Pseudo-dynamic source modelling with 1-point and 2-point statistics of earthquake source parameters

Ground motion prediction is an essential element in seismic hazard and risk analysis. Empirical ground motion prediction approaches have been widely used in the community, but efficient simulation-based ground motion prediction methods are needed to complement empirical approaches, especially in the regions with limited data constraints. Recently, dynamic rupture modelling has been successfully adopted in physics-based source and ground motion modelling, but it is still computationally demanding and many input parameters are not well constrained by observational data. Pseudo-dynamic source modelling keeps the form of kinematic modelling with its computational efficiency, but also tries to emulate the physics of source process. In this paper, we develop a statistical framework that governs the finite-fault rupture process with 1-point and 2-point statistics of source parameters in order to quantify the variability of finite source models for future scenario events. We test this method by extracting 1-point and 2-point statistics from dynamically derived source models and simulating a number of rupture scenarios, given target 1-point and 2-point statistics. We propose a new rupture model generator for stochastic source modelling with the covariance matrix constructed from target 2-point statistics, that is, auto- and cross-correlations. Our sensitivity analysis of near-source ground motions to 1-point and 2-point statistics of source parameters provides insights into relations between statistical rupture properties and ground motions. We observe that larger standard deviation and stronger correlation produce stronger peak ground motions in general. The proposed new source modelling approach will contribute to understanding the effect of earthquake source on near-source ground motion characteristics in a more quantitative and systematic wa

Comparison of finite difference and boundary integral solutions to three-dimensional spontaneous rupture

The spontaneously propagating shear crack on a frictional interface has proven to be a useful idealization of a natural earthquake. The corresponding boundary value problems are nonlinear and usually require computationally intensive numerical methods for their solution. Assessing the convergence and accuracy of the numerical methods is challenging, as we lack appropriate analytical solutions for comparison. As a complement to other methods of assessment, we compare solutions obtained by two independent numerical methods, a finite difference method and a boundary integral (BI) method. The finite difference implementation, called DFM, uses a traction-at-split-node formulation of the fault discontinuity. The BI implementation employs spectral representation of the stress transfer functional. The three-dimensional (3-D) test problem involves spontaneous rupture spreading on a planar interface governed by linear slip-weakening friction that essentially defines a cohesive law. To get a priori understanding of the spatial resolution that would be required in this and similar problems, we review and combine some simple estimates of the cohesive zone sizes which correspond quite well to the sizes observed in simulations. We have assessed agreement between the methods in terms of the RMS differences in rupture time, final slip, and peak slip rate and related these to median and minimum measures of the cohesive zone resolution observed in the numerical solutions. The BI and DFM methods give virtually indistinguishable solutions to the 3-D spontaneous rupture test problem when their grid spacing Δx is small enough so that the solutions adequately resolve the cohesive zone, with at least three points for BI and at least five node points for DFM. Furthermore, grid-dependent differences in the results, for each of the two methods taken separately, decay as a power law in Δx, with the same convergence rate for each method, the calculations apparently converging to a common, grid interval invariant solution. This result provides strong evidence for the accuracy of both methods. In addition, the specific solution presented here, by virtue of being demonstrably grid-independent and consistent between two very different numerical methods, may prove useful for testing new numerical methods for spontaneous rupture problems

Rupture Reactivation during the 2011 M_w 9.0 Tohoku Earthquake: Dynamic Rupture and Ground-Motion Simulations

Near‐source ground‐motion observations and kinematic source inversions suggest that the rupture process of the 2011 M_w 9.0 Tohoku earthquake involved rupture reactivation, that is, repeated rupture nucleation in the same hypocentral area. This unusual phenomenon may have provided a second breath to the rupture that enhanced its final size. Here, we propose that rupture reactivation may have been governed by a slip‐weakening friction model with two sequential strength drops, the second one being activated at large slip. Such frictional behavior has been previously observed in laboratory experiments and attributed to pressurization of fault‐zone fluids by mineral decomposition reactions activated by shear heating, such as dehydration and decarbonation. Further evidence of this double‐slip‐weakening friction model is obtained here from the dynamic stress changes in the hypocentral region derived from a finite source inversion model. We incorporate this friction model in a dynamic rupture simulation comprising two main asperities constrained by source inversion models and several deep small asperities constrained by backprojection source imaging studies. Our simulation produces ground‐motion patterns along the Japanese coast consistent with observations and rupture patterns consistent with a kinematic source model featuring rupture reactivation. The deep small asperities serve as a bridge to connect the two main asperities, and the rupture reactivation mechanism is needed to reproduce the observed ground‐motion pattern. Therefore, we argue that rupture reactivation during the 2011 Tohoku earthquake is consistent with a second strength drop, possibly caused by activation of thermochemical weakening processes at large slip

Evaluating the effect of network density and geometric distribution on kinematic source inversion models

The effect of network density and geometric distribution on kinematic non-linear source inversion is investigated by inverting synthetic ground motions from a buried strike-slip fault (Mw 6.5), that have been generated by dynamic spontaneous rupture modelling. For the inversion, we use a physics-based regularized Yoffe function as slip velocity function. We test three different cases of station network geometry: (i) single station, varying azimuth and epicentral distance; (ii) multistation circular configurations, that is stations at similar distances from the fault, and regularly spaced around the fault; (iii) irregular multistation configurations using different numbers of stations. Our results show: (1) single station tests suggest that it may be possible to obtain a relatively good source model even using a single station. The best source model using a single station is obtained with stations at which amplitude ratios between three components are not large. We infer that both azimuthal angle and source-to-station distance play an important role in the design of optimal seismic network for source inversion. (2) Multistation tests show that the quality of the inverted source systematically correlates neither with the number of stations, nor with waveform misfit. (3) Waveform misfit has a direct correlation with the number of stations, resulting in overfitting the observed data without any systematic improvement of the source. It suggests that the best source model is not necessarily derived from the model with minimum waveform misfit. (4) A seismic network with a small number of well-spaced stations around the fault may be sufficient to obtain acceptable source inversio

Finite difference modelling of rupture propagation with strong velocity-weakening friction

We incorporate rate- and state-dependent friction in explicit finite difference (FD) simulations of mode II dynamic ruptures in elastic media, using the Mimetic Operators Split-Node (MOSN) method, with adjustable order of spatial accuracy (second-, fourth- or mixed-order accurate), including an option that is fourth-order accurate at the fault discontinuity as well as in the elastic volume. At fault points, the rate and state equations combined with the spatially discretized momentum conservation equations form a coupled system of ordinary differential equations (ODEs) for slip velocity and state variable. As a consequence of the rapid damping of velocity perturbations due to the direct effect, this system exhibits numerical stiffness that is inversely proportional to velocity squared. Approximate solutions to this velocity-state system are achieved by two different implicit schemes: (i) a fourth-order Rosenbrock integration of the full system using multiple substeps and (ii) low order integrations (backward Euler and trapezoidal) of the velocity equation, time-staggered with analytic integration of the state equation under the approximation of constant slip velocity over the time step. In assessing the numerical schemes, we use three test problems: ruptures with frictional resistance controlled by (i) a slip evolution law with strong velocity-weakening behaviour at high slip rates, representing thermal weakening due to flash heating of microscopic asperity contacts, (ii) the classic (low-velocity) slip evolution law and (iii) the classic aging evolution law. A convergence analysis is carried out using reference solutions from a spectral boundary integral equation method (BIEM) (a method restricted to homogeneous media, with nominal spectral accuracy in space and second-order accuracy in time for smooth solutions). Errors are measured by root-mean-square differences of fault-plane time histories (slip, slip rate, traction and state). MOSN shows essentially the same convergence rates as BIEM: second-order convergence for slip and state-variable misfits, with slower (but at least first-order) convergence for slip rates and tractions. For a given grid spacing, fourth-order MOSN is as accurate as BIEM for all variables except slip-rate. MOSN-Rosenbrock nominally has fourth-order temporal accuracy for the fault-plane velocity-state ODE integration (compared to lower-order accuracy for the other two MOSN schemes) and therefore provides an important theoretical benchmark. However, it is sensitive to details of the elastic calculation scheme and occasionally its adaptive substepping performs poorly, leading to large excursions from the reference solution. In contrast, MOSN-trapezoidal is robust and reliable, much easier to implement than MOSN-Rosenbrock, and in all cases achieves precision as good as the latter without recourse to substepping. MOSN-Euler has the same advantages as MOSN-trapezoidal, except that its nominal first-order temporal accuracy ultimately leads to larger errors in slip and state variable compared with the higher-order MOSN schemes at sufficiently small grid spacings and time step

Fault zone signatures from ambient vibration measurements: a case study in the region of Visp (Valais, Switzerland)

Investigations of tectonic features, such as faults, are important challenges for geologists and engineers. Although direct investigational methods, such as boreholes and trenches, have the potential to provide accurate data, these direct methods are usually expensive and time consuming, and give only punctual insights into subsurface structures. Geophysical methods, for example electric surveys and ground penetrating radar, are less expensive and faster to implement. However, these geophysical methods may be difficult or sometimes even impossible to apply in regions with rough topography or regions which are highly urbanized. In this study, we propose an easy-to-use and affordable method to detect fault zones based on ambient vibration observations. We apply this method in the region between Visp and Unterstalden (canton Valais, Switzerland) on a small fault branch, which has no explicit surface expression, and which is linked to a major fault zone, the Simplon Fault Zone. The assumption is that the fault of interest is surrounded by damage zone consisting of fractured rock, and that this results in lateral changes of both seismic velocity and attenuation. The objective was, first, to identify such lateral changes in the observed seismic wave-field, and second, to map any anomalies and combine them with the available geological information. In this way, we were able to follow the fault trace even without a clear surface expression of the fault. Our observations showed the existence of a signature in the power spectra of the seismic noise that may correspond to a damage zone. Such signature is observed along the trace of the expected faul

Rupture Reactivation during the 2011 M_w 9.0 Tohoku Earthquake: Dynamic Rupture and Ground-Motion Simulations

Near‐source ground‐motion observations and kinematic source inversions suggest that the rupture process of the 2011 M_w 9.0 Tohoku earthquake involved rupture reactivation, that is, repeated rupture nucleation in the same hypocentral area. This unusual phenomenon may have provided a second breath to the rupture that enhanced its final size. Here, we propose that rupture reactivation may have been governed by a slip‐weakening friction model with two sequential strength drops, the second one being activated at large slip. Such frictional behavior has been previously observed in laboratory experiments and attributed to pressurization of fault‐zone fluids by mineral decomposition reactions activated by shear heating, such as dehydration and decarbonation. Further evidence of this double‐slip‐weakening friction model is obtained here from the dynamic stress changes in the hypocentral region derived from a finite source inversion model. We incorporate this friction model in a dynamic rupture simulation comprising two main asperities constrained by source inversion models and several deep small asperities constrained by backprojection source imaging studies. Our simulation produces ground‐motion patterns along the Japanese coast consistent with observations and rupture patterns consistent with a kinematic source model featuring rupture reactivation. The deep small asperities serve as a bridge to connect the two main asperities, and the rupture reactivation mechanism is needed to reproduce the observed ground‐motion pattern. Therefore, we argue that rupture reactivation during the 2011 Tohoku earthquake is consistent with a second strength drop, possibly caused by activation of thermochemical weakening processes at large slip

Análise dinâmica de estruturas reticuladas sobre base elástica

Dissertação (mestrado)—Universidade de Brasília, Faculdade de Tecnologia, Departamento de Engenharia Civil e Ambiental, 1995.Este trabalho descreve dois modelos matemáticos de análise dinâmica de interação solo-estrutura, aplicados a problemas de estruturas reticuladas com fundações superficiais, onde os elementos da superestrutura são acoplados aos elementos da fundação e estes, por sua vez, ao solo. O primeiro modelo consiste em estruturas reticuladas sobre base elástica, os elementos da fundação sendo modelados através da hipótese de Winkler para viga sobre base elástica, utilizando-se molas contínuas (modelo matemático mais simples de interação solo-estrutura). Os referidos elementos são então combinados com elementos de pórtico comum, formando um sistema acoplado de estrutura reticulada sobre base elástica. Aplica-se o modelo a problemas de excitações aplicadas diretamente na estrutura e de movimentos na base incluindo-se, por exemplo, sismos. A resposta dinâmica é então obtida através do método de superposição modal ou de integração numérica através do esquema de Newmark; para problemas sísmicos, considera-se também o método de análise modal espectral. O segundo modelo consiste em uma combinação do método de elementos finitos para a estrutura com o método de elementos de contorno para o solo. No estudo do solo, o método de reciprocidade dual é utilizado para gerar uma integral de contorno a partir da integral de domínio correspondente às forças de inércia. Emprega-se portanto a solução fundamental de Kelvin (estática) para o problema resultante. A resposta dinâmica é então obtida através da integração numérica da equação de movimento do sistema acoplado solo-estrutura, por intermédio do esquema de Newmark. São resolvidos exemplos numéricos e apresentam-se resultados fornecidos pelos dois modelos.Here two mathematical models are described for dynamic analysis of soil-structure interaction, applied to problems of framed structures with shallow foundations, in which the elements of the superstructure are coupled to the foundation elements which are in tum coupled to the soil. The first model consists of framed structures on an elastic foundation, the foundation elements being obtained through the Winkler hypothesis for a beam on an elastic foundation by utilizing continuous springs (the simplest mathematical model for soil-structure interaction). These elements are then combined with the usual frame elements, forming a coupled system of a framed structure on an elastic foundation. The model is applied to problems of excitations applied directly to the structure and those due to support motions including, for example, earthquakes. The dynamic response is obtained by using either modal superposition or numerical integration by means of the Newmark scheme; for seismic problems the method of spectral modal analysis is also employed. The second model consists of a combination of the finite element method for the structure and the boundary element method for the soil. For the soil model, the method of dual reciprocity is employed to take the domain integral due to inertia term to the boundary. The model thus employs the Kelvin fundamental solution for the problem. The dynamic response is then obtained through the numerical integration of the equation of motion of the coupled soil-structure system using the Newmark scheme. Numerical results for both models are presented

サンジゲン リサンカ ヨウソホウ オ モチイタ ジシンジ ノ ドウテキ センダン オヨビ ヒッパリ クラック デンパ

京都大学0048新制・課程博士博士(理学)甲第9329号理博第2464号新制||理||1265(附属図書館)UT51-2002-G87京都大学大学院理学研究科地球惑星科学専攻(主査)教授 入倉 孝次郎, 教授 梅田 康弘, 教授 モリ ジム学位規則第4条第1項該当Doctor of ScienceKyoto UniversityDA