute has been issued at irregular intervals by the Meteorological Research Institute (MRI) since 1978 as a medium for the publication of technical report including methods, data and results of research, or comprehensive report compiled from published papers. The works described in the Technical Reports of the MRI have been performed as part of the research programs of MRI.

©2017 by the Meteorological Research Institute.

The copyright of reports in this journal except that of reprints from other publications belongs to the Meteorological Research Institute (MRI). Republication, reproduction, translation, and other uses of any extent of reports in this journal require written permission from Copyright holders.

TECHNICAL REPORTS OF THE METEOROLOGICAL RESEARCH INSTITUTE No.77

Research on rapid estimation of the parameters for large earthquakes along trenches

BY

Seismology and Tsunami Research Department

気象研究所技術報告 第 77 号

海溝沿い巨大地震の地震像の即時的把握に関する研究

地震津波研究部

気 象 研 究 所

METEOROLOGICAL RESEARCH INSTITUTE, JAPAN

日本海溝、千島海溝、南海トラフ、琉球海溝など海溝沿いで巨大地震が発生 した場合、震源域が広範囲に及ぶことから、とりわけ陸地に近いところで発生 した場合には地震発生直後の大規模津波の襲来や強い地震動により、広域にわ たる甚大な被害が懸念される。津波や強い揺れの発生は、震源域の広がりや震 源断層上のすべり分布に左右されるが、これらを即時的に把握する技術が開発 できれば、津波予測の大幅な精度向上、強い揺れの精度の高い推定につながり、

被害把握や災害の軽減に直結する地震防災情報の提供が可能となるであろう。

このような考えから、気象研究所では平成 22 年度より 5 か年の計画で「海溝沿 い巨大地震の地震像の即時的把握に関する研究」を開始した。その目標は、巨 大地震が発生した直後に、地震の規模や震源断層の広がり、断層すべり分布、

長周期を含めた地震動を把握するための技術開発を行うことである。研究を開 始した 1 年後、図らずも未曽有の大災害が発生した。平成 23 年（2011 年）東 北地方太平洋沖地震（M9.0）である。この地震は、その規模の巨大さゆえに、

地震規模の推定、津波警報の切替、緊急地震速報の精度低下など当時の気象庁 の地震処理技術に様々な課題があることを明らかにした。その課題の一つが、

まさに 1 年前から開始した本研究が解決を目指してきた課題であった。その後 本課題の研究を加速し、特に緊急に対処すべき規模の過小評価の課題について は、その解決のための新しい技術を気象庁のシステムに早急に取り込むことが できた。その他の課題についても新しい技術開発を順次進め、当初の予定を 1 年延長し平成 27 年度末をもって、 本研究は一応の区切りをつけた。 本報告書は、

この 6 年間の研究の成果をまとめたものである。 この研究による成果の多くは、

既に気象庁の地震津波監視システムに取り込まれており、有効に活用されてい る。惜しむらくは、東北地方太平洋沖地震の発生の前に本研究の成果が現業化 されていればとの思いがあり、残念でならない。なお、地震像の即時把握技術 については、なおいくつかの課題が残されている。地震の揺れの大きさに比べ、

巨大な津波を引き起こす、いわゆる津波地震をより精度よく把握することはそ の一つである。これらの残された課題については、新たな枠組みで研究を進め ることにしており、今後のさらなる研究の進展が期待される。

気象研究所 地震津波研究部長

前 田 憲 二

本報告は，重点研究「海溝沿い巨大地震の地震像の即時的把握に関する研究」 （平成

年～

年度）

において得られた成果を、巨大地震の規模等の把握・震源断層の広がりとすべり分布の把握・余震分 布の把握・地震動分布の把握というテーマに分けてとりまとめたものである。

第

章では，巨大地震の規模等の把握について報告する。これは平成

年（

年）東北地方太 平洋沖地震の発生の際に顕在化した巨大地震の規模把握の問題に取り組んだ結果開発した手法を中心 に記述している。1.1 節では、強震動域の広がりに基づく手法などの様々な早期規模推定法について 記述している。1.2 節では、フィルターの遮断周期を様々に変えた場合の変位の最大振幅から規模を 推定する手法について記述している。1.3 節では、強震動の継続時間から推定される断層破壊の伝播 に関して記述している。1.4 節では、発震機構の分類手法に関して記述している。

第

章では、震源断層の広がりや断層すべり分布の推定手法について報告する。2.1 節では震度分 布のみから震源域を推定する手法について記述している。2.2 節では、長周期地震波動の重ね合わせ を用いて、巨大地震の大すべり域を推定する手法について記述している。

節では、平成

年（2011 年）東北地方太平洋沖地震について遠地及び近地地震波形を用いて解析した詳細な震源過程について 記述している。2.4 節では、平成

年（2011 年）東北地方太平洋沖地震前後に発生した主な地震の震 源過程解析結果について記述している。2.5 及び

節では、長周期におけて優れた特性を示す

データ等を用いて津波波源を即時推定する手法について記述している。

第

章では、自動震源決定を含め余震を早期かつ正確に推定するための手法について報告する。3.1 節では、逐次的にベイズ推定を用いて信頼性の高い震源位置を推定する手法について記述している。

3.2

節では、地震頻発時にも用いることができるよう、エンベロープデータに基づく震源推定手法に ついて記述している。3.3 節では、高精度の震源を得るために南海トラフ域で行った自己浮上式海底 地震計観測と、推定した海溝外側の地震活動域について記述している。3.4 節では、海域の地震観測 能力向上のために開発した長期型自己浮上式海底地震計について記述している。3.5 節では、震源決 定精度向上を目的として、日本列島の地殻構造を推定した結果について記述している。3.6 節では、

更にその三次元速度構造を用いて高速に震源決定を行う手法について記述している。3.7 節では、平 成

年（2011 年）東北地方太平洋沖地震後に各地で活発化した地震活動の状況について記述してい る。

第

章では、地震発生直後に長周期を含めた地震動を推定するための手法について報告する。4.1 節では、様々な周期の地震動と複数の地盤構造情報との相関について調査した結果と、それを用いた 地震動分布推定手法について記述している。4.2 節では、平成

年（2011 年）東北地方太平洋沖地震 において観測された地震動の特徴について記述している。4.3 節では、データ同化手法を用いてリア ルタイムに地震動の時間履歴を推定する手法について記述している。

ここで報告している手法のいくつかは、平成

年

月の気象庁における津波警報の改善のための手

法として採用された。

This report presents the results of the project “Research on rapid estimation of the parameters for large earthquakes along trenches”, which was conducted by the Seismology and Tsunami Research Department, MRI, over six years from FY 2010 to FY 2015. The report consists of four chapters.

Chapter 1: Estimation of earthquake magnitude and related parameters Chapter 2: Estimation of fault rupture length and slip distribution Chapter 3: Estimation of aftershock distribution

Chapter 4: Estimation of distribution of strong ground motion

Chapter 1 reports on methods of rapid estimation of earthquake magnitude and source parameters that were developed to overcome difficulties encountered during determination of the magnitude of the 2011 off the Pacific coast of Tohoku Earthquake (2011 Tohoku earthquake hereafter). Section 1.1 describes various methods for the rapid determination of magnitude of great earthquakes. Section 1.2 describes a method of magnitude estimation based on peak ground displacement for various cut-off periods. Section 1.3 describes the characteristics of rupture propagation inferred from the duration of strong motion. Section 1.4 describes a method for categorizing focal mechanisms.

Chapter 2 reports on methods for rapid estimation of the length of rupture of the earthquake fault and the slip distribution. Section 2.1 describes a method for estimation of the length of rupture of the earthquake fault from the distribution of seismic intensity. Section 2.2 describes a method to estimate the area of large coseismic slip by using an array technique for long-period seismic waves. Section 2.3 describes the source process analysis for the 2011 Tohoku earthquake. Section 2.4 describes the source process analyses for major aftershocks of the 2011 Tohoku earthquake. Sections 2.5 and 2.6 describe real-time methods for estimation of tsunami source parameters using both of onshore GNSS data and offshore tsunami data.

Chapter 3 reports on methods of hypocenter determination, related studies of aftershocks, and improvements in the precision of hypocenter determinations. Section 3.1 describes an automated method of hypocenter determination that uses Bayesian analysis. Section 3.2 describes an automated method for estimation of aftershock distributions by using envelope data. Section 3.3 describes seismicity recorded by pop-up OBSs in the outer rise area of the Nankai trough. Section 3.4 describes long-term pop-up OBSs that were developed to improve seismic observation data in offshore areas. Section 3.5 describes a crustal structure model of the Japanese islands estimated to improve the precision of hypocenter determinations. Section 3.6 describes a method for fast determination of hypocenters by using 3D traveltime tables. Section 3.7 describes seismicity activated after the 2011 Tohoku earthquake in various areas of Japan.

Chapter 4 reports on methods for estimation of the distribution of strong ground motion. Section 4.1 describes the relationship between subsurface structure and ground motion of various periods. Section 4.2 describes the strong ground motion of the 2011 Tohoku earthquake. Section 4.3 describes a method for estimation of seismic wave propagation by using a data assimilation technique.

Some of the methods described here have been used to improve tsunami warnings since March 2013.

目 次

第

章 巨大地震の規模等の把握

様々な早期規模推定手法

1.2

最大変位振幅を用いた早期規模推定

強震動の継続時間による破壊伝播特性把握

メカニズムタイプ変化の統計的検出

第

章 震源断層の広がりとすべり分布の把握

2.2

長周期バックプロジェクション法による大すべり域の推定

平成

年（

年）東北地方太平洋沖地震の震源過程解析

2.4 平成23

年（2011 年）東北地方太平洋沖地震前後の地震の震源過程解析

2.5 GNSS

データ等を用いた津波波源の即時推定（1）

2.6 GNSS

データ等を用いた津波波源の即時推定（

）

第

章 余震分布の把握

3.1 ベイズ推定を用いた自動震源推定

3.2 エンベロープデータを用いたイベント自動検出 3.3 海底地震計を用いた南海トラフ周辺の震源位置の把握 3.4 長期型自己浮上式海底地震計の整備とその試験運用について 3.5 日本列島の地殻構造

3.6 三次元走時表を用いた震源決定

3.7 平成23

年（2011 年）東北地方太平洋沖地震以降に活発化した地震活動

第

章 地震動分布の把握

4.1 長周期地震動と地盤構造との関係

4.2 平成23

年（2011 年）東北地方太平洋沖地震の地震動

4.3 データ同化手法を用いた地震動推定

第 1 章 巨大地震の規模等の把握

本項の論文は，著者からの転載許可を受けて掲載している。

（

）

RAPID SOURCE PARAMETER ESTIMATION OF GREAT EARTHQUAKES FOR TSUNAMI

WARNING

Akio KATSUMATA¹, Shigeki AOKI², Yasuhiro YOSHIDA³, Hiroshi UENO⁴ and Takashi YOKOTA⁵

1 Head of The Second Research Laboratory, Seismology and Volcanology Research Department, Meteorological Research Institute, Japan Meteorological Agency,

Tsukuba, Japan, [email protected]

2 Senior Researcher, Seismology and Volcanology Research Department, MRI, JMA, Tsukuba, Japan, [email protected]

3 Senior Researcher, Seismology and Volcanology Research Department, MRI, JMA, Tsukuba, Japan, [email protected]

4 Senior Researcher, Seismology and Volcanology Research Department, MRI, JMA, Tsukuba, Japan, [email protected]

5 Director of Seismology and Volcanology Research Department, MRI, JMA, Tsukuba, Japan, [email protected]

ABSTRACT: One of major problems in the tsunami warning for the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0) was a lack of awareness of underestimation of the earthquake magnitude at the time soon after the occurrence. Displacement magnitude, which is usually used for the first tsunami warning a few minutes after the earthquake occurrence, could not evaluate such large magnitude. Seismic moment could not be determined from the regional seismological network data due to over range of broadband sensor outputs. To overcome these difficulties in earthquake magnitude estimation, several methods are being developed to estimate proper magnitude roughly and to understand possible magnitude underestimation soon after such large earthquakes.

Key Words: rapid magnitude determination, great earthquakes, tsunami warning, area of strong shaking, strong motion duration

INTRODUCTION

The tsunami height of the first tsunami warning by Japan Meteorological Agency (JMA) is estimated based on earthquake magnitude. The first tsunami warning should be issued within a few minutes after the detection of the earthquake occurrence. Displacement magnitude (Katsumata, 2004) is used for the first tsunami warning. Seismic moment tensor is also estimated after the first tsunami warning to estimate size of the earthquake more accurately (Usui et al., 2010). The tsunami height estimation is updated from data including the seismic moment tensor and sea level observations. At the time of the occurrence of the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0), the magnitude was not estimated properly due to too short cutoff period (six seconds) of the filter for the displacement

magnitude compared with the rupture duration (about three minutes [Yoshida et al., 2011a]).

Seismic moment could not be estimated from the regional seismological network data due to over-range of broadband sensor (STS-1 and STS-2) outputs, and it took longer time to estimate it from global data. These caused a lack of awareness of underestimation of the earthquake magnitude at the time soon after the occurrence.

To overcome these difficulties in earthquake magnitude estimation, we are developing several methods to estimate proper magnitude roughly and to understand possible magnitude underestimation soon after such large earthquakes. A large earthquake causes strong shaking in a wide area, long strong motion duration, and large seismic amplitude in long period range as well as in short period range. These observations could be used for the magnitude estimation.

MAGNITUDE DETERMINATION FROM SPAN OF STRONG MOTION AREA

Large earthquakes cause strong motion in a wide area. Span of strong-motion area is related to earthquake magnitude. Seismic intensity distribution in Japan can be known in a few minutes after earthquake occurrence owing to a dense on-line network of seismic intensity meter in Japan. It is possible to estimate earthquake magnitude roughly from the area of strong shaking.

Figure 1 shows the distributions of seismic intensity of the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0) and the 2003 Off-Tokachi Earthquake (Mw 8.0). The span of 5-lower or the greater of the JMA seismic intensity scale of the 2011 off the Pacific coast of Tohoku Earthquake reached about 700 km. The span of the 2003 Off-Tokachi Earthquake was about 300 km, which was much less than that of the 2011 off the Pacific coast of Tohoku Earthquake.

Fig. 1. Distributions of seismic intensity of the 2011 off the Pacific coast of Tohoku Earthquake and the 2003 Off-Tokachi Earthquake. The contours in maps denote slip distributions estimated by Yoshida (2005) and Yoshida et al. (2011a).

SOURCE AREA ESTIMATION FROM SEISMIC INTENSITY DISTRIBUTION

The place of observed strong motion would be close to the seismic source. Source area can be estimated from the area of strong-motion. At each station, distance from the fault is estimated from the seismic intensity with the formula by Si and Midorikawa (1999). To estimate the source area, grid points are set on the plate boundary. At each grid points, number of stations where the distance between the station and the grid point is larger than the estimated fault distance is counted. If the grid

point is on the source area, the number of inconsistent stations (where the distance between the station and the grid point is larger than the estimated fault distance) should not exceed some number. Figure 2 shows the estimated source area of the 2011 off the Pacific coast of Tohoku Earthquake and the 2003 Off-Tokachi Earthquake from the number of the inconsistent stations. Whereas it is possible to estimate the close edge of a fault with this method, it is difficult to estimate the far edge of an offshore fault properly. A different color map is used for the area off the trench axis in Figure 2. When the seismic fault lies along the island arc, like the 2011 off the Pacific coast of Tohoku Earthquake, it is able to estimate length of the fault.

Fig. 2. Estimated source area of the 2011 off the Pacific coast of Tohoku Earthquake and the 2003 Off-Tokachi Earthquake from seismic intensity distribution [Yokota and Kaida, 2011].

DURATION OF STRONG MOTION

The duration of the strong motion becomes also longer for larger earthquakes. Durations of strong motion were investigated for large earthquakes in and around Japan.

Figure 3 shows distribution of strong-motion durations for the 2003 Off-Tokachi Earthquake. The colors denote strong-motion duration at stations. Data from K-NET [Kinoshita, 1998] and KiK-net [Aoi et al. 2000] is used for this analysis. The durations in the north of the epicenter are shorter than those in the other directions in the figure. The duration difference is considered due to directivity effect. Figure 4 shows azimuthal distribution of the duration, which shapes a sinusoidal curve. It is possible to estimate fault length and rupture direction from the distribution (Izutani and Hiraswa, 1987). The arrow in Figure 3 indicates estimated fault length and rupture direction. When the faulting is simple unilateral, this method is useful for rapid estimation of the fault parameters.

Figure 5 shows relationship between moment magnitude and strong-motion duration of earthquakes which occurred in and around Japan. Good correlation is seen between strong-motion duration and earthquake magnitude. The duration of the earthquake in March, 2011 exceeded eighty seconds, which was the longest among those of the large earthquakes. It is difficult to estimate the accurate moment magnitude on the basis of the duration due to the large scatter. We can, however, judge possible magnitude underestimation by the duration.

Fig. 3. Distribution of strong-motion duration of the 2003 Off-Tokachi Earthquake [Aoki et al., 2011].

The star indicates the epicenter of the earthquake, and the arrow indicates estimated fault length and rupture direction by the method of Izutani and Hirasawa (1987).

Fig. 4. Azimuthal distribution of strong-motion duration of the 2003 Off-Tokachi Earthquake [Aoki et al., 2011]. Blue curve indicates the theoretical distribution of the estimated fault.

Fig. 5. Relationship between moment magnitude (after the Global CMT Project) and strong-motion duration Dobs of earthquakes which occurred in and around Japan [Aoki, et al., 2011]. The red circle denotes that of the 2011 off the Pacific coast of Tohoku Earthquake.

MAGNITUDE ESTIMATION FROM P-WAVE

Some magnitude determination methods from P-wave have been proposed. Yoshida (1995) proposed a magnitude determination method from P-wave displacement amplitude, Mp. Figure 6 shows the station magnitude Mp of the 2011 off the Pacific coast of Tohoku Earthquake. The horizontal axis of Figure 6 denotes time of magnitude determination from the origin time of the earthquake which corresponds to S-wave arrival time at the station. The magnitude grows before about four minutes.

This reflects the extension of the rupture area.

Tsuboi et al. (1995) developed a method of estimating moment magnitude, Mwp, from integrated P-wave. Figure 7 shows the magnitude Mwp of the 2011 off the Pacific coast of Tohoku Earthquake.

Ogawara et al. (2004) showed a magnitude determination method, Mwliss, based on squared amplitude of broadband seismic wave. Figure 8 shows the magnitude Mwliss of the 2011 off the Pacific coast of Tohoku Earthquake.

These magnitudes show similar variation along the time from the origin time, and reach about nine in five minutes. It is possible to determine the magnitude of this earthquake properly in five minutes with these methods. Dispersion of Mwp is smaller compared with other P-wave magnitudes.

Fig. 6. Mp of the 2011 off the Pacific coast of Tohoku Earthquake (Mw 9.0) [Yoshida et al., 2011b].

The red circle denotes station magnitude calculated from seismic wave between P and S arrivals at each station. The blue small dot denotes that calculated from seismic wave contaminated with S-wave. The horizontal axis shows the time when the magnitude is estimated at each station measured from the origin time.

Fig. 7. Mwp [Tsuboi et al., 1995] of the 2011 off the Pacific coast of Tohoku Earthquake [Yoshida et al., 2011b]. The symbols are the same as those in Figure 6.

Fig. 8. Mwliss [Ogawara et al., 2004] of the 2011 off the Pacific coast of Tohoku Earthquake [Yoshida et al., 2011b]. The symbols are the same as those in Figure 6.

MAGNITUDE DETERMINATION FROM LONG-PERIOD SEISMIC WAVE

It takes a long time to complete a rupture of a large earthquake. Excitation of long-period seismic wave is one of features of large earthquakes. The cutoff period (6 s) for the displacement magnitude used for the first tsunami warning was too short for the 2011 off the Pacific coast of Tohoku Earthquake. Usage of long period components of seismic wave would help to estimate earthquake magnitude properly.

Figure 9 shows seismic waves processed with filters of different frequency responses. The figure shows seismic waves of the 2011 off the Pacific coast of Tohoku Earthquake (the left) and the 2003 Off-Tokachi Earthquake (the right). The upper of the figure shows seismic waves with the same response for the displacement magnitude. The lower shows those processed with a filter of 200-1000 second pass-band. While amplitudes of short-period seismic wave are not so different between the two earthquakes, those of long-period seismic wave differ very much. This is one method to distinguish the difference of these magnitudes.

Magnitude determination methods from various frequency ranges are developed. Peak displacements of seismic waves of 1, 2, 5, 10, 20, 50 and 100 second cutoff periods are used to determine magnitude. Phase type is not cared in this method, and peaks are possibly those of S-waves.

Figure 10 shows estimated durations to determine magnitude only from P-wave and from S-wave. It is necessary to wait for the completion of fault rupture to get enough length of data. At a station close to source area, S-P time would be shorter than the rupture duration. It is considered that magnitude determination from S-wave peak is more rapid than that only from P-wave peaks when local seismic data are available. Figure 11 shows growth of the magnitude with time from the origin time on the horizontal axis. The averaged magnitudes calculated from closest ten stations are shown in the figure.

The magnitudes from long-period seismic wave reach the final values within three minutes for the earthquake.

Fig. 9. Filtered Seismic waves of the 2011 off the Pacific coast of Tohoku Earthquake (the left) and the 2003 Off-Tokachi Earthquake (the right) [Yoshida et al., 2011b]. The upper shows seismic waves for the displacement magnitude used for the tsunami warning, and the lower shows those processed with a filter of a 200-1000 second pass-pand.

Fig. 10. Assumed time to estimate earthquake magnitude from P-wave (the green broken curve) and S-wave (the red solid curve) [Katsumata et al., 2011]. The curves indicate relationships between epicentral distance and sum of travel time and assumed rupture duration. Sixty seconds is assumed as the rupture duration here.

Fig. 11. Growth of magnitude from seismic waves of various cutoff-periods [Katsumata et al., 2011].

The horizontal axis shows time from the origin time of the earthquake. The numerals indicate cutoff periods of the filters.

CONCLUSIONS

Several magnitude determination methods are being developed to estimate earthquake magnitude soon after occurrence of a large earthquake for tsunami warning. Magnitude estimation from span of strong-motion area, strong-motion duration, P-wave, and S-wave amplitudes were examined.

Combination of these methods is expected to help us to issue a proper tsunami warning for the next great earthquake.

ACKNOWLEDGMENTS

Data from NIED K-NET, KiK-net, F-net, and the JMA seismic network were used in this study.

Hypocenter parameters of the unified seismic catalog of Japan and Global CMT Project are referred to.

The unified seismic catalog of Japan is based on data from the National Research Institute for Earth Science and Disaster Prevention, Hokkaido University, Hirosaki University, Tohoku University, University of Tokyo, Nagoya University, Kyoto University, Kochi University, Kyushu University, Kagoshima University, the National Institute of Advanced Industrial Science and Technology, Tokyo metropolitan government, Shizuoka prefectural government, Kanagawa prefectural government, the City of Yokohama, the Japan Marine Science and Technology Center, and the Japan Meteorological Agency. We thank Y. Kaida for many valuable discussions about source area estimation from seismic intensity distribution.

REFERENCES .

Aoki, S., Y. Yoshida, and A. Katsumata (2011), “The characteristics of rupture propagation deduced from strong motion duration”, Programme and Abstract of The Seismological Society of Japan Fall Meeting, P2-42.

Aoi, S., K. Obara, S. Hori, K. Kasahara, and Y. Okada, (2000), “New strong-motion observation network: KiK-net”, EOS. Trans. Am. Geophys. Union, Vol. 81, F863.

Usui, Y., S. Aoki, N. Hayashimoto, T. Shimoyama, D. Nozaka, and T. Yoshida (2010), “Description of and advances in automatic CMT inversion analysis”, Quart. J. Seism., Vol 73, 169-184.

Izutani, Y. and T. Hirasawa (1987), “Use of strong motion duration for rapid evaluation of fault parameters”, J. Phys. Earth, Vol. 35, 171-190.

Katsumata, A. (2004), “Revision of the JMA displacement magnitude”, Quart. J. Seism., Vol. 67, 1-10.

(in Japanese with English abstract)

Katsumata, A., S. Aoki, Y. Yoshida and K. Kimura (2011), “Quick magnitude determination based on peak velocity and displacement”, Programme and Abstract of The Seismological Society of Japan Fall Meeting, P2-67.

Kinoshita, S. (1998), “Kyoshin Net (K-NET)”, Seismological Research Letters, Vol. 69, 309-332.

Ogawara, T., T. Furudate and M. Okada (2004), “Preliminary empirical formula to estimate moment magnitude of teleseismic event by using LISS data”, Technical Reports of the Matsushiro Seismological Observatory, JMA, Vol. 21, 75-81.

Si, H. and S. Midorikawa (1999), “New attenuation relationship for peak ground acceleration and velocity considering effect of fault type and site condition”, J. Struct. Constr. Eng., Vol. 523, 63-70.

(in Japanese with English abstract and figure captions)

Tsuboi, S., K. Abe, K. Takano, and Y. Yamanaka (1995), “Rapid determination of Mw from broadband P waveforms”, Bull. Seism. Soc. Am., Vol. 85, 606-613.

Yokota, T. and Y. Kaida (2011), “Estimation of magnitude using distribution of seismic intensity”, Programme and Abstract of The Seismological Society of Japan Fall Meeting, P2-22.

Yoshida, Y (1995), “Magnitude determination from P-wave amplitude”, JMA Technical Note of Seismology and Volcanology, Vol. 71, 41-52.

Yoshida, Y. (2005), “Rupture process of the 2003 Off-Tokachi Earthquake”, Technical Report of Japan Meteorological Agency，Vol. 126, 9-14.

Yoshida, Y., H. Ueno, D. Muto and S. Aoki (2011a), “Source process of the 2011 off the Pacific coast of Tohoku Earthquake with the combination of teleseismic and strong motion data”, Earth Planets Space, Vol. 63, 565-569.

Yoshida, Y., S. Aoki, A. Katsumata and T. Yokota (2011b), “Evaluation of rapid Mw determination method”, Programme and Abstract of The Seismological Society of Japan Fall Meeting, P2-69.

1.2 最大変位振幅を用いた早期規模推定

本項の論文は，著者からの転載許可を受けて掲載している。

（

）

Earth Planets Space,65, 843–853, 2013

Rapid magnitude determination from peak amplitudes at local stations

Akio Katsumata¹, Hiroshi Ueno¹, Shigeki Aoki¹, Yasuhiro Yoshida², and Sergio Barrientos³

1Meteorological Research Institute, JMA, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan

2Ministry of Education, Culture, Sports, Science and Technology in Japan, 3-2-2 Kasumigaseki, Chiyoda-ku, Tokyo 100-8959, Japan

3Departamento de Geofisica, Universidad de Chile, Blanco Encalada 2002, Santiago, Chile

(Received August 9, 2012; Revised March 12, 2013; Accepted March 12, 2013; Online published September 17, 2013)

The rapid determination of its magnitude soon after a great earthquake is necessary for the issuing of effective tsunami warnings, as demonstrated in the great earthquake off Tohoku district in Japan on March 11, 2011. The earthquake magnitude for the first tsunami warning was underestimated due to magnitude saturation. This paper proposes a method to determine magnitude rapidly from peak velocity and displacement of long-period seismic waves up to 100 seconds at local stations. When waveform data at local stations are available, the magnitude fromS-wave peaks is expected to be determined faster than that from only P-wave peaks. It takes about 140 seconds to estimate a magnitude of about 9 for the March 11, 2011, earthquake, which would enable us to issue the first tsunami warning within three minutes after the same type of earthquake.

Key words:Magnitude determination, tsunami warning, long-period seismic wave, great earthquakes.

1. Introduction

The displacement magnitude determined by the Japan Meteorological Agency (JMA) (Katsumata, 2004) indi- cated saturation during the 2011 off the Pacific coast of Tohoku Earthquake on March 11 of Mw9.0 (Hiroseet al., 2011). Magnitude determination is a key to issuing an ef- fective tsunami warning. The JMA displacement magni- tude is determined from the logarithm of the maximum dis- placement amplitude recorded with seismographs of natural period 6 s and damping coefficient of 0.55. Displacement records are currently obtained from acceleration records by numerical integration and digital filtering. Using longer- period seismic waves for magnitude determination should overcome the problem of magnitude saturation (Aki, 1967).

Here, we use the peak velocity and displacement of a longer period than that used for the JMA magnitude to rapidly de- termine the magnitude.

Several magnitude determination methods have been pro- posed for a tsunami warning based on P-wave before the S-wave arrival (Tsuboiet al., 1995; Yoshida, 1995; Hara, 2007; Kanamori and Rivera, 2008; Lomax and Michelini, 2009). When the fault rupture lasts a long time, the epicen- tral distance of data should be great enough to get aTS−TP

exceeding the rupture duration, where TP andTS are the travel times ofPandSwaves.

The broken curve in Fig. 1 indicates the time when the P-wave magnitude can be determined. The time is consid- ered to be the sum of theP-wave travel time and the source duration of the earthquake. The source duration of an earth- quake is assumed to be sixty seconds in the figure. Since

Copyright cThe Society of Geomagnetism and Earth, Planetary and Space Sci- ences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sci- ences; TERRAPUB.

doi:10.5047/eps.2013.03.006

theS-wave amplitude often exceeds theP-wave amplitude, theP-wave magnitude should be determined from the data before the S-arrival. TheTS−TP time should exceed the source duration (D) for the P-wave magnitude. The range ofTS−TP <Dis not shown in the figure. The solid curve in the figure denotes TS +D, which is the time when the S-wave magnitude can be determined. When data at lo- cal stations are available, the magnitude can be determined more quickly from the amplitude ofS-waves than from that of onlyP-waves.

Quick magnitude determination methods have been pro- posed also for early earthquake warning (Wuet al., 1998;

Kamigaichi, 2004; Wu and Zhao, 2006; Zolloet al., 2006).

However, those methods are based on the amplitude mea- sured on waveforms of intermediate period, or the ampli- tude of the initial parts after the onsets, and do not fit magni- tude determination for great and long source duration earth- quakes.

For the P-wave magnitude determination, it is neces- sary to restrict the amplitude search range within P- and S-arrivals to avoidS-wave contamination. When any phase type indicating the peak amplitude can be used, time win- dows for the amplitude search are not needed. This makes the process flow simple and robust. Here, we examine the magnitude determined from the peak amplitude of any phases including long-periodS-waves and surface waves.

2. Method and Data

The peak velocity (m/s) or displacement (m)Aand mag- nitudeMare assumed to be expressed as follows:

M =alog₁₀A+blog₁₀R+c. (1) Here,a,b, andcare constants, andR(km) is the hypocen- tral distance. Ais measured over a seismic record on a ver- tical component obtained at a local station. A dip slip along

Fig. 1. Assumed time to determine earthquake magnitude fromP-wave (the broken curve) and fromS-wave (the solid curve). The curves indicate relationships between the epicentral distance and the sums of travel times (TP,TS) and the assumed rupture duration (D). The rupture duration is assumed to be sixty seconds.

Fig. 2. Examples of waveform data used in this study. Filters of various cutoff periods (Tc) are used to obtain the displacement records. The waveform was obtained for the 2011 off the Pacific coast of Tohoku Earthquake on March 11 at an epicentral distance of 319 km.

a plate boundary may cause a large tsunami, and is expected to generate largeP-SVmode seismic waves, which appear on the vertical component.

Velocity and displacement records are obtained from strong-motion acceleration records with numerical integra-

tion and low-cut filters. Second- (for velocity) and Third- (for displacement) order low-cut Bessel filters (Katsumata, 1993) are used in this study. The filters are recursive, and can be applied in real-time processing.

Several cutoff periods are used to measure A. Cutoff

Fig. 3. Station map of the data used in this study. Circles denote the locations of the stations.

Fig. 4. Epicenters of the earthquakes for which the seismic records were obtained in this study. (a)–(e) indicate events in Fig. 9.

periods of low-cut filters are set at 1, 2, 5, 10, 20, 50, and 100 seconds. Various cutoff periods (Tc) are used to accommodate a broard range of magnitudes. Examples of waveforms are presented in Fig. 2. Constantsa,bandcare estimated so as to minimize the difference between M in Eq. (1) andMwof the Global CMT solutions. The constants in Eq. (1) are estimated for velocity/displacement and each

cutoff period. We assume a common value ofa for all Tc

in Eq. (1), since we expect to see magnitude saturation in the result. The values ofbandcare estimated for eachTc, individually.

Parameter a is first estimated with data of earthquakes Mw > 7, then b and c are estimated with data includ- ing those of smaller events. When the constantsa,b, and

Table 1. Velocity magnitude determination coefficients in Eq. (1).

Tc(s) a b c

1 1.43 4.08 1.18

2 1.43 3.96 1.20

5 1.43 3.68 1.64

10 1.43 3.25 2.56

20 1.43 2.81 3.60

50 1.43 2.67 3.90

100 1.43 2.47 4.39

Table 2. Displacement magnitude determination coefficients in Eq. (1).

Tc(s) a b c

1 1.23 3.48 3.02

2 1.23 3.21 3.17

5 1.23 2.61 4.10

10 1.23 1.99 5.31

20 1.23 1.46 6.39

50 1.23 1.22 6.80

100 1.23 1.24 6.64

c are estimated simultaneously, M of great earthquakes (Mw > 8) diverges further fromMw. We adopt the value ofa for aTcwhich indicates the least dispersion for earth- quakes including small ones, since such a value would be applicable to great earthquakes as well as to moderate ones.

The acceleration records were obtained with a seismic network installed by JMA. The station map is presented in Fig. 3. The accelerometers record ground motion up to±3 G with a resolution of 0.5×10⁻⁵m/s²(Japan Meteorolog- ical Agency, 2011), which corresponds to a 22-bit resolu- tion. We use only velocity and displacement amplitudes that exceed 0.5×10⁻⁵/(2π/Tc)m/s and 0.5×10⁻⁵/(2π/Tc)² m.

Records of fifty-five earthquakes ofMw>6.0 from 2001 to 2011 are used. The epicenter map of the earthquakes is presented in Fig. 4.

3. Results

Tables 1 and 2 list the obtained values of coefficientsa, bandcfor the magnitude determination. We adopted the estimateda for the cutoff period of fifty seconds, since it provided the smallest standard deviation for earthquakes, including smaller ones than those used for estimating a (Mw > 7). The coefficient for the amplitudea in Eq. (1) is greater for velocity than for displacement. This relation- ship has been seen previously for short-period amplitude measurements (Watanabe, 1971; Katsumata, 2001).

Figures 5 and 6 present data plots with the fitted lines.

The relationship between hypocentral distance and ampli- tude depends on the cutoff periods: the shorter the cutoff period, the steeper the attenuation. The displacement am- plitude attenuation depends more on the cutoff period than does the velocity amplitude. The dependence on the pe- riod would be related to inelastic attenuation and the seis- mic wave type that exhibits a peak amplitude. Data deviates from the fitted line at short epicentral distances. The disper- sion of log₁₀Aranges from 0.22²to 0.33²for the velocity magnitude, and from 0.21² to 0.34² for the displacement

magnitude. Amplitude data of velocity and displacement have similar data dispersions.

Figures 7 and 8 illustrate the relationship between the moment magnitudeM_wand the difference of the estimated magnitude M (Eq. (1)) from Mw. Since a common value of a is used in Eq. (1), magnitude saturation is seen in shorter cutoff periods (Figs. 7 and 8). Standard deviations ofM −Mwrange from 0.18 (Tc =100 s) to 0.32 (Tc=1 s) for velocity magnitude and from 0.15 (Tc = 100 s) to 0.27 (Tc = 1 s) for displacement magnitude. Deviations of velocity magnitudes are slightly larger than those of dis- placement magnitudes.

4. Discussion

4.1 Velocity magnitude and displacement magnitude In this section, we will briefly discuss the suitability for tsunami warning of velocity and displacement magnitudes.

Dispersion of data (Figs. 5 and 6) and differences fromMw

(Figs. 7 and 8) do not clearly differ between velocity and displacement magnitudes. Data from accelerometers are used here with numerical integration, and data availability is limited byaR/ωfor velocity andaR/ω²for displacement, whereaR is the sensor resolution of the accelerometer and ωis the angular frequency. Velocity magnitude is available for more events due to the limitation on the amplitude range.

For tsunami earthquakes such as the 1992 Nicaragua earthquake (Kanamori and Kikuchi, 1993), the low- frequency component is more dominant than in normal earthquakes. The displacement magnitude is more sensitive to the low-frequency component than is the velocity mag- nitude. The displacement magnitude is thus preferable for tsunami warnings. The displacement magnitude is mainly examined in the following sections.

The integral of displacement is proportional to the seis- mic moment, and this might be better for tsunami warning than the displacement amplitude. However, accelerometers do not have enough resolution for more integration. When data of strong motion velocity meters are used for the same purpose, a longer-period component could be used. Since accelerometer networks are more dense than strong motion velocity meter networks, we use accelerometer data in this study.

4.2 Application to rapid magnitude determination The proposed magnitude is considered to be used to ob- serve the growth of magnitude value in real-time process- ing. Since recursive filters are used to obtain the veloc- ity/displacement records and the transmission and process- ing delay could be no more than several seconds, it is possible to see the magnitude value change soon after the hypocenter determination. Because they are not used, in- version analysis and phase identification do not introduce additional delay.

The proposed magnitude determination method is ap- plied to some large earthquakes, and the results are pre- sented in Fig. 9. The horizontal axis in the figure represents time from the earthquake occurrence. The magnitude is determined from maximum amplitudes measured until the time indicated on the horizontal axis at the closest three to ten stations. The magnitude value changes with the arrivals of larger seismic waves. It reaches a stable value when peak

Fig. 5. Relationship between hypocentral distance and velocity amplitude. The line denotes the fitted relationship (Eq. (1)). The data plots are shifted in peak amplitude by(7−Mw)/ato adjust magnitude differences.

Fig. 6. Relationship between hypocentral distance and displacement amplitude. The line denotes the fitted relationship (Eq. (1)). The data plots are shifted in peak amplitude by(7−Mw)/ato adjust magnitude differences.

amplitudes are observed at all of the closest ten stations.

The epicenters of the events in Fig. 9 are labeled (a)–(e).

Event (f) is an earthquake off the coast of Chile in 2010.

Data obtained by the University of Chile are used for event (f).

For the 2011 off the Pacific coast of Tohoku earthquake, the magnitude reached the final value within 140 seconds.

The target time of the first tsunami warning in JMA is three minutes, so 140 seconds is a satisfactory time for the first tsunami warning. The final magnitude was 8.8 in the figure,

Fig. 7. Difference between magnitude determined from the peak velocity of various cutoff periods (Tc) and the moment magnitude.

which is less thanM_w9.1.

The time to reach the final magnitude of other earth- quakes is less than three minutes. The times are delayed for events with epicenters far from the closest stations such as earthquakes off the Kuril Islands. However, tsunami ar- rivals at the nearest coasts would also be delayed for those earthquakes.

As expected, magnitude saturation is observed in Fig. 9.

Magnitudes of shorter cutoff periods are generally smaller than those of longer cutoff periods. Differences amongM20, M50 andM100are not so large, but the difference between M10 andM20 is relatively large (the subscript denotes the cutoff period). Two large pulsed peaks with widths of about twenty seconds are seen in the seismic records in Fig. 2.

The asperity size and its slip process would have defined the pulse width which is related to the characteristics of the magnitude saturation. The similarity of M , M and

M₁₀₀might be related to fault-rupture characteristics of the regions.

For the 2010 Chile event, short-period magnitudes are greater than long-period magnitudes. This reversed magni- tude relationship would be related to the concentrated dis- tribution of the used stations in the northern region of the source area, the relatively southern location of the epicen- ter, and a large slip in the northern area (Layet al., 2010).

Since the amplitude decay is steeper in short-period mag- nitudes than in long-period magnitudes (Fig. 6), the uneven station distribution and the improper assumption of the dis- tance to the source affect the short-period magnitudes more.

Even in such a case, the long-period magnitude is consid- ered to be more reliable than the short-period magnitude.

The time to reach the final value and the final magnitude depend on the station distribution and the upper limit of sta- tion numbers. Figure 10 presents variations of estimated

Fig. 8. Difference between magnitude determined from the peak displacement of various cutoff periods (Tc) and the moment magnitude.

Table 3. Velocity structure model used to calculate synthetic records for Fig. 12.

Depth (Top) Velocity (P) Velocity (S) Density QP QS

km km/s km/s g/cm³

0 3.0 1.44 2.3 150 75

1 5.0 2.90 2.55 300 150

4 6.3 3.60 2.75 400 200

12 7.1 3.95 2.95 400 200

25 7.8 4.30 3.15 400 200

magnitudes with the period from the event origin time for various upper limits of station numbers for the 2011 off the Pacific coast of Tohoku earthquake. As expected, the mag- nitude reaches the final value earlier for fewer upper limit stations. However, the time difference in reaching the final value is not large in Fig. 10. The final magnitude increases with more stations, and approachesM (9.1). No large dif-

ference in dispersion is seen. The upper limit station num- ber can be set arbitrarily, and could be determined based on the required time limit and the difference from the final value.

The magnitudes obtained in this study are compared with Mwp(Tsuboiet al., 1995; Whitmoreet al., 2002) in Fig. 11 for the 2011 off the Pacific coast of Tohoku earthquake.

Fig. 9. Variation of displacement magnitudes versus elapsed time from the event origin time. The magnitudes are calculated from data acquired at the closest three to ten stations. The colors indicate the periods of the low-cut filters. Epicenters (a)–(e) are presented in Fig. 4. The origin times are local times except for event (f).

Station magnitudes are shown in the figure with the time when the peak amplitudes were measured on the horizontal axis. A short peak-time generally means a short epicen- tral distance. Both magnitudes are determined from data of strong motion velocity meters installed by the National Research Institute for Earth Science and Disaster Preven- tion. The instrumental response is corrected with the recur- sive deconvolution filter proposed by Kanamori and Rivera (2008). Since the seismic wave forMwpis restricted to the period betweenP andS arrivals, andTS−TP at a station of short epicentral distance is less than the source duration, the resultant M_wp at a close station is much less than the moment magnitude of the event (M_w9.1). M_wpat stations become stable after about four minutes from the event ori- gin time. On the other hand, the magnitude of this study scatter around the magnitude 9 even at close stations. How- ever, the station magnitude scatter of this study seems to be larger than that ofMwp.

4.3 Effect of fault type

Events of the same size with a different focal mechanism radiate seismic waves of different amplitude. The amplitude difference due to the fault type is investigated with synthetic records, and the results for dip and strike slip events are shown in Fig. 12. The synthetic records are calculated with the method of Takeo (1985), assuming a velocity structure in Table 3, a focal depth of 20 km, and a triangle source time function of sixty second duration. A high-pass filter of 100-s cutoff is applied to the records.

The amplitude reduces considerably when the station is located in the direction of the nodal planes. Since the compression/tension axis is usually oriented normal to the trench axis for events around a convergent plate boundary and the stations are installed in inland areas, it is considered that the observed amplitude would not become so small for local events. When seismic waves from events near Kuril Islands are observed on the Japan Islands, the stations are distributed around the direction of the null axis of the events and the magnitude would be underestimated. For the strike-