We theoretically study thermoporoelastic effects on dynamic earthquake rupture and succeed in explaining diversity of dynamic earthquake behavior. We first present the governing equations assuming a thermoporoelastic medium, based largely on the work of Pride et al. [1992] and temperature change is taken into account in the constitutive equations. Our study provides a detailed numerical simulation of thermoporoelastic effects on dynamic fault rupture. Our treatment is much more reasonable than earlier studies, which are limited by weaknesses in their assumptions. For example, Andrews [2002] made an a priori assumption of a specific form for spatiotemporal change in fault slip, such that it is impossible to use his model to investigate changes in fault slip due to thermoporoelastic effects on the model framework.

　We then include an effect of inelastic porosity change in the mathematical framework. We find that a single nondimensional parameter controls two types of feedback appearing in the system behavior. We found that the single nondimensional parameter S controls the system behavior in 1D fault model. This parameter is proportional to the ratio of Dc, the characteristic distance appearing in the governing equation of temporal change in fluid pressure, to dc, the characteristic fault slip for the inelastic porosity evolution. If S satisfies the condition that the fluid pressure decreases monotonically with time (S>-P0*), the single feedback is found to appear. The feedback suppresses the rate of fluid pressure change and finally the static equilibrium state is attained. We show in this paper that two qualitatively different feedbacks appear in the system behavior when the condition S<-P0* is satisfied; the nature of fault slip behavior is dependent on which of the two feedbacks is dominant. We also demonstrate that one of the feedbacks can be transformed into the other because the feedback mechanism is non-linear. This nonlinearity produces a system behavior in our model that differs significantly from predictions based on the Griffith crack model.

　When we study dynamic fault slip assuming a one-dimensional (1D) fault model based on the derived system of equations, we observe slip-weakening behavior due to thermoporoelastic effects if the parameter S is small. The slip-weakening behavior and gradual slip onset observed in our study are clearly related to the non-linear feedback. We derived the approximate solution for the slip-weakening distance in a simple form; seismological estimates are consistent with our model predictions. It is also shown that temperature increase is suppressed because of the reduction in the effective normal stress acting on the fault plane. Our simulation shows that the elevated rock temperature during slip remains below the melting temperature of rocks provided that the rate of fluid outflow from the heated fault zone is relatively low; this has previously been documented by Lachenbruch [1980] and Mase and Smith [1987]. The normal stress acting on a fault surface asymptotically approaches zero with ongoing slip, where the heat source term becomes zero; this acts to suppress the temperature rise.

　On the other hand, when S 〜 1 or S > 1, the slip-hardening behavior appears. The slip ceases spontaneously because of the reduction in the stress drop induced by fluid pressure decrease. The shear stress recovers the initial strength after some slipping when S > 1 and the fluid outflow is negligible. The difference in permeability produces difference of the recovered shear stress level, which is consistent with some observational results that the shear stress does not always recover the initial stress. Temperature increase is again suppressed because of reduction in slip velocity due to stress drop decrease induced by fluid pressure decrease. This mechanism of temperature suppression explains again the unexpectedly rare occurrence of pseudotachylyte as a consequence of low permeability within porous fault zones. If permeability increase occurs because of the inelastic porosity increase, temperature increase may be larger; as the normal stress acting on a fault surface remains large in this situation, temperature continues to increase upon the fault plane and in surrounding rock, which may result in localized melting.

　In a two-dimensional (2D) antiplane shear fault model, when the parameter is around zero, smaller events tend to have smaller static stress drops. Our simulation predicts fault slip duration that is generally longer than that predicted by the classical Griffith crack model when S〓 0. We also found that smaller-size ruptures tend to have smaller static stress drops; this is consistent with some seismological observations. These two findings are closely associated with the increase in stress drop that accompanies fluid-pressure build-up and ongoing fault slip. Previous analyses of earthquake fault processes, however, have found that fault slip duration is much smaller than that expected from the Griffith crack [Heaton, 1990]. Such a proposal is contradictory to the above findings; however, the slip behavior described by Heaton [1990] can be explained by considering the inelastic porosity change. If the rate of fluid flow into microcracks is larger than the rate of fluid build-up on the fault surface, then fluid pressure on the fault plane decreases for a period of time. The fluid pressure decreases in this way, which can explain the observation of Heaton [1990] in the framework of our model. Our study revealed that the static stress drop averaged over the fault plane is smaller for smaller earthquakes. This relationship occurs because of fluid pressure increase with increasing fault slip. This observation is consistent with the findings of Kanamori and Rivera [2004], given that the rupture velocity can be assumed to be independent of earthquake size.

　We then consider the inelastic porosity effect, in which we observe a propagating slip pulse due to the inelastic porosity change and the slip-hardening behavior in some parameter ranges. The stress drop weakly depending on the earthquake size appears, which is consistent with some previous studies. The problem that the radiation efficiency sometimes exceeds unity is solved by considering the inelastic porosity change. This paradox has been attributed to estimation errors of, for example, radiated energy, though some authors suggested the effect of change in a constitutive law [Venkataraman and Kanamori, 2004]. It should be emphasized that earthquakes having the radiation efficiency larger than unity in the study of Venkataraman and Kanamori [2004] agree well with those showing pulse-like slip, which are concluded to have large S values.

　The effects of temperature, fluid pressure, inelastic porosity and slip velocity on earthquake source mechanics have been studied by many authors, while they have frequently studied those effects individually. We suggested that those effects should be treated in a unified way in earthquake source mechanics because they interact and the interaction plays fundamental roles in dynamic earthquake rupture. This 'unified-way understanding' of earthquake source mechanics is necessary to the step of earthquake source physics. Our model explains many aspects of dynamic earthquake rupture such as temperature change, slip-strain relationship and slip velocity distribution on fault planes. Dynamic earthquake rupture should not be investigated in separate aspects; non-linear interaction among quantities such as temperature and fluid pressure affects the rupture process, which results in that effects of all quantities should be considered.

　本論文は，地震の動的破壊過程に及ぼす熱及び流体を含む多孔質弾性体の影響を理論的考察及び数値シミュレーションにより解明したものである．野外のおける断層の観察より，地震断層は単なる弾性体の中に生じた食い違いではなく断層破砕帯を挟む食い違いであり，微視的な観察では断層運動によって生じたメルトの存在も知られている．又，破砕帯内部の流体が断層運動に影響を及ぼすことも知られている．これまでにも，断層破砕帯を多孔質弾性体として扱い，流体や熱の効果も考慮した研究は行われている．しかし，それらの研究では，例えば，運動方程式や歪み一応力の関係式を直接解いていないものや，断層のすべりを仮定するものなど，動的破壊過程を解明する上で大きな弱点を持っていた．本論文では，これらの弱点を克服して，熱及び流体を含む多孔質弾性体が地震の動的破壊過程にどのような効果をもたらすかを，適切な仮定の下で支配方程式を解くことにより明らかにした．

　本論文の構成は，第2章で支配方程式の定式化を行い，第3章でこの方程式系の挙動を支配する重要なパラメータの導出を行っている．第5章及び第6章では，1次元モデル及び2次元モデルの元で支配方程式系を差分法及び境界積分方程式法を用いて数値シミュレーションを行い，動的破壊過程に及ぼす種々の効果を解明している．第7章ではこれまで自然地震の断層運動の解析から得られた知見と比較検討を試み，本論文で定式化した方程式系で多くの観測事実を説明できることを示した．

　先ず，方程式系の定式化は，基本的にこれまでの多孔質弾性体における定式化を援用しているが，非弾性の空隙率変化に独自の知見を持ち込むことで，熱と流体圧変化の相互作用による系のフィードバックシステムを単一の無次元化したパラメータで適切に識別できることを示した．さらに，均質媒質中での1次元モデルの数値シミュレーションを元に，このパラメータにより断層運動で現れるすべり弱化則からすべり強化則までの幅広い摩擦構成則を再現できることを示した．又、断層でのメルト発生の条件もこのパラメータにより判別できることを示した。これに加えて2次元モデルの数値シミュレーションでは，自然地震の観測・解析でしばしば指摘されているパルス状のすべりが，特別の先験的仮定を用いることなく，支配パラメータがある条件下にあるときに自然に出現することを明らかにした．さらに，このモデルは，地震規模と応力降下量の関係についても，これまでに観測研究から解明されている種々の特徴を合理的に説明できるものとなっている．このように自然地震の動的破壊過程に見られる多様な様相を統一的に再現するモデルはこれまで提唱されておらず，本論文の学術的価値は高いと言える．

　論文提出者は，以上のように，断層運動の動的破壊過程に熱及び流体が及ぼす効果を統一的に取り扱う定式化を確立し，その挙動を支配する単一の無次元パラメータを明らかにした．そして，均質媒質中での数値シミュレーションではあるが，これらの支配方程式系により，地震の動的破壊糧の多様性が再現できることを示した．この成果は，地震学，特に地震発生過程研究の分野で大きな貢献であると同時に、従来の研究にはない独創的な内容を含んでおり、高く評価できる．なお，本論文の一部は，山下輝夫との共同研究であるが，論文提出者が中心となって定式化を進め数値実験を行ったもので，その寄与は十分であると判断する．

　したがって，審査員全員一致で博士(理学)の学位を授与できると認める．