Deterministic Wave Propagation Research Articles

The evaluation of EMI characteristics of 4G-IMT system on FAST around its RQZ

Mobile communication base stations have become ubiquitous with the popularization and development of mobile communication services. Although the Chinese government has designated a radio quiet zone (RQZ) specifically for Five-hundred-meter Aperture Spherical radio Telescope (FAST), the 4G International Mobile Telecommunications (4G-IMT) system is still heavily used to meet the communication needs around the RQZ. To assess the Electromagnetic Interference (EMI) caused by 4G-IMT base stations on the performance of FAST, this paper employs the International Telecommunication Union (ITU) deterministic radio wave propagation prediction model. The interference of 4G-IMT base stations on FAST is evaluated based on relevant parameters, such as the frequency used by both FAST and the base station, in conjunction with the FAST threshold protection requirements. The results indicate that 47.73 % of the data exceed the radio astronomy protection threshold of FAST. In addition, a field experiment was conducted to verify the accuracy of the radio wave propagation prediction method used. The root-mean-square error between the predicted value and the measured value was found to be 6.94 dB, supporting the accuracy of the predicted results. The findings of this study can help suppress interference from mobile communication services around the RQZ of FAST and optimize the electromagnetic environment around FAST.

Machine learning simulation of one-dimensional deterministic water wave propagation

Deterministic phase-resolved prediction of the evolution of surface gravity waves in water is challenging due to their complex spatio-temporal dynamics. Physics-based methods of varying complexity are available, but the conflicting objectives of numerical efficiency and accuracy impede real-time wave prediction. Data-driven methods may be able to overcome this challenge by using training data generated by complex numerical methods. This work explores the potential of a machine learning (ML) approach based on a fully convolutional encoder–decoder architecture for the efficient and accurate prediction of water waves. The high-order spectral (HOS) method forms the foundation for the generation of the training data. The HOS method is applied for different, consecutive orders of nonlinearity starting from first order up to fourth order. The JONSWAP wave energy spectrum serves as the basis for modeling the one-dimensional irregular sea states. The overall objective of this work is to evaluate whether the complex non-linear physical processes can be identified and learned by the ML approach. The trained ML flow mapper is used to perform time integration of an initial sea state. The results indicate that the proposed ML approach is able to reproduce the distinctive physical processes of the different orders of nonlinearities. It is shown that the ML approach enables fast and accurate predictions of one-dimensional waves over a time horizon that spans multiple peak periods.

Fault Damage Zone Effects on Ground Motions during the 2019 Mw 7.1 Ridgecrest, California, Earthquake

ABSTRACT We have simulated 0–3 Hz deterministic wave propagation in the Southern California Earthquake Center Community Velocity Model (CVM) version CVM-S4.26-M01 for the 2019 Mw 7.1 Ridgecrest earthquake. A data-constrained high-resolution fault zone model (Zhou et al., 2022) is incorporated into the CVM to investigate the effects of the near-fault low-velocity zone (LVZ) on the resulting ground motions, constrained by strong-motion data recorded at 161 stations. The finite-fault source used for the simulation of the Ridgecrest event was obtained from the Liu et al. (2019) kinematic inversion, enriched by noise following a von Karman correlation function above ∼1 Hz with a f−2 high-frequency decay. Our results show that the heterogeneous near-fault LVZ inherent to the fault zone structure significantly perturbs the predicted wave field in the near-source region, in particular by more accurately generating Love waves at its boundaries. The fault zone decreases the 0.1–0.5 Hz mean absolute Fourier amplitude spectrum bias to seismic recordings for all sites in the model and in the Los Angeles basin area (∼200 km from the source) by 16% and 26%, respectively. The fault zone structure generally improves modeling of the long-period features in the data and lengthens the coda-wave trains, in better agreement with observations. The favorable fit to data was obtained with a model including high-resolution surface topography, a 700-m-thick geotechnical layer and frequency-dependent anelastic attenuation in the model domain, with QS=0.1VS and QS(f)=0.1VSf0.5 (VS in m/s) for frequencies lower and higher than 1 Hz, respectively. We recommend that a data-constrained fault zone velocity structure, where available, be included in ground-motion modeling to obtain the least-biased fit to observed seismic data.

A Potential Game Approach to Multi-UAV Accurate Coverage Based on Deterministic Radio Wave Propagation Model in Urban Area

A Potential Game Approach to Multi-UAV Accurate Coverage Based on Deterministic Radio Wave Propagation Model in Urban Area

0–5 Hz deterministic 3-D ground motion simulations for the 2014 La Habra, California, Earthquake

SUMMARYWe have simulated 0–5 Hz deterministic wave propagation for a suite of 17 models of the 2014 Mw 5.1 La Habra, CA, earthquake with the Southern California Earthquake Center Community Velocity Model Version S4.26-M01 using a finite-fault source. Strong motion data at 259 sites within a 148 km × 140 km area are used to validate our simulations. Our simulations quantify the effects of statistical distributions of small-scale crustal heterogeneities (SSHs), frequency-dependent attenuation Q(f), surface topography and near-surface low-velocity material (via a 1-D approximation) on the resulting ground motion synthetics. The shear wave quality factor QS(f) is parametrized as QS, 0 and QS, 0fγ for frequencies less than and higher than 1 Hz, respectively. We find the most favourable fit to data for models using ratios of QS, 0 to shear wave velocity VS of 0.075–1.0 and γ values less than 0.6, with the best-fitting amplitude drop-off for the higher frequencies obtained for γ values of 0.2–0.4. Models including topography and a realistic near-surface weathering layer tend to increase peak velocities at mountain peaks and ridges, with a corresponding decrease behind the peaks and ridges in the direction of wave propagation. We find a clear negative correlation between the effects on peak ground velocity amplification and duration lengthening, suggesting that topography redistributes seismic energy from the large-amplitude first arrivals to the adjacent coda waves. A weathering layer with realistic near-surface low velocities is found to enhance the amplification at mountain peaks and ridges, and may partly explain the underprediction of the effects of topography on ground motions found in models. Our models including topography tend to improve the fit to data, as compared to models with a flat free surface, while our distributions of SSHs with constraints from borehole data fail to significantly improve the fit. Accuracy of the velocity model, particularly the near-surface low velocities, as well as the source description, controls the resolution with which the anelastic attenuation can be determined. Our results demonstrate that it is feasible to use fully deterministic physics-based simulations to estimate ground motions for seismic hazard analysis up to 5 Hz. Here, the effects of, and trade-offs with, near-surface low-velocity material, topography, SSHs and Q(f) become increasingly important as frequencies increase towards 5 Hz, and should be included in the calculations. Future improvement in community velocity models, wider access to computational resources, more efficient numerical codes and guidance from this study are bound to further constrain the ground motion models, leading to more accurate seismic hazard analysis.

Ground motion simulation and validation of the 2008 Chino Hills earthquake in scattering media

SUMMARYWe simulate 0–2.5 Hz deterministic wave propagation in 3-D velocity models for the 2008 Chino Hills, CA, earthquake using a finite-fault source model and frequency-dependent anelastic attenuation. Small-scale heterogeneities are modeled as 3-D random fields defined using an elliptically anisotropic von Kármán autocorrelation function with its parameters constrained using Los Angeles basin borehole data. We superimpose the heterogeneity models on a leading deterministic community velocity model (CVM) of southern California. We find that models of velocity and density perturbations can have significant effects on the wavefield at frequencies as low as 0.5 Hz, with ensemble median values of various ground motion metrics varying up to ±50 per cent compared to those computed using the deterministic CVM only. In addition, we show that frequency-independent values of the shear-wave quality factor (Qs0) parametrized as Qs0 = 150Vs (Vs in km s–1) provides the best agreement with data when assuming the published moment magnitude (Mw) of 5.4 (M0 = 1.6 × 1017 Nm) for the finite-fault source model. This model for Qs0 trades off with Qs0 = 100Vs assuming Mw = 5.5 (M0 = 2.2 × 1017 Nm), which represents an upper bound of the Mw estimates for this event. We find the addition of small-scale heterogeneities provides limited overall improvement to the misfit between simulations and data for the considered ground motion metrics, because the primary sources of misfit originate from the deterministic CVM and/or the finite-fault source description.

Broadband (0–5 Hz) Fully Deterministic 3D Ground‐Motion Simulations of a Magnitude 7.0 Hayward Fault Earthquake: Comparison with Empirical Ground‐Motion Models and 3D Path and Site Effects from Source Normalized Intensities

Author(s): Rodgers, AJ; Pitarka, A; Anders Petersson, N; Sjogreen, B; McCallen, DB; Abrahamson, N | Abstract: We report on high-performance computing (HPC) fully deterministic simulation of ground motions for a moment magnitude (Mw) 7.0 scenario earthquake on the Hayward fault resolved to 5 Hz using the SW4 finite-difference code. We computed motions obeying physics-based 3D wave propagation at a regional scale with an Mw 7.0 kinematic rupture model generated following Graves and Pitarka (2016). Both plane-layered (1D) and 3D Earth models were considered, with 3D subsurface material properties and topography interpolated from a model of the U.S. Geological Survey (USGS). The resulting ground-motion intensities cover a broader frequency range than typically considered in regional-scale simulations, including higher frequencies relevant for engineering analysis of structures. Median intensities for sites across the domain are within the reported between-event uncertainties (τ) of ground-motion models (GMMs) across spectral periods 0.2-10 s (frequencies 0.1-5 Hz). The within-event standard deviation ϕ of ground-motion intensity measurement residuals range 0.2-0.5 natural log units with values consistently larger for the 3D model. Source-normalized ratios of intensities (3D/ 1D) reveal patterns of path and site effects that are correlated with known geologic structure. These results demonstrate that earthquake simulations with fully deterministic wave propagation in 3D Earth models on HPC platforms produce broadband ground motions with median and within-event aleatory variability consistent with empirical models. Systematic intensity variations for the 3D model caused by path and site effects suggest that these epistemic effects can be estimated and removed to reduce variation in site-specific hazard estimates. This study motivates future work to evaluate the validity of the USGS 3D model and investigate the development of path and site corrections by running more scenarios.

Alternative Hybrid Empirical Ground‐Motion Model for Central and Eastern North America Using Hybrid Simulations and NGA‐West2 Models

Abstract An alternative hybrid empirical ground‐motion model for central and eastern North America (CENA) is proposed. The new ground‐motion model (GMM) is developed for the average horizontal components (RotD50) of peak ground acceleration, peak ground velocity, and 5%‐damped pseudospectral accelerations at 0.01–10 s spectral periods. Hybrid empirical estimates are derived using the regional modification factors between two regions (host and target), along with empirical GMMs from the host region. The regional adjustment factors are ratios of the intensity measures from the generated synthetics in the host (western North America [WNA]) and target (CENA) regions. In this study, the recent updated empirical GMMs developed by the Pacific Earthquake Engineering Research Center for the Next Generation Attenuation West2 (NGA‐West2) project (Bozorgnia et al. , 2014) are incorporated. We used a broadband simulation technique proposed by the authors (Shahjouei and Pezeshk, 2015a) to generate synthetics for both the WNA and CENA regions in which the high‐frequency and low‐frequency parts of synthetics are calculated through a stochastic finite‐fault method and kinematic source models along with the deterministic wave propagation, respectively. The updated seismological and geological parameters are deployed in simulations. The new ground‐motion model is developed, as part of the NGA‐East research project, considering multiple shaking scenarios that characterize the magnitude in the M 5.0–8.0 range. The proposed GMM represents the level of ground shaking in the distance range of 2–1000 km and are developed for the reference rock site condition with V S 30 =3 km/s in CENA. The results are compared with some other existing models in the region. In addition, a comprehensive residual analysis is performed using the recorded earthquakes available in the NGA‐East database.

Near-optimal control of a wave energy device in irregular waves with deterministic-model driven incident wave prediction

This paper investigates wave-by-wave control of a wave energy converter using incident wave prediction based on up-wave surface elevation measurement. The goal of control is to approach the hydrodynamically optimum velocity leading to optimum power absorption. This work aims to study the gains in energy conversion from a deterministic wave propagation model that accounts for a range of group velocities in deriving the prediction. The up-wave measurement distance is assumed to be small enough to allow a deterministic propagation model, and further, both wave propagation and device response are assumed to be linear. For deep water conditions and long-crested waves, the propagation process is also described using an impulse response function (e.g. [1]). Approximate low and high frequency limits for realistic band-limited spectra are used to compute the corresponding group velocity limits. The prediction time into the future is based on the device impulse response function needed for the evaluation of the control force. The up-wave distance and the duration of measurement are then determined using the group velocity limits above.A 2-body axisymmetric heaving device is considered, for which power capture is through the relative heave oscillation between the two co-axial bodies. The power take-off is assumed to be linear and ideal as well as capable of applying the necessary resistive and reactive load components on the relative heave oscillation. The predicted wave profile is used along with device impulse response functions to compute the actuator force components at each instant. Calculations are carried out in irregular waves generated using a number of uni-modal wave spectra over a range of energy periods and significant wave heights. Results are compared with previous studies based on the use of instantaneous up-wave wave-profile measurements, both without and with oscillation constraints imposed. Considerable improvements in power capture are observed with the present approach over the range of wave conditions studied.

Synthetic Seismograms Using a Hybrid Broadband Ground‐Motion Simulation Approach: Application to Central and Eastern United States

Abstract Broadband synthetic time histories for central and eastern United States are generated using a proposed hybrid broadband simulation technique. The low‐frequency (LF) portion of synthetics is calculated using kinematic source modeling and deterministic wave propagation. Using the COMPSYN software package (Spudich and Xu, 2003), a discrete wavenumber/finite‐element method is implemented for the LF Green’s functions generation. The procedure makes use of the reciprocity theorem and numerical techniques to assess the representation theorem integrals on a fault surface. Spatial random field models are employed to characterize the complexity of the slip distribution on the heterogeneous fault. In this study, the variability of some of the kinematic source modeling’s parameters (e.g., hypocenter locations, slip distribution, source time function, and rupture propagation) is taken into account to produce multiple seismograms that contain a broader range of intensity measures such as peak ground motions and spectral accelerations. A stochastic finite‐fault simulation model is employed to attain the high‐frequency (HF) portion of synthetics. Combining HF and LF synthetics in a magnitude‐dependent transition frequency, the broadband seismograms are constructed for M 5.5, M 6.5, and M 7.5 earthquakes in a distance range of 2–200 km. Broadband synthetics will be compared with some of the existing ground‐motion prediction equations for spectral accelerations at 0.2, 1.0, and 3.0 s, and the results will be discussed. A compatibility assessment of the stochastic point source and the finite source is performed. The generated seismograms could be implemented in engineering seismology applications such as structural seismic analysis/design and seismic‐hazard analysis.

Broadband Ground-Motion Simulation Using Energy-Constrained Rise-Time Scaling

Abstract The simulation of realistic ground motions associated with large earthquakes is of utmost importance for engineering concerns, for example, in testing the seismic performance of buildings. It is also needed to estimate the level of ground shaking for future earthquakes. In this paper, we focus on two aspects of ground‐motion modeling. First, we use deterministic wave propagation for the entire frequency range but account for source variability by implementing self‐similar slip distributions and rough fault interfaces. Second, we scale the rise time of the source time function so that the modeled waveforms represent the correct radiated seismic energy. The method is validated for the 2008 Wenchuan, China, earthquake and the 2003 Tokachi‐Oki, Japan, earthquake. We demonstrate the robustness of our approach with regard to changes of the assumed rupture velocity. We find the fine source discretizations combined with the small scale source variability ensure that the high frequencies (1–8 Hz) are satisfactorily introduced, justifying the deterministic wave propagation approach even at high frequencies. The adjustment of the rise time via the radiated seismic energy permits a simulation without making assumptions on the stress drop, as is usually done by other modeling approaches. By varying different parameters, such as the energy magnitude, the simulation approach could be especially useful for estimating the range of possible ground motions issuing from a distinct fault in a future earthquake. The rise‐time scaling may also be used for seismogram modeling in the context of early‐response systems as the energy magnitude, which is the parameter needed for the scaling, is available shortly after the earthquake. Online Material: Tables of kinematic rupture models for 2008 Wenchuan and 2003 Tokachi‐Oki, and Fourier spectra of simulations.

Modeling of spatially correlated, site-reflected, and nonstationary ground motions compatible with response spectrum

Seismic risk analysis and mitigation of spatially extended structures require the synthesis of spatially varying ground motions in the response history analysis of these structures. These synthetic motions are usually desired to be spatially correlated, site reflected, nonstationary, and compatible with target design response spectra. In this paper, a method is presented for simulating spatially varying ground motions considering the nonstationarity, local site effects, and compatibility of response spectra. The scheme for generating spatially varying and response spectra compatible ground motions is first established for spatial locations on the ground surface with varying site conditions. The design response spectrum is introduced as the “power” spectrum at the base rock. The site amplification approach is then derived based on the deterministic wave propagation theory, by assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the site with assumed incident angles, from which tri-directional spatial ground motions can be generated. The phase difference spectrum is employed to model ground motions exhibiting nonstationarity in both frequency and time domains with different site conditions. The proposed scheme is demonstrated with numerical examples.

Stochastic seismic analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional multiple excitations

This paper presents a comprehensive theoretical analysis of a concrete-filled steel tubular (CFST) arch bridge under tridirectional spatial seismic motions using the pseudo-excitation method. Formulations for modelling tridirectional spatial ground motions at varying site conditions are first derived. A site response analysis is presented for the tridirectional motions based on deterministic wave propagation theory, assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SV waves propagating into the multiple layered site with an assumed incident angle. Integration between the structural health monitoring (SHM) technique and the structural seismic analysis is proposed and conducted for the finite element (FE) model calibration of the CFST arch bridge through the model updating approach. Using the calibrated FE model, stochastic seismic analysis of the CFST arch bridge is conducted in a comprehensive and systematic way, by considering the dimensionality, incoherence effect, wave-path effect of ground motions, and local site effects with different and irregular site conditions. Critical conclusions are drawn and can be applied in the actual seismic design of the half-through CFST arch bridges under tridirectional multiple excitations.

Probabilistic tsunami hazard in the Mediterranean Sea

Estimating the occurrence probability of natural disasters is critical for setting construction standards and, more generally, prioritizing risk mitigation efforts. Tsunami hazard in the Mediterranean region has traditionally been estimated by considering so‐called “most credible” scenarios of tsunami impact for limited geographical regions, but little attention has been paid to the probability of any given scenario. We present here the first probabilistic estimate of earthquake‐generated tsunami hazard for the entire Mediterranean Sea. We estimate the annual probability of exceeding a given tsunami amplitude at any coastal location in the region by applying a Monte Carlo based technique. Earthquake activity rates are estimated from the observed seismicity, and tsunami impact is derived from deterministic tsunami wave propagation scenarios. The highest hazard is in the eastern Mediterranean owing to earthquakes along the Hellenic Arc, but most of the Mediterranean coastline is prone to tsunami impact. Our method allows us to identify the main sources of tsunami hazard at any given location and to investigate the potential for issuing timely tsunami warnings. We find that the probability of a tsunami wave exceeding 1 m somewhere in the Mediterranean in the next 30 years is close to 100%. This underlines the urgent need for a tsunami warning system in the region.

Modelling and simulation of spatially varying earthquake ground motions at sites with varying conditions

In a flat and uniform site, it is reasonable to assume that the spatially varying earthquake ground motions at various locations have the same power spectral density or response spectrum. If an engineering site with varying soil conditions at different structural supports is considered, this assumption is no longer valid because of different local site amplification effect. This paper presents an approximate method to model and simulate spatially varying ground motions on the surface of an uneven site with non-uniform conditions at different locations in two steps. In the first step, the base rock motions at different locations are assumed to have the same intensity, and are modelled by a filtered Tajimi–Kanai power spectral density function or other stochastic ground motion attenuation models. The base rock ground motion spatial variation is modelled by an empirical coherency loss function. The power spectral density functions of the surface motions on the site with multiple soil layers are derived based on the deterministic 1D wave propagation theory, neglecting the wave scattering on the uneven canyon surface, and assuming that the base rock motions consist of out-of-plane SH wave or in-plane combined P and SVwaves propagating into the site with an assumed incident angle. In the second step, a stochastic method to generate spatially varying time histories compatible with non-uniform spectral densities and a coherency loss function is developed to generate ground motion time histories on an uneven site. Two numerical examples are presented to demonstrate the proposed method. Each generated ground motion time history is compatible with the derived power spectral density at a particular point on the site or response spectrum corresponding to the respective site conditions, and any two of them are compatible with a model coherency loss function.

Modelling basin effects on earthquake ground motion in the Santiago de Chile basin by a spectral element code

SUMMARY Simulations of strong ground motion within the Santiago de Chile Metropolitan area were carried out by means of 3-D deterministic wave propagation tool based on the spectral element method. The simulated events take into account the pronounced interface between the low-velocity sedimentary basin and the bedrock as well as topography of the area. To verify our model we simulated a regional earthquake recorded by a dense network installed in the city of Santiago for recording aftershock activity after the 2010 February 27 Maule main shock. The results proof the alluvial basin amplification effects and show a strong dependence of spectral amplification in the basin on the local site conditions. Moreover, we studied the seismic response due to a hypothetical Mw= 6.0 event occurring along the active San Ramon Fault, which is crossing the eastern edge of the city. The scenario earthquakes exhibit that an unfavourable interaction between fault rupture, radiation mechanism and complex geological and topographic conditions in the near-field region may give rise to large values of peak ground velocity in the basin. Finally, 3-D numerical predictions of ground motion are compared with the one computed according to ground motion prediction equations selected among the next generation attenuation relationships, in terms of ground motion peak values and spectral acceleration. The comparison underlines that the 3-D scenario simulations predict a significantly higher level of ground motion in the Santiago basin, especially over deep alluvial deposits. Moreover, also the location of the rupture nucleation largely influences the observed shaking pattern.

CyberShake: A Physics-Based Seismic Hazard Model for Southern California

CyberShake, as part of the Southern California Earthquake Center’s (SCEC) Community Modeling Environment, is developing a methodology that explicitly incorporates deterministic source and wave propagation effects within seismic hazard calculations through the use of physics-based 3D ground motion simulations. To calculate a waveform-based seismic hazard estimate for a site of interest, we begin with Uniform California Earthquake Rupture Forecast, Version 2.0 (UCERF2.0) and identify all ruptures within 200 km of the site of interest. We convert the UCERF2.0 rupture definition into multiple rupture variations with differing hypocenter locations and slip distributions, resulting in about 415,000 rupture variations per site. Strain Green Tensors are calculated for the site of interest using the SCEC Community Velocity Model, Version 4 (CVM4), and then, using reciprocity, we calculate synthetic seismograms for each rupture variation. Peak intensity measures are then extracted from these synthetics and combined with the original rupture probabilities to produce probabilistic seismic hazard curves for the site. Being explicitly site-based, CyberShake directly samples the ground motion variability at that site over many earthquake cycles (i.e., rupture scenarios) and alleviates the need for the ergodic assumption that is implicitly included in traditional empirically based calculations. Thus far, we have simulated ruptures at over 200 sites in the Los Angeles region for ground shaking periods of 2 s and longer, providing the basis for the first generation CyberShake hazard maps. Our results indicate that the combination of rupture directivity and basin response effects can lead to an increase in the hazard level for some sites, relative to that given by a conventional Ground Motion Prediction Equation (GMPE). Additionally, and perhaps more importantly, we find that the physics-based hazard results are much more sensitive to the assumed magnitude-area relations and magnitude uncertainty estimates used in the definition of the ruptures than is found in the traditional GMPE approach. This reinforces the need for continued development of a better understanding of earthquake source characterization and the constitutive relations that govern the earthquake rupture process.

An approach to include stochastic rough surface scattering into deterministic ray-optical wave propagation modeling

A new method to include rough surface scattering into deterministic ray-optical wave propagation modeling is derived. It can be utilized in conjunction with the concept of ray launching. Similar to the Kirchoff formulations, the approach is based on a tangential plane approximation, i.e., it is applicable to surfaces with gentle undulations, whose horizontal dimensions are large compared to the incident wavelength. However, in contrast to the Kirchoff models, which are only valid for either slightly rough or very rough surfaces, the proposed scattering approach includes both the coherent and incoherent components at the same time. The purely deterministic ray-based modeling is expanded by a stochastic component, allowing, for the first time, to account for nondeterministic scattering in ray-optical wave propagation modeling.

Multipath Propagation of Radio Waves in 3-Dimensional Terrains

A 3-Dimensional (3D) deterministic wave propagation model is developed to study signal propagation in natural 3D terrains in the frequency range of VHF/UHF. The propagation model is based on the physical principles of Geometrical Optics (GO) and the Uniform Geometrical Theory of Diffraction (UTD). Significant ray-paths and their EM field properties at the observation point are computed efficiently from the physical theory. For the initial model, a simple 3D terrain consisting of a single mountain modelled by a dielectric circular cylinder with ground plane on both sides of the cylinder is considered. Currently, the UTD formulation for the 3D dielectric circular cylinder is not available. In this paper, the UTD formulation for the 3D dielectric circular cylinder is obtained from the direct generalisation of the UTD formulation for the 2D case.

Replication of apparent nonlinear seismic response with linear wave propagation models

It is necessary to understand ground-motion amplification by sediment, defined as the ratio of ground motions at sediment sites to those at rock sites, to predict seismic loadings for earthquake engineering. At sediment sites, observed weak-motion amplifications from magnitude 3 to 4 aftershocks of the 1994 Northridge earthquake were twice as large as magnitude 6.7 mainshock amplifications. Amplitude-dependent (nonlinear) amplification by sediment is one explanation. However, earthquake simulations with empirical impulse responses and elastic finite-difference calculations with weakly heterogeneous, random three-dimensional (3D) crustal velocity variations show that linear wave propagation can explain observed (apparently nonlinear) sediment responses. Random 3D velocity variations also reproduce the observed log-normal dispersion of peak ground motions. Deterministic wave propagation models are not adequate to quantify the scaling and dispersion of near-source ground motions.