Stochastic Source Model Research Articles

Probabilistic Seismic Hazard Analysis and Synthetic Ground Motion Generation for Seismic Risk Assessment of Structures in the Northeast India

This article outlines the performance-based seismic risk assessment (PBSRA) of structures requiring probabilistic seismic hazard analysis (PSHA) to obtain hazard curves and an evaluation of the demand model by a nonlinear structural response analysis under properly selected ground motion records. Unfortunately, such site-specific information is not readily available for Northeast region of India. The present study focuses on these two aspects to supplement the PBSRA. The estimations of hazard curves are demonstrated by considering the seismicity within 300 km radius around the considered locations and specified exposure period. Due to limited availability of natural records in this region, synthetic accelerograms are generated using stochastic point source models by identifying the most contributing magnitude distance combinations from disaggregation of the PSHA results. The significant variabilities observed in the estimated hazard, synthetic accelerograms and nonlinear building responses in the various locations indicate the need of explicit site-specific analysis for PBRSA of structures in the region.

Stochastic Residential Harmonic Source Modeling for Grid Impact Studies

With the introduction of more non-linear loads, e.g., compact fluorescent lamps, electric vehicles, photovoltaics, etc., the need to determine the harmonic impact of the residential load is rising, illustrated by the many studies performed on their harmonic impact. Traditionally, these studies are performed for a single new device and single penetration level, neglecting the harmonic interaction between new types of devices, as well as giving little information at which moment in time possible problems may arise. A composite approach to access the impact of harmonic sources on the distribution network is therefore proposed. This method combines a bottom-up stochastic modeling of the residential load with harmonic measurement data and harmonic load-flows all based on a scenario analysis. The method is validated with measurement data and shows a good prediction of the current level of harmonics in a residential neighborhood for the current situation. To demonstrate the applicability of the proposed method, case studies are performed on the IEEE European Low Voltage Test Feeder. These case studies show a marked difference between applying individual device-based models and a composite modeling approach, demonstrating why the proposed approach is an adequate method for the determination of the impact of new devices on the harmonics.

Tsunami Energy, Ocean-Bottom Pressure, and Hydrodynamic Force from Stochastic Bottom Displacement

Tsunami generation and propagation due to a randomly fluctuating of submarine earthquake modeled by vertical time-dependent of a stochastic bottom displacement are investigated. The increase in oscillations and amplitude in the free surface elevation are controlled by the noise intensity parameter of the stochastic bottom displacement. Evolution of kinetic and potential energy of the resulting waves by the stochastic bottom displacement is examined. Exchange between potential and kinetic energy was achieved in the propagation process. The dynamic ocean-bottom pressure during tsunami generation is investigated. As the vertical displacement of the stochastic bottom increases, the peak amplitude of the ocean-bottom pressure increases through the dynamic effect. Time series of the maximum tsunami wave amplitude, kinetic and potential energy, wave and ocean-bottom pressure gauges and the hydrodynamic force caused by the stochastic source model under the effect of the water depth of the ocean are investigated.

Estimation of strong motion parameters in the coastal region of gujarat using geotechnical data

Seven boreholes are drilled in the coastal region of Gujarat; three in Kachchh (at Jangi, Mandvi and Mundra), one in Saurashtra (Jodiya) and three in mainland Gujarat(Dahej, Kamboi and Dholera) to depth of 27–80m for estimating the surface strong ground motion parameters. These parameters are required for seismic resistant design of structures in the areas. The adopted methodology comprises of three parts: (i) soil modeling and estimation of depth to Engineering Bed Layer (EBL) (a prominent subsurface soil layer with shear wave velocity of 450m/s to 760m/s with SPT N value of more than 80) (ii) Estimation of the ground motion at EBL (iii) estimation of ground motion at the surface by 1D ground response analysis using SHAKE program. The soil models are prepared from borehole data and shear wave velocity/ N-values. The ground motion at EBL is estimated using Stochastic Finite Fault source Modeling Technique by considering scenario earthquakes along two major faults of Kachchh (Kachchh Mainland Fault (Mw7.6) and Katrol Hill Fault (Mw7.5)), one of Saurashtra (North Kathiawar Fault (Mw 6.5)) and one of Mainland Gujarat (West Cambay Fault (Mw 6.0)). The surface ground motion is estimated by passing ground motion simulated at EBL through prepared soil models of each site using SHAKE program. The surface peak ground acceleration from 0.076g to 0.396g and peak spectral acceleration from 0.24g to 1.4g are estimated at seven coastal sites. Spectral accelerations are found higher than Bureau of Indian Standard (BIS) suggested values at Jangi (between 0.1 and 0.3s & 0.8–1.4s), Jodiya (0.1–0.3s), Mundra (0.3–0.6s) and Dholera (0.1–0.4s) sites, where the importance factor of 1.5 needs to be considered. The study suggests taking BIS values at Dahej, Kamboi and Mandvi coastal sites.

New Scaling Relationships of Earthquake Source Parameters for Stochastic Tsunami Simulation

New scaling relationships of key earthquake source parameters are developed by uniformly and systematically analyzing 226 finite-fault rupture models from the SRCMOD database (http://equake-rc.info/srcmod/). The source parameters include the fault width, fault length, fault area, mean slip, maximum slip, Box-Cox power, correlation lengths along dip and strike directions, and Hurst number. The scaling relationships are developed by distinguishing tsunamigenic models from non-tsunamigenic models; typically, the former occurs in ocean and has gentler dip angles than the latter. The new models are based on extensive data, including recent mega-thrust events, and thus Eire more reliable. Moreover, they can be implemented as multivariate probabilistic models that take into account uncertainty and dependency of the multiple source parameters. The comparison between new and existing models indicates that the new relationships are similar to the existing ones for earthquakes with magnitudes up to about 8.0, whereas the relationships for the fault width and related parameters differ significantly for larger mega-thrust events. An application of the developed scaling relationships in tsunami hazard analysis is demonstrated by synthesizing stochastic earthquake source models in the Tohoku region of Japan. The examples are aimed at providing practical guidance as to how the developed scaling relationships can be implemented in stochastic tsunami simulation. The numerical results indicate that the effects of magnitude scaling of the source parameters and their uncertainties have major influence on the tsunami hazard assessment.

How heterogeneous coseismic slip affects regional probabilistic tsunami hazard assessment: A case study in the South China Sea

AbstractRupture complexity, typically in the form of heterogeneous slip distribution pattern, significantly affects the local tsunami wave field. However, the effect of rupture complexity is not commonly considered in any form of tsunami hazard assessment. Taking rupture complexity into account significantly increases the computational load, particularly in regional‐scaled probabilistic tsunami hazard assessments (PTHAs) that usually require a large number of simulations based on synthetic scenarios. In this study, we investigate how the heterogeneous slip distribution affects the regional‐scaled PTHA by taking the South China Sea (SCS) as an example. By doing this, we update PTHA for the SCS by incorporating the best available information of seismic tsunamigenic sources along the Manila megathrust. We integrate a stochastic source model into a Monte Carlo‐type simulation, in which a broad range of slip distribution patterns is generated for large numbers of synthetic earthquake events. Green's function technique is employed to efficiently calculate the nearshore tsunami wave amplitude along the SCS coastlines. Our result suggests that for a relatively small and confined region like the SCS, the commonly used approach based on the uniform slip model significantly underestimates tsunami hazard not only in the near‐source region like west Luzon, as expected, but also in the relative far field, such as south China and central Vietnam. Additionally, our sensitivity test of the patch size effects suggests that large patch size is unable to adequately resolve the details of heterogeneous seafloor deformation, and such approaches considerably underestimate the potential tsunami hazard for the SCS coasts.

Non-linear resonant coupling of tsunami edge waves using stochastic earthquake source models

Non-linear resonant coupling of tsunami edge waves using stochastic earthquake source models

Near- and far-field tsunami amplitudes by a moving curvilinear stochastic submarine slide shape based on linearized water wave theory

The process of tsunami generation caused by a moving curvilinear stochastic submarine landslide with constant and variable velocity, driven by two Gaussian white noise processes in the x- and y-directions is investigated. Generation of tsunami is described initially by a rapid curvilinear down and uplift faulting, then propagating to a significant length to produce curvilinear stochastic three-dimensional model represented by a depression slump, and a displaced accumulation slide model and finally represented by the movement of the accumulation block slide. The moving curvilinear stochastic block slide acts to reduce wave focusing. This model is used to study the tsunami amplitude under the effect of the noise intensities and times of the curvilinear stochastic source model. The increase of the normalized noise intensities leads to an increase in oscillations and amplitude in the free surface elevation. Tsunami waveforms using linearized water wave theory for uniform water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space). The normalized peak amplitude is analyzed as a function of the propagation length, width, noise intensities of the source model and the water depth. Tsunami propagation waveform is demonstrated after the slide stops moving at different propagation times.

Probabilistic Tsunami Damage Assessment Considering Stochastic Source Models: Application to the 2011 Tohoku Earthquake

A computational framework for probabilistic tsunami risk assessment due to a mega-thrust subduction earthquake is developed and is applied to the 2011 Tohoku Tsunami from retrospective viewpoints. The uncertain tsunami source characteristics are represented by multiple source inversion models and their stochastic variations that are generated using the spectral analysis and synthesis method. By conducting Monte Carlo tsunami simulation, stochastic inundation depth maps can be developed, which are subsequently integrated with tsunami fragility curves to develop stochastic tsunami risk maps. The stochastic tsunami risk maps display spatial variability of tsunami damage probabilities for a building portfolio, reflecting not only possible tsunami scenarios but also uncertain tsunami resistance of buildings. The numerical results indicate that both stochastic tsunami risk maps and risk curves are affected by the local terrain features, proximity to major tsunami sources, and building characteristics (material type and story number). Consideration of different reference tsunami source models in probabilistic tsunami risk assessment are identified as one of the critical contributors to the overall uncertainty of the tsunami risk predictions. Therefore, in determining critical scenarios for tsunami evacuation and risk mitigation, a wide range of possible tsunami scenarios should be considered in light of the current limited seismological knowledge for the mega-thrust subduction earthquake.

A Laboratory Earthquake‐Based Stochastic Seismic Source Generation Algorithm for Strike‐Slip Faults and its Application to the Southern San Andreas Fault

There is a sparse number of credible source models available from large-magnitude past earthquakes. A stochastic source-model-generation algorithm thus becomes necessary for robust risk quantification using scenario earthquakes. We present an algorithm that combines the physics of fault ruptures as imaged in laboratory earthquakes with stress estimates on the fault constrained by field observations to generate stochastic source models for large-magnitude (M w 6.0–8.0) strike-slip earthquakes. The algorithm is validated through a statistical comparison of synthetic ground-motion histories from a stochastically generated source model for a magnitude 7.90 earthquake and a kinematic finite-source inversion of an equivalent magnitude past earthquake on a geometrically similar fault. The synthetic dataset comprises three-component ground-motion waveforms, computed at 636 sites in southern California, for 10 hypothetical rupture scenarios (five hypocenters, each with two rupture directions) on the southern San Andreas fault. A similar validation exercise is conducted for a magnitude 6.0 earthquake, the lower magnitude limit for the algorithm. Additionally, ground motions from the M w 7.9 earthquake simulations are compared against predictions by the Campbell–Bozorgnia Next Generation Attenuation relation, as well as the ShakeOut scenario earthquake. The algorithm is then applied to generate 50 source models for a hypothetical magnitude 7.9 earthquake originating at Parkfield, California, with rupture propagating from north to south (toward Wrightwood), similar to the 1857 Fort Tejon earthquake. Using the spectral element method, three-component ground-motion waveforms are computed in the Los Angeles basin for each scenario earthquake and the sensitivity of ground-shaking intensity to seismic source parameters (such as the percentage of asperity area relative to the fault area, rupture speed, and rise time) is studied. Online Material: Figures of source and simulated peak ground motions for an M w 6.05 scenario on the southern San Andreas fault, and table of V S30 and basin depth at stations.

The Information Carried by Scattered Waves: Near-Field and Nonasymptotic Regimes

The number of spatial degrees of freedom of the field radiated in a two-dimensional setting by a time-harmonic, arbitrary square-integrable current density and in the presence of a random distribution of scattering elements is determined. It is shown that the active power associated to the $k$ th singular value of the near field in the presence of scatterers external to the cut presents a heavy tail decay as a function of its index, rather than the usual exponential attenuation occurring beyond a critical index term observed in free space. This near-field information gain due to scattering was recently anticipated by Janaswamy using a stochastic source model, it is extended here to arbitrary sources, and it is shown to disappear in the limit of large radiating systems. It is also shown that the same information gain and asymptotic cut-off occurs for the singular values of the field radiating in free space. Collectively, these results show that while the presence of scatterers external to the cut can increase the number of channels that can be exploited for communication by the active power in the near field, they do not change the number of channels associated to the field, nor the asymptotic behavior of the number of degrees of freedom.

Stochastic earthquake source model: the omega-square hypothesis and the directivity effect

Recently A. Gusev suggested and numerically investigated the doubly stochastic earthquake source model. The model is supposed to demonstrate the following features in the far-field body waves: 1) the omega-square high-frequency (HF) behavior of displacement spectra; 2) lack of the directivity effect in HF radiation; and 3) a stochastic nature of the HF signal component. The model involves two stochastic elements: the local stress drop (SD) on a fault and the rupture time function (RT) with a linear dominant component. The goal of the present study is to investigate the Gusev model theoretically and to find conditions for (1, 2) to be valid and stable relative to receiver site. The models with smooth elements SD, RT are insufficient for these purposes. Therefore SD and RT are treated as realizations of stochastic fields of the fractal type. The local smoothness of such fields is characterized by the fractional (Hurst) exponent H, 0 < H < 1. This allows us to consider a wide class of stochastic functions without regard to their global spectral properties. We show that the omega-square behavior of the model is achieved approximately if the rupture time function is almost regular (H~1) while the stress drop is rough function of any index H. However, if the rupture front is linear, the local stress drop has to be function of minimal smoothness (H~0). The situation with the directivity effect is more complicated: for different RT models with the same fractal index, the effect may or may not occur. The nature of the phenomenon is purely analytical. The main controlling factor for the directivity is the degree of smoothness of the two dimensional distributions of RT random function. For this reason the directivity effect is unstable. This means that in practice the opposite conclusions relative to the statistical significance of the directivity effect are possible

Linearized Shallow-water Wave Theory of Tsunami Generation and Propagation by Three-dimensional Stochastic Seismic Bottom Topography

Tsunami generation and propagation resulting from lateral spreading of a stochastic seismic fault source model driven by two Gaussian white noises in the x- and y- directions are investigated. Tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the random sea floor uplift represented by a sliding Heaviside step function under the influence of two Gaussian white noise processes in the x- and y- directions. This model is used to study the tsunami amplitude amplification under the effect of the noise intensity and rise times of the stochastic fault source model. The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to the geometric spreading and also due to dispersion. We derived and analyzed the mean and variance of the random tsunami waves as a function of the time evolution along the generation and propagation path.

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Tsunami generation and propagation caused by stochastic seismic fault driven by two Gaussian white noises in the x- and y-directions are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading uplift length and rise times of the three-dimensional stochastic fault source model. Tsunami waveforms within the frame of the linearized shallow-water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space). The amplification of tsunami amplitudes builds up progressively as time increases during the generation process due to wave focusing while the maximum wave amplitude decreases with time during the propagation process due to the geometric spreading and also due to dispersion. The maximum amplitude amplification is proportional to the propagation length of the stochastic source model and inversely proportional to the water depth. The increase of the normalized noise intensities on the bottom topography leads to an increase in oscillations and amplitude in the free surface elevation. We derived and analyzed the mean and variance of the random tsunami waves as a function of the propagated uplift length, noise intensities, and the average depth of the ocean along the generation and propagation path.

Buffer overflow simulation in self-similar queuing networks with finite buffer capacity

The paper recommends an approach to estimate effectively probability of buffer overflow in self-similar queuing networks with finite buffer capacity. Simulations with stochastic (or long-range dependent) traffic source models are conducted. A new efficient algorithm, based on the RESTART method, is developed and applied to accelerate the buffer overflow simulation in a finite buffer single server model under long-range dependent self-similar traffic load with different buffer sizes. Numerical examples and simulation results are provided.

Modeling of tsunami generation and propagation under the effect of stochastic submarine landslides and slumps spreading in two orthogonal directions

Tsunami generation and propagation caused by stochastic submarine landslides and slumps driven by a Gaussian white noise in the x-and y-direction are investigated. This model is used to study the tsunami amplitude amplification under the effect of the noise intensities, spreading velocities, length and width of sliding and times of the stochastic landslides and slumps in the two-dimensional movements. This study shows that focusing and amplification of tsunami amplitudes can occur in an arbitrary direction, determined by the velocities of spreading. Tsunami waveforms within the frame of the linearized shallow water theory for constant water depth are analyzed analytically by transform methods (Laplace in time and Fourier in space) for the stochastic source model. We derived and analyzed the mean and variance of the random tsunami waves in the two orthogonal directions as a function of the propagated uplift length and width, noise intensities of the stochastic source model and the average depth of the ocean along the generation and propagation path.

Stochastic Finite Fault Modeling of Subduction Zone Earthquakes in Northeastern India

In this article, a stochastic finite fault source model is calibrated to estimate ground motion in northeastern India for intermediate depth events originating in the Indo-Burmese tectonic domain. A total of 47 three-component accelerograms from eight events with magnitudes ranging from M w 4.8–6.4 are used to estimate the input source and site parameters of the finite fault source model. Key seismic parameters such as stress drop (Δσ) and site amplification function are determined from the recorded strong motion data. The obtained stress drop of the eight recorded events lies in between 105 and 165 bars.

추계학적 그린함수법으로 합성된 지반운동에 대한 단층 파라미터의 영향

이 연구에서는 추계학적 그린함수법에 의한 단층 모델을 이용하여 지진파를 합성하고 단층 파라미터의 변화에 의한 지반 운동의 차이를 평가하였다. 모멘트 규모 6.5의 단층을 예제로 선정하였고 아스페리티 면적의 통계값을 이용하여 슬립의 분포를 모델링하였다. 평가를 위해 고려된 단층 파라미터들은 진원의 위치, 전단파 속도 대비 파열 전파속도 비, 상승시간, 절점주파수 그리고 고주파감쇠 필터 등 이었다. 요소지진원에 적용된 파라미터들은 구조권역별 특성이 다른 지역의 값을 사용하였고 다른 파라미터들은 발생 가능한 임의의 값을 사용하였다. 생성된 지반운동 시간이력으로부터 응답스펙트럼을 작성하였으며, 파라미터의 값을 달리하여 비교하였다. 이로부터 각각의 단층파라미터에 의해 영향을 받는 주파수 구간 및 스펙트럼 가속도의 차이를 평가하였다. In this study, the ground motion was synthesized using the finite fault model by the stochastic green function method, and the difference in the ground motions was evaluated by using various values of the source parameters. An earthquake with a moment magnitude of 6.5 was assumed for the example fault model. The distribution of the slip in the fault plane was calculated using the statistical data of the asperity area. The source parameters considered in this study were the location of the hypocenter in the fault plane and the ratio of the rupture to the shear wave velocity, the rise time, the corner frequency of the source spectrum, and a high frequency filter. The values of the parameters related to the stochastic element source model were adjusted for different tectonic regions, and the others were selected for several possible cases. The response spectra were constructed from the synthesized ground motion time history and compared with the different parameter values. The frequency range affected by each parameter and the differences of the spectral accelerations were evaluated.

Study about effects of self-similar IP network traffic on queuing and network performance

The paper examines self-similar properties of real communication network traffic data over a wide range of time scales. These self-similar properties are very different from the properties of traditional models based on Poisson and Markov-modulated Poisson processes. Advanced self-similar models of sequentional generators and fixed-length sequence generators, and efficient algorithms that are used to simulate self-similar behaviour of IP network traffic processes are developed and applied. Simulations and numerical results are shown and analysed. Furthermore, simulations with stochastic and long range dependent traffic source models are conducted; and efficient algorithms for buffer overflow simulation in finite buffer single server model under self-similar traffic load are developed and applied. Simulations and numerical results are shown and analysed.

Broadband trailing-edge noise prediction with a stochastic source model

A RANS-based numerical technique for the prediction of the airfoil trailing-edge broadband noise is presented. The definition of the sound sources from RANS turbulence statistics is based on a stochastic reconstruction of the turbulent velocity fluctuations. The method, named Eulerian Solenoidal Digital Filter, accounts for the convective transport and for the solenoidality of the velocity field. The acoustic near field is computed solving the Acoustic Perturbation Equations in the frequency domain. The integral formulation of Ffowcs Williams and Hawkings is used to evaluate the far-field radiation. The ESDF method is validated for the case of homogeneous isotropic turbulence and it is applied to the calculation of the broadband trailing-edge noise of a NACA 0012 airfoil. Near-field and far-field results are compared with analytical and experimental data.