High-frequency seismic wave with frequency f > 1 Hz shows very complicated waveforms, such as distortion of the energy partitioning among three-component seismograms and developments of long duration P- and S-wave coda waves. Such complicated behaviors are considered to be caused by the structural heterogeneities, such as complex slip distribution, heterogeneities in subsurface velocity structure, irregular surface topography, and localized site amplification effect. Since waveform complication appears mostly in high-frequencies, it is considered that small-scale heterogeneities with scale comparable to the wavelength of seismic wave are its dominant causes. Such characteristics of complicated high-frequency seismic waves and their relation with heterogeneous structures have extensively been studied by many researchers based on theoretical and numerical approaches [e.g. Sato, 1984; Furumura and Kennett, 2005, 2008; Miyatake et al., 2008; Kumagai et al., 2011]. A detailed understanding of the characteristics of the high-frequency seismic waves is very important for revealing the physical properties of the source rupture process during the large earthquake and the propagation characteristics of high-frequency seismic waves in the Earth's interior. Moreover, it is equally important for understanding the cause of strong motion disasters for past earthquakes and for predicting strong motion disasters associated with future large earthquakes.

In this thesis, we examined in detail the features of the complicated high-frequency seismic waves associated with the scattering of high-frequency seismic waves due to heterogeneous velocity structure and irregular topography. We analyze a large number of seismograms recorded by dense seismic KiK-net, K-NET and Hi-net arrays of more than 1000 stations across Japan for several hundred earthquakes, in order to examine the change in the waveforms with increasing frequency and propagation distance.

Dramatic change in the high-frequency P and S waveforms with increasing propagating distance and frequency is confirmed by analyzing 1) the collapse of the apparent S-wave radiation pattern, and 2) the increase in the P- wave signal of the transverse component. Then, the physical process, that governs the propagation of high-frequency seismic waves through heterogeneous structures, is examined by 2-D and 3-D FDM simulation of seismic wave propagation using heterogeneous structure model including irregular topography and stochastic random velocity fluctuation. Through the direct comparison of the observed characteristics from dense seismic array and the results of FDM simulation of seismic waves, the process of the disruption of high-frequency seismic waves during propagation in heterogeneous structures is clarified in detail.

In order to understand the complicated properties of high-frequency seismic wavefield and its dramatic change with increasing frequencies, we first examined the distortion of the apparent S-wave radiation pattern observed in dense seismic network. The observed waveforms from the dense KiK-net stations during the aftershock sequence of the 2000 Tottori-Ken Seibu earthquake demonstrated that the apparent S-wave radiation pattern observed during the strike-slip fault earthquakes is gradually distorted from a typical four-lobe shape to isotropic circular pattern as frequency increases over 1 Hz, and it shows almost isotropic circular pattern irrespective of the direction from the fault strike as frequencies approach to f = 5 Hz. Such collapsing of the apparent S-wave radiation pattern is also emphasized with increasing hypocentral distance and the effect is much stronger for high-frequency seismic waves. Therefore, it is expected that the major cause of such distortion in apparent radiation pattern is the scattering of high-frequency (f > 1 Hz) seismic waves due to small-scale heterogeneities along the wave propagation path, rather than due to other small-scale heterogeneities only near the source area or just below stations, such as caused by irregular source-rupture process and localized site amplification effect below station, respectively. In order to confirm this hypothesis, we conducted FDM simulation of seismic wave propagation using 2-D heterogeneous velocity structure model which is described by stochastic random velocity fluctuation. We employed a stochastic random velocity fluctuation model characterized by a von Karman power spectrum density function (PSDF) which has long been used to model small-scale heterogeneities in the lithosphere. The results of simulations clearly demonstrated (i) the effect of strong scattering of the high-frequency seismic waves due to heterogeneities with scale length comparable to or smaller than wavelength of seismic waves, and (ii) the distortion of the apparent S-wave radiation pattern during propagation through the heterogeneous structure. By comparing the results between the FDM simulations using a set of stochastic random velocity fluctuation models and observations, the velocity fluctuation for southwestern Japan upper crust model which is characterized by a von Karman-type PSDF with correlation distance of a < 5 km, fluctuation strength of ε = 0.07 and order κ = 0.5 can explain the observed features of the distortion of the apparent S-wave radiation pattern with increasing frequency and propagation distances.

Then, scattering strength of high-frequency wavefield is analyzed by examining relative strength of the P-wave energy of the transverse (T) component for the beginning part of seismograms, which is often used as an indicator of the strength of the seismic wave scattering in heterogeneous medium [e.g. Nishimura et al., 2002; Sato, 2006; 2007, Kubanza et al., 2007]. The results of this analysis showed that the PEPT increases gradually with increasing frequency, but not with increasing travel distance. However, this value increases suddenly at larger hypocentral distances D > 150 km, where Pn phase propagating along the crust/mantle boundary (Moho discontinuity) is the dominant phase as the initial P waveform rather than the direct P wave. This may mean that the distribution properties of the small-scale velocity fluctuation in the upper, lower crust and upper mantle are completely different and causes different effects on the high-frequency seismic wavefield. Such difference in the distribution properties of the small-scale velocity fluctuation in the crust and upper mantle was confirmed by 3-D FDM simulation of seismic wave propagation using a layered structural model with different stochastic random velocity fluctuations. From the simulation results, we found much stronger fluctuation in velocity (ε > 9 %) and smaller correlation distance (a < 5km), associated with reflective lower crust and laminar sub-Moho structures, just below or above the Moho boundary, to explain data both from seismic reflection and dense array observation of earthquakes [e.g. Iwasaki et al., 2002; Iidaka et al., 2006]. We can roughly reproduce the observed properties of the high-frequency P wave propagation in heterogeneous structure by the FDM simulation with a velocity fluctuation model which was obtained by the analysis of the apparent S-wave radiation pattern. In addition, in order to reproduce the observed feature of the high-frequency wavefield more quantitatively, we should also employ another heterogeneous model such as explained by irregular surface topography and shallow low-velocity structure just beneath the station.

Another important cause of scattering of high-frequency seismic waves due to irregular surface topography is examined by 2-D and 3-D FDM simulation of seismic wave using the high-resolution structure model including irregular topography and comparing with that of ordinary flat surface model. The results of simulation clearly demonstrate how the complex irregular surface topography modify reflection pattern of the seismic waves. The results of simulation reproduce the observed feature of the complex coda envelope shape, increase in the P-wave amplitude of the transverse component and the distortion of the apparent S-wave radiation pattern as they propagate through the heterogeneous structure with realistic irregular surface topography. It is also found that the mean strength of seismic wave scattering due to topography can be explained by the power spectral density of the irregular topography for each area.

Such topographic scattering of the direct P and S waves has minor effect on the distortion of the high-frequency seismic waves compared with that due to velocity fluctuations as mentioned above, because the topographic scattering occurs only once below station and it is not accumulated during propagation of seismic waves for long distances. It is expecting that the strength of the velocity fluctuation and resulting seismic scattering energy may be overestimated more than 20 % if the effect of irregular topography is not taking into accounted in the simulation model.

The spatial distribution of the strength of the topographic scattering can be examined by calculating the PSD of topography for each region of Japan. Many researchers, including the results of present study, have claimed that there scattering of high-frequency seismic waves is strong in the back-arc side of northeastern Japan compared with the fore-arc side of northern Japan and other areas [e.g. Obara and Sato, 1995; Carcole and Sato; 2009]. According to the spectral analysis of the surface topography for each region, there is no clear difference in the PSD of larger wavenumber components among the back-arc side of northern Japan and other areas. Therefore, it is concluded that such a regional difference in the strength of scattering of high-frequency waves is mainly caused by local sub-surface structure i.e., different distribution property of small-scale velocity fluctuation in the crust and upper mantle. Strong scattering of high-frequency signals in the back-arc side of northeastern Japan can be explained by the heterogeneities characterized by 3-4% stronger fluctuation ε in velocity and smaller κ.

The results of waveform analysis for scattering high-frequency seismic waves were confirmed by FDM simulations of seismic wave propagation using the structure model including large-scale layered velocity structure, irregular surface topography and estimated velocity fluctuation model in each layer. It is confirmed that the observed seismic wavefield of relatively low-frequency (f < 0.5 Hz) signals are mostly controlled by large scale heterogeneities, which is often explained by a layered structure very effectively, but the propagation of the high-frequency (f > 2 Hz) wave field with shorter wavelength cannot be reproduced without including small-scale heterogeneities in each layer and realistic irregular surface topography Using this model, the feature of the observed high-frequency seismic wavefield, such as waveform shapes, energy decay, and distribution pattern of the P and S waves, can be well reproduced.

Through the improvements of the knowledge of high-frequency seismic wave propagation in actual heterogeneous structures and the developments of high-resolution simulation model including realistic surface topography and stochastic random velocity fluctuation, steadily increasing computer power and large-scale computational techniques will realize high-frequency seismic wave propagation simulation better in very near future.

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、高周波地震動に影響を及ぼす原因を概観するとともに、主たる原因としての不均質地下構造・地形による地震波散乱に関する観測およびシミュレーション研究、さらに地震波動計算に関する既往研究がまとめられ、本論文の目的、位置づけについて適切に記されている。

続く2つの章では、伝播距離や周波数の増加に伴う高周波P・S波の変化に関する観測波形解析結果、及び波動伝播シミュレーション結果がまとめられ、両者の比較に基づいて、媒質のランダム不均質性を表現する地震波速度ゆらぎパラメタの推定が行なわれている。具体的には、横ずれ型発震機構解を有する地震のS波放射パターンに着目し、1 Hz以下の低周波数側では理論通りの4象限型であるのに対し、2 Hz以上の高周波数側では周波数や震源距離とともに崩れ、等方的放射パターンに近づいていくことから、伝播経路における高周波数地震動の散乱によるものであることを明らかにした。また、地震波散乱の強度を表す指標としてTransverse成分に染み出すP波エネルギーの相対強度に着目し、これが周波数とともに増加し、震源距離に対しては150 kmを超えたところから突然増加を始めることから、地殻とマントルの不均質性に違いがある可能性を明らかにした。いずれも、高密度の地震観測網で得られた膨大な地震波形データを使用した丹念な解析・整理による結果であり、地震波散乱に関する特徴を定量的に抽出したことは、高く評価される。さらに、様々な不均質パラメタを与えて波動伝播シミュレーションを実施し、地震波散乱の特徴と不均質性との関係を明らかにしたとともに、観測事実を最も良く説明するモデルとして、上部・下部地殻、上部マントルのランダム不均質性のスペクトル、相関距離、揺らぎ強度の最適値を推定した。特に、下部地殻において強い不均質性が推定されたことは、反射法構造探査等の結果と調和的であり、地殻形成過程を議論する上でも大変興味深い結果である。

第4、5章では、観測から抽出された波動伝播の特徴の再現性をより高めるため、媒質の不均質性に加えて地表の複雑な地表面地形による散乱を考慮したシミュレーション手法を開発し、地形効果の評価を行った。まず単純な地形モデルが地震波形に及ぼす影響を定量的に評価し、さらに現実の地形モデルとランダム不均質媒質による地震波散乱の相違を明らかにした。また第2、3章で推定されたランダム不均質性も考慮し、複合した不均質モデルに基づく地震波動伝播シミュレーションにより、観測された波動伝播の特徴と調和的であることを明らかにした。第5章は、既往研究から得られたフィリピン海プレート等の成層モデルを背景の速度構造としてさらに媒質の不均質性と現実の地形を組み込んだシミュレーション結果と、広帯域観測波形との比較である。その結果、特に高周波観測波形の特徴を形作るランダム不均質構造と複雑な地表地形による地震波散乱の特徴を押さえ、これらをともに適切にモデル化することが不可欠であることが示された。これまで、媒質の不均質性や複雑な地形を考慮した波形計算は、それぞれ個別的には実施されてきたが、両者を合わせた波動伝播シミュレーションはほとんど例がなく、本論文によってはじめて実現されたと言っても過言ではない。

第6章では、本論文で明らかになった結論がまとめられている。媒質の不均質性のみならず、複雑な地形もまた高周波地震波動形成に大きく寄与し、さらに両者は地震波散乱に対して異なった働きかけをすることが明らかにされたことは、強震動予測においても重要な知見であり、地震ハザードを正しく評価する上で、地形まで考慮した波動伝播シミュレーションの必要性を示すものである。また、本論文のシミュレーションでもなお観測結果との差が存在することが課題として述べられており、サイト増幅度やメソスケールの不均質性などが影響している可能性が議論されている。このように、本研究で一定の成果が得られたことにより、さらに地震動予測を高精度化する上で今後取り組むべき課題が提起されたという点も評価に値する。本論文では、フォワードで媒質の不均質パラメタの推定が行われたが、本論文の成果に基づき、地形等の影響を正しく評価することで、今後は、ランダム不均質パラメタの空間変化をインバージョンによって推定するなど、地球内部構造研究や地下資源探査への貢献が期待される。

なお第2章は、古村孝志、齋藤竜彦、前田拓人との共同研究、第3章は、古村孝志、前田拓人との共同研究であるが、論文提出者が主体となって解析および検証を行ったもので、論文提出者の寄与が十分であったと判断する。

したがって、博士(理学)の学位を授与できると認める。