Model for Basin Effects on Long‐Period Response Spectra in Southern California

Attenuation relations are derived for central Japan (broadly spanning the Kantō, Tokai, and Chubu regions) using recordings of small earthquakes (2.0≤ M JMA ≤4.0 [Japan Meterological Agency magnitude]) and moderate- to large-magnitude earthquakes (3.0≤ M JMA ≤7.2). We independently analyze data from both small-magnitude and moderate- to large-magnitude earthquakes to provide an insight into the use of attenuation relations derived in regions of low seismic activity. A strong correlation is found between the attenuation parameters derived from each dataset. We find that Q is strongly depth dependent and that apparent geometrical decay increases with increasing hypocentral distance. This is modeled by using a three segment decay function, with the initial decay forced to 1/ R . Moment magnitudes are close to the published M JMA magnitude, but are, on average, slightly higher. An increase in stress drop with magnitude is required in order to model both the small-magnitude and moderate- to large-magnitude datasets. Alternatively we show that a constant stress-drop model is suitable to model the response spectra of both small-magnitude and moderate- to large-magnitude earthquakes when considering the saturation of the source-corner frequency due to a static site filter such as f max or κ . We test our ability to predict strong ground motion by using our attenuation and source-scaling relations derived from the small-magnitude recordings to stochastically simulate peak ground acceleration, peak ground velocity, and 5% damped response spectral ordinates over a range of magnitudes and distances. The residuals of this simulation are found to be largely independent of distance and magnitude. We compare our attenuation relations against other relations derived for Japan. The residuals of these relations are analyzed and compared against those obtained from the model found in this study. We find that, in this study, the prediction of strong ground motions is possible using small-magnitude data and that the validity of the prediction extends across all magnitudes available for comparison (2.0≤ M JMA ≤7.8). On the other hand, by using an alternative published predictive relation for Japan, derived using large-magnitude events, peak ground acceleration is significantly overestimated for small-magnitude earthquakes.

The objective of this technical note is to characterize seismic ground motion at the Savannah River Site (SRS) by postulated earthquakes that may impact facilities at the site. This task is accomplished by reviewing the deterministic and probabilistic assessments of the seismic hazard to establish the earthquakes that control the hazard to establish the earthquakes that control the hazard at the site and then evaluate the associated seismic ground motions in terms of response spectra. For engineering design criteria of earthquake-resistant structures, response spectra serve the function of characterizing ground motions as a function of period or frequency. These motions then provide the input parameters that are used in the analysis of structural response. Because they use the maximum response, the response spectra are an inherently conservative design tool. Response spectra are described in terms of amplitude, duration, and frequency content, and these are related to source parameters, travel path, and site conditions. Studies by a number of investigators have shown by statistical analysis that for different magnitudes the response spectrum values are different for differing periods. These facts support Jennings' position that using different shapes of design spectra for earthquakes of different magnitudes and travel paths is a better practice than employing a single, general-purpose shape. All seismic ground motion characterization results indicate that the PGA is controlled by a local event with M[sub w] < 6 and R < 30km. The results also show that lower frequencies are controlled by a larger, more distant event, typically the Charleston source. The PGA of 0.2 g, based originally on the Blume study, is consistent with LLNL report UCRL-15910 (1990) and with the DOE position on LLNL/EPRI.

A representative attenuation relationship is one of the key components required in seismic hazard assessment of a region of interest. Attenuation relationships for peak ground acceleration, peak ground velocity and response spectral accelerations for Sumatran megathrust earthquakes, covering Mw up to 9.0, are derived based on synthetic seismograms obtained from a finite‐fault kinematic model. The relationships derived are for very hard rock site condition and for a long‐distance range between 200 and 1500 km. They are then validated with recorded data from giant earthquakes on the Sumatran megathrust occurring since year 2000. A close examination of the recorded data also shows that spectral shapes predicted by most of the existing attenuation relationships and that specified in the IBC code are not particularly suitable for sites where potential seismic hazard is dominated by large‐magnitude, distant, earthquakes. Ground motions at a remote site are typically signified by the dominance of long‐period components with periods longer than 1 s, whereas the predominant periods from most of the existing attenuation relationships and the IBC code are shorter than 0.6 s. The shifting of response spectrum towards longer period range for distant earthquakes should be carefully taken into account in the formulation of future seismic codes for Southeast Asia, where many metropolises are located far from active seismic sources. The attenuation relationship derived in the present study can properly reproduce the spectral shape from distant subduction earthquakes, and could hopefully give insights into the formulation of future seismic codes. Copyright © 2009 John Wiley &amp; Sons, Ltd.

The Virtual Seismologist method for earthquake early warning uses a Bayesian approach to find the most probable magnitude and location estimates given the incoming ground motions envelopes from a rupturing earthquake. Ground motion ratios and ground motion envelope attenuation relationships are used to estimate magnitude and epicentral location as early as 3 seconds after the initial P wave detection. The use of prior information distinguishes this method from other proposed methods for seismic early warning. The state of health of the seismic network, previously observed seismicity, fault locations, and the Gutenberg-Richter relationship are the types of prior information useful in resolving trade-offs in the initial source estimates which are unresolved by the limited data. Short-term earthquake forecasts are ideal priors for seismic early warning. Having a high density of stations with real-time telemetry reduces the complexity involved in finding the most probable source estimates and communicating these estimates to early warning subscribers. The benefits of prior information are most evident for regions with low station density. Most early warning studies are focused exclusively on either the source estimation problem, or how subscribers use the warning information. The inclusion of prior information ultimately requires a level of coordination and communication between the network broadcasting the early warning information and the subscribers that is not consistent with this divide. The need for a more integrated approach to seismic early warning which considers the source estimation and user response as interacting and interrelated parts of a single problem is discussed. A parameterization that decomposes observed ground motion envelopes into Pwave, S-wave, and ambient noise envelopes is developed and applied to a large suite of observed ground motion envelopes recorded within 200 km of 2 ! M ! 7.3 Southern California earthquakes. Separate attenuation relationships are developed to describe vi the magnitude, distance, and site dependence of various channels of P- and S-wave envelopes. The P-wave relationships allow the early warning source estimates to be obtained from observed P-wave amplitudes. Aside from early warning applications, these envelope attenuation relationships are used to investigate the average properties of ground motions recorded by the Southern California Seismic Network. Stationspecific amplification factors for 150 Southern California Seismic Network stations were obtained for horizontal and vertical acceleration, velocity, and displacement amplitudes, and are included (Excel format) as external multimedia objects.

We assess how well the Next‐Generation Attenuation‐West 2 (NGA‐West2) ground‐motion models (GMMs), which are used in the US Geological Survey’s (USGS) National Seismic Hazard Model (NSHM) for crustal faults in the western United States, predict the observed basin response in the Great Valley of California, the Reno basin in Nevada, and Portland and Tualatin basins in Oregon. These GMMs rely on site parameters such as the time‐averaged shear‐wave velocity ( V S ) in the upper 30 m of Earth’s crust ( V S30 ) and depths to 1.0 and 2.5 km/s shear‐wave isosurfaces ( Z 1.0 and Z 2.5 ) to capture basin effects and were developed using observations and simulations primarily from the Los Angeles region in southern California. Using ground‐motion records from mostly small‐to‐moderate earthquakes and mixed‐effects regression analysis, we find that the GMMs perform well with our local basin‐depth models for the California Great Valley. With our local basin‐depth models for Reno, the GMMs do not perform as well for this relatively shallow basin and exhibit little sensitivity to the basin parameters used in the NGA‐West2 GMMs. We also find good performance for the local Z 1.0 model across the Portland region, whereas the local Z 2.5 model provides little predictive power except at sites in the deepest part of the Tualatin basin. Additional work could improve the performance of the site and basin terms in the NGA‐West2 GMMs for regions with geologic structure different than the deep basins in southern California and the Great Valley. In addition, we find significant discrepancies among the GMMs in how the uncertainty in the ground motion varies with basin depth and pseudospectral period. Our results can help guide seismic hazard analyses on whether to include these local basin‐depth models.

Source‐to‐site simulations form a strong basis for risk‐based probabilistic seismic hazard analysis. With an emerging database of synthetic ground motions, there is a growing need to assess the feasibility of the application of these motions for structural analysis. This article evaluates the robustness of a numerical framework to link high‐fidelity geophysics models with local finite element (FE) models to perform site response analysis (SRA) and soil–structure interaction (SSI) evaluation. The regional‐scale simulations are carried out in SW4, a physics‐based finite difference scheme for seismic wave propagation, from which synthetic ground motions are extracted to be applied at the base of a local FE model of a nuclear reactor building in Livermore Software Technology Corporation (LSTC) Dynamic Analysis (LS‐DYNA), an advanced multiphysics simulation software package. The seismic event chosen for simulation is an aftershock from the 2007 Niigata Chuetsu‐Oki earthquake. Ground motions recorded at Kashiwazaki Kariwa Nuclear Power Plant (KKNPP) in Japan are used to validate the numerical simulations conducted with both the finite difference and FE methods. Moreover, an inter‐code comparison is made between the free‐field motions generated by SW4 and LS‐DYNA to assess the consistency between these two simulation codes. The simulations conducted in this study focus on horizontal ground motions resolved up to a maximum of 3 Hz. The conclusions recognize the importance of compatibility of near‐surface properties when employing simulated ground motions toward SRA and SSI for a successful linking approach.

Under the effect of earthquake, loss of soil stiffness results in loss of bearing capacity which subsequently lost the support of basic structures that tilt and therefore pack down. The study of settlement of granular media under seismic loading, although it has not retained the attention of many researchers in the past, is crucial if we are to guarantee the good performance of embankments, dikes or land upon which some works at risk. Numerical simulation of soil behavior is performed by numerical methods such as finite difference and finite element method. These methods are programmed in software simulation of increasingly sophisticated. The main objective of this paper is to investigate, by numerical modeling with the code of finite element PLAXIS, variation in settlement of a soil under a rock fill dam port

Introduction. Computer Program Packages. Typical Problems. Classification of Equations. Discrete Methods. Finite Differences and Computational Molecules. Finite Difference Operators. Method of Weighted Residuals. Finite Elements. Method of Lines. Errors. Stability and Convergence. Irregular Boundaries. Choice of Discrete Network. Dimensionless Forms. Parabolic Equations: Introduction. Properties of a Simple Explicit Method. Fourier Stability Method. Implicit Methods. Additional Stability Considerations. Matrix Stability Analysis. Extension of Matrix Stability Analysis. Consistency, Stability, And Convergence. Pure Initial Value Problems. Variable Coefficients. Examples of Equations with Variable Coefficients. General Concepts of Error Reduction. Methods of Lines (MOL) for Parabolic Equations. Weighted Residuals and the Method of Lines. Bubnov-Galerkin Scheme for Parabolic Equations. Finite Elements and Parabolic Equations. Hermite Basis. Finite Elements and Parabolic Equations. General Basis Fucntion. Finite Elements and Parabolic Equations. Special Basis Functions. Explicity Finite Difference Methods for Nonlinear Problems. Further Applications on One Dimentions. Asymmetric Approximations. Elliptic Equations: Introduction. Simple Finite Difference Schemes. Direct Methods. Iterative Methods. Linear Elliptic Equations. Some Poit Iterative Methods. Convergence of Point Iterative Methods. Rates of Convergence. Accelerations. Conjugate Gradient Method. Extensions of SOR. Auliative Examples of Over-Relaxation. Other Point Iterative Methods. Block Iterative Methods. Alternating Direction Methods. Summary of ADI Results. Triangular Elements. Boundary Element Method (BEM). Spectral Methods. Some Nonlinear Examples. Hyperbolic Equations: Introduction. The Quasilinear System. Introductory Examples. Method of Characteristics. Constant States and Simple Waves. Typical Application of Characteristics. Finite Differences for First-Order Equations. Lax-Wendroff Methods and Other Algorithms Dissipation and Dispersion. Explicity Finite Difference Methods. Attenuation. Implicit Methods for Second-Order Equations. Time Quasilinear Examples. Simultaneous First-Order Equations. Explicit Methods. An Implicity Method for First-Order Equations. Hybrid Methods for First-Order Equations. Finite Elements and the Wave Equation. Spectral Methods and Periodic Systems. Gas Dyunamics in One Space Variable. Eulerian Difference Equations. Lagrangian Difference Equations. Hopscotch Methods for Conservation Laws. Explicity-Implicity Schemes for Conservation Laws. Special Topics: Introduction. Singularities. Shocks. Eigenvale Problems. Parabolic Equations in Segeral Space Variables. Additional Comments on Elliptic Equations. Hyperbolic Equations in Higher Dimensions. Mixed Systems. Higher Order Equations in Elasticity and Vibrations. Computational Fluid Mechanics. Stream Function. Vorticity Method for Fluid Mechanics. Primitive Variable Methods for Fluid Mechanics. Vector Potential Methods for Fluid Mechanics. Introduction to Monte Carlo Mehtods. Fast Fourier Transform and Applications. Method of Fractional Steps. Applications of Group Theory in Computation. Computational Ocean Acoustics. Enclosure Methods. Chapter References. Author Index. Subject Index.

The creation of earthquake hazard maps requires various datasets with selected attenuation relations. Based on the selected attenuation relation, the calculation time varies from half an hour to a couple of days. The length of time needed to create an earthquake hazard map also depends on the resolution of the resulting map. The time gets longer as the resolution of the resulting earthquake hazard map gets higher. The basic form of an attenuation relation requires complex calculation algorithms including geospatial information related to the region of interest. Nowadays, next-generation attenuation (NGA) models are introduced to generate more realistic earthquake hazard maps. However, the more complex the attenuation relation is, the longer time will be required to create a hazard map. This paper offers a new method to create high-resolution earthquake hazard maps, faster than using traditional attenuation relation methods, by using an analytic hierarchy process of spatial multi-criteria decision analysis and geographic information systems. This method has been generated and tested for the city of Istanbul. The resulting maps are compared with the earthquake hazard maps created for the city of Istanbul by using the NGA model of Boore and Atkinson (in Boore–Atkinson NGA ground motion relations for the geometric mean horizontal component of peak and spectral ground motion parameters (trans: Engineering Co, University of California B). Pacific Earthquake Engineering Research Center 2007). A second output of this paper is a map of the elements at risk (EaR) for the population and buildings of Istanbul, and the introduction of a new approach of net elements at risk (NEaR).

Site-specific ground motion modeling for a historical Cairo site as a step towards computation of seismic input at cultural heritage sites

We present a high-resolution, three-dimensional P-wave seismic veloc- ity model of the sedimentary basin in the Salton Trough, southern California, and use the model for spectral-element method (SEM) wave propagation and ground- motion simulations to quantitatively assess seismic hazard in the region. The basin geometry is defined by a surface representing the top of crystalline basement, which was constrained by seismic refraction profiles and free-air gravity data. Sonic logs from petroleum wells in the Imperial Valley and isovelocity surfaces defined by seismic refraction studies were used to define P-wave velocity within the sedimentary basin as a function of two variables:(1) absolute depth and (2) depth of the underlying crystalline basement surface (CBS). This velocity function was used to populate cells of a three-dimensional spatial array (voxet) defining the P-wave velocity structure in the basin. The new model was then resampled in a computational mesh used for earthquake wave propagation and strong ground motion simulations based upon the SEM (Komatitsch et al., 2004). Simulation of the 3 November 2002 Mw 4.2 Yorba Linda earthquake demonstrates that the new model provides accurate simulation of strong ground motion amplification effects in the Salton Trough sedimentary basin, offering substantial improvements over previous models. A hypothetical Mw 7.9 earthquake on the southern San Andreas fault was then simulated in an effort to better understand the seismic hazard associated with the basin structure. These sim- ulations indicate that great amplification will occur during large earthquakes in the region due to the low seismic velocity of the sediments and the basin shape and depth.

Traditionally reservoir simulation has been accomplished by solution of reservoir flow models using variations of the methods of finite differences and less frequently by finite elements. The accuracy of these methods depends heavily on the size of grid blocks and time steps employed for the numerical solution. Consequently, computational time and memory requirements may be overwhelming in many cases. In the present study, a recently proposed method called the finite analytic method is shown to alleviate the difficulties associated with the conventional methods. The finite analytic method is operationally and principally different than the conventional finite difference and finite element methods in that a general analytical solution of the simulation model is used over mesh elements to obtain a numerical scheme. Therefore, for comparable accuracy, finite analytic method can lead to higher order approximations than those achieved by the finite difference and finite element techniques. Finite analytic schemes are derived from the reservoir flow models and therefore they are naturally problem dependent. This is the reason for the efficiency of the finite analytic method. By this method problems such as numerical diffusion, numerical instability, slow convergence, as well as requirements of large number of time steps and grid blocks are significantly reduced. In this study, the methodology of formulating and calculating with this method is illustrated by means of a typical two-phase immiscible flow problem described by the Buckley-Leverett equation. The results are compared with the analytic solution of Buckley-Leverett problem and solutions obtained by finite difference and finite element methods. The present study demonstrates that the finite analytic method is capable of producing accurate flow behavior in porous media even when relatively large time steps and grid blocks are used.

Design horizontal and vertical earthquake response spectra for the replacement Cooper River Bridge in Charleston, South Carolina were developed based on site-specific probabilistic and deterministic ground motion studies. Two basic analyses were completed to develop horizontal response spectra for soft rock conditions. The first was a probabilistic seismic hazard analysis (PSHA) for hard rock conditions. The information used to conduct the PSHA includes the characterization of ground motion attenuation relationships applicable to hard rock in the eastern United States. The second basic analysis conducted for the study was an analysis of crustal response to the hard rock motions. For this analysis, the response of soft rock extending from the top of hard rock at 800 m depth to the base of Cooper Marl at 100m depth was evaluated. The presence of a thick, relatively low velocity soft rock layer having a strong velocity (impedance) contrast with the underlying hard rock resulted in a substantial amplification of long-period ground motions in the analysis. Two additional supporting analyses that were completed include development of deterministic response spectra and vertical response spectra.

A generalization of conventional deterministic finite element and difference methods to deal with spatial material fluctuations hinges on the problem of determination of stochastic constitutive laws. This problem is analyzed here through a paradigm of micromechanics of elastic polycrystals and matrix-inclusion composites. Passage to a sought-for random meso-continuum is based on a scale dependent window playing the role of a Representative Volume Element (RVE). It turns out that the microstructure cannot be uniquely approximated by a random field of stiffness with continuous realizations, but, rather, two random continuum fields may be introduced to bound the material response from above and from below. Since the RVE corresponds to a single finite element, or finite difference cell, not infinitely larger than the crystal size, these two random fields are to be used to bound the solution of a given boundary value problem at a given scale of resolution. The window-based random continuum formulation is also employed in analysis of rigid perfectly-plastic materials, whereby the classical method of slip-lines is generalized to a stochastic finite difference scheme. The present paper is complemented by a comparison of this methodology to other existing stochastic solution methods.

It is important to investigate the effect of the uncertainty of the condition of a fault model to the results of the ground motion prediction for scenario earthquake. In such investigation, many case studies of the ground motion prediction are required. In order to calculate the ground motions efficiently, we proposed the simple evaluation method of seismic response spectrum using a fault model. The proposed method using the simplification which assumed the random vibration can obtain easier the mean response spectrum than the calculation of a large number sample by the statistical Green's function method. Then, the effect of the uncertainty of the fault parameters to the result of the ground motion prediction for the scenario earthquake was investigated by the simulation based on many samples of fault model using the proposed method. Although the spatial distribution of the mean response spectrum was simple, the standard deviation of response spectrum showed complex spatial distribution. The standard deviation of response spectrum was large near a fault edge and at the points on the extension of a fault strike. Since the variability of the predicted response spectrum changes with locations of a calculation point, when evaluating the seismic hazard in consideration of the uncertainty of the fault parameters for the scenario earthquake, it is necessary to scrutinize the effect of the uncertainty for every target calculation point.