Introduction

The similarity and dissimilarity between the rupture growths of large and small earthquakes is quite interesting and essential issue in not only earthquake seismology but also disaster prevention by earthquake early warning. To address this issue, there have been so many scaling studies of rupture processes of earthquakes. However most of them were on the source parameters in the eventual state of earthquakes, such as fault dimensions, average fault slip, average stress drop, source duration, and so on.

Now we focus on the scaling of earthquake rupture growth (temporal development of earthquake rupture), which has been rarely done. In this thesis, we analyze six earthquakes in a wide magnitude range, Mw 1.7-6.0, by slip inversion analyses. And, based on the comparison of their rupture process in terms of their moment rate and cumulative moment functions, we discuss on earthquake rupture growth.

Multiscale slip inversion

Slip inversion analysis is very useful to reveal an earthquake rupture growth process. However ordinary slip inversion analyses cannot resolve the very beginning of rupture process. Therefore, we developed a multiscale slip inversion algorithm [Uchide and Ide, 2007] employing a multiscale source model which is constructed by renormalizing source models with different node intervals and fault dimensions. Our multiscale approach enables to investigate the early stage and the whole processes of an earthquake in detail simultaneously.

Multiscale slip inversion of the 2004 Parkfield earthquake

Focusing on the early stage of a large earthquake, we investigate the 2004 Parkfield earthquake (Mw 6.0) by the multiscale slip inversion analysis, reviewed in the previous section. The data of GEOS and CGS strong-motion network are in use. The employed multiscale source model is composed of three models at different scales. For the smaller two scales, we construct empirical Green's functions from observed waveforms of three earthquakes each. For the largest scale, we calculate Green's functions by assuming a layered crust structure.

Our multiscale approach successfully reveals a detailed image in the early stage of the large earthquake together with the entire rupture process (Figure 2). From its very onset, the rupture is complex with a high slip rate and high rupture propagation speed. Rupture begins bilaterally, and the rupture velocity is about 3.0 km/s and slip-rate is as high as 3 m/s even at 0.2 s, though our resolution within the first 0.1 s is limited. The high-speed initial rupture inferred from our model is consistent with that of the 2004 mid-Niigata Prefecture, Japan, earthquake (Mw 6.6) [Uchide and Ide, 2007], which implies that such characteristics may be quite general.

At the 0.2 s from the onset, the cumulative seismic moment is equivalent to Mw 3.9, and only 0.1 % of the eventual seismic moment. Is this high-speed rupture process in the early stage identical to medium earthquakes, such as Mw 4-5? This problem will be approached in the next section by comparing earthquake growth process of earthquakes with different final sizes.

Scaling of earthquake rupture growth

Next we investigate the rupture process of five earthquakes (Mw 1.7-4.6) by standard (not multiscale) slip inversion analyses employing data of GEOS and HRSN and empirical Green's functions, for the comparison with the Mw 6.0 event studied in the previous section.

Figure 3 shows scaled moment rate functions of the six earthquakes studied, where time and moment rate is scaled by a reference source duration, To=2.7×10(-6) Mo(1/3) (Mo is the final magnitude), and average moment rate, Mo/To, respectively. The moment rate functions of all earthquakes except Mw 6.0 event are similar to each other and approximately symmetric bell-shaped. We term the process before the peak (or earlier half of rupture process) "growth stage," and that after the peak (or latter half) "decline stage." On the other hand, the scaled moment rate function of Mw 6.0 event is quite different from others, and almost constant at a much lower level than the peaks of other events.

The representative figure of this thesis is Figure 4, which shows the cumulative moment functions of six earthquakes we investigated in a log-log graph. For all events in their growth stages, the cumulative moment functions increase along a common growth line, Mo(t)=2×10(17)t3, independent of its eventual magnitude. The proportionality of the cumulative moment to the cube of the time from the onset implies the self-similarity of earthquake rupture growth. According to the self-similar model, the proportionality coefficient is proportional to the stress drop and the cube of the rupture propagation speed.

The cumulative moment function of the Mw 6.0 earthquake shows the break of t3-proportionality at 1 s, after which the cumulative moment function is roughly proportional to the time. That is likely because the rupture was suppressed by the finite thickness of a seismogenic layer by following reasons. Figure 5 shows the final slip distribution of the Mw 6.0 event and the seismicity on the San Andreas Fault. According to the seismicity, the thickness of the seismogenic layer around the hypocenter of the Mw 6.0 event is limited within 5-10 km in depth. The slip of the Mw 6.0 is confined within the estimated seismogenic layer, though the assumed source models included the shallower part of the San Andreas Fault. The time of the break of t3-proportionality, 1 s, is comparable to the time when the rupture front reached at the top and bottom of the seismogenic layer around the hypocenter. The effect of the finite thickness of the seismogenic layer produces the difference between the scaled moment rate functions of Mw 6.0 and other smaller earthquakes.

The rupture process of the Mw 6.0 earthquake before 1 s and the entire rupture processes of other smaller earthquakes appear not to be affected by the limitation of the seismogenic zone. Besides the rupture process in the growth stage seems not to be dependent on its own final size. These implications are probably because small rupture involves only a surrounding small zone. The magnitude of earthquakes is not determined before the deceleration, but by chance. Therefore the switch to the decline stage is probably important for determining the eventual magnitude of an earthquake. For the estimation of the eventual magnitude on the purpose of earthquake early warning, we should wait for, at least, the transition from the growth stage to the decline stage.

Figure 1

Map of Parkfield area. Squares, inverted triangles, normal triangles indicate the station location. Stars indicate the epicenter of earthquakes we investigate.

Figure 2

Slip-rate distribution history and final slip distribution of our preferred multiscale fault model. The gray circles indicate the hypothetical rupture front, within which slip is allowed, propagating at 3.0 km/s from the hypocenter.

Figure 3

Scaled moment functions of the six target events (Mw 1.7-6.0). Time and moment rate are normalized by To and Mo/To, respectively, where To=2.7×10(-6) Mo(1/3) and Mo is the final seismic moment of each event.

Figure 4

Cumulative moment functions of six target events (Mw 1.7-6.0) in the log-log graph. Intervals of points are same as the node intervals of the source models.

Figure 5

Slip distribution of the Mw 6.0 event (red contours; contour interval is 0.2 m) and hypocenters (grey circles; January 1, 1984-June 30, 2005; relocated by Thurber et al. [2006]) on the cross section at San Andreas Fault.

本論文は6章からなる。第1章は、イントロダクションであり、本研究で取り組む課題である地震現象に見られるスケーリング則についての概要を述べるとともに、地震破壊を理解する上では、その時間的成長についてのスケーリング則の理解が重要であることが特に強調されている。また、本研究では米国カリフォルニア州パークフィールド地域に発生した地震を解析し、それに基づいて地震破壊の時間的成長について詳細な検討が行われているが、第1章では、その地域の地震学的特徴についても記述がなされている。地震破壊の解析には、インバージョン法というデータ解析手法が用いられるが、第2章では、広く用いられている通常のインバージョン法と、論文提出者らが新たに開発したマルティスケールインバージョン法それぞれの概要や特色が述べられている。さらに、動的地震の始まり直後から終わりまでの全体を精度よく解析するには、マルティスケールインバージョン法が大きな利点を有すると結論づけている。第3章では、マルティスケールインバージョン法を用いて、2004年パークフィールド地震(マグニチュード6)を解析し、動的地震破壊の開始直後の時点において、断層破壊の成長速度と滑り速度は主要破壊のものに匹敵するほど、すでに十分に大きいことを見いだした。第4章では、同じパークフィールド地域で発生した規模の小さな5つの地震を、通常用いられている経験的グリーン関数法を用いてインバージョン解析を行った。第4章では、さらに、上記の6つの地震について得られた累積モーメントの時間変化についての結果を総合し、地震の動的成長過程について詳細な考察を行っている。これが、本論文の主要な成果の一つと言える。すなわち、上記6つの地震すべてについて、累積モーメントは動的地震の開始時には、時間の3乗に比例し地震の最終的な規模に依らない時間変化をすることが明らかになった。また、地震破壊成長の終末期に達すると、累積モーメントの成長が抑えられるようになり、上に述べた3乗則からのずれがすべての地震について見られることも明らかにされた。しかし、2004年パークフィールド地震の場合、3乗則からのきわめて特徴的なずれが明らかにされたが、これは、断層破壊面の先端が地震発生層の最上部と底部に達したために、モーメントの成長が強く抑制されたものと、解釈された。これは、地震活動の震源分布や断層破壊の成長速度とも調和的である。第5章では、第4章で得られた結果に基づき、緊急地震速報についての問題点の指摘などがなされている。また、最後の第6章では、結論が要約されている。

地震の動的開始時に累積モーメントは地震の規模に依らない時間変化をするということは、地震の最終的な規模は地震破壊の開始時には予測できないという重要な示唆を本論文は行っている。独創的なデータ解析手法の開発と、それを用いた地震破壊現象について新たな理解は、地震学における大きな貢献であると判断される。

なお、本論文第2章、第4章および第5章は井出哲氏との、また、第3章は井出哲氏およびG.C.Beroza氏との共同研究であるが、論文提出者が主体となって開発したもので、論文提出者の寄与が十分であると判断する。

したがって、博士(理学)の学位を授与できると認める。