Simulation Of Seismic Waves Research Articles

Modeling of 3D Basin Structures for Seismic Wave Simulations Based on Available Information on the Target Area: Case Study of the Osaka Basin, Japan

Practical procedures for modeling basin structure are proposed. One is to construct a smooth 3D basin structure model under and around the target site for low-frequency strong motion simulation. The other is to make a 1D velocity structure model just under the target site for high frequencies. These procedures were applied to the Osaka basin, Japan, in which numerous exploration studies were conducted before and after the 1995 Hyogoken-Nanbu (Kobe) Earthquake. The published results of those explorations in addition to those from our several investigations were compiled to construct the model. A two-dimensional third-order B-spline function was used to establish a smooth structure model from available depth data. Microtremor array observations were used to model the velocities and densities of the sedimentary layer structures. A four-layer model well explains the dispersion characteristics of Rayleigh waves that make up the microtremors. By adding a detailed shallow velocity structure to the top of the deeper four-layer model, adequate site responses for a wide frequency range of ground motions can be obtained. This proposed procedure can be used to determine the basement geometry of other sedimentary basins.

A 3D discrete numerical elastic lattice method for seismic wave propagation in heterogeneous media with topography

A three‐dimensional elastic lattice method for the simulation of seismic waves is presented. The model consists of particles arranged on a cubic lattice which interact through a central force term and a bond‐bending force. Particle disturbances are followed through space by numerically solving their equations of motion. A vacuum free‐surface boundary condition is implicit in the method. We demonstrate that a numerical implementation of the method is capable of modelling seismic wave propagation with complex topography. This is achieved by comparing the scheme against a finite‐difference solution to the elastodynamic wave equation. The results indicate that the scheme offers an alternative 3D method for modelling wave propagation in the presence of strong topography and subsurface heterogeneity. We apply the method to seismic wave propagation on Mount Etna to illustrate its applicability in modelling a physical system.

Seismic wave simulation in the presence of real volcano topography

We use a finite-difference method on a 3-D staggered grid to simulate seismic wave propagation in the presence of strong topographic variations. An application to Merapi volcano, Indonesia, is presented. In order to focus on the effect of topography on the seismic wave field, calculations are performed for a rather simple model with an isotropic point source and a homogeneous subsurface medium. Despite this simplicity of the model a complex wave field evolves. Results of the computation are shown in synthetic seismograms, snapshots of the wave field and in a particle motion analysis. Waves reflected and converted at the free surface can be identified. The first P-wave arrivals show linear polarization whereas at later times the wave field is a superposition of shear and Rayleigh waves resulting in a more complicated particle motion pattern. The effect of volcano topography on seismic waves can be clearly demonstrated. We confirm that the finite-difference method we use is apt for numerical modeling in volcano seismology.

Staggered Grid Real Value FFT Differentiation Operator and its Application for Wave Propagation Simulation in Heterogeneous Medium

AbstractIn the present analysis, a new differentiation operator, namely “staggered grid real value FFT differentiation operator” is introduced. It is one third faster on average than the traditional differentiation method by using the complex FFT differentiation. Furthermore, the new method has higher accuracy and higher stability than the traditional grid real value FFT method. The accuracy of staggered grid real value FFT differentiation operator is confirmed by comparing with the analytic Cagniard‐De Hoop method for wave simulations in the infinite half space. The results in the present analysis show that the staggered grid real value FFT differentiation operator for the pseudospectral method is effective for seismic wave simulation in the heterogeneous medium.

3-D finite-difference simulation of seismic fault zone waves—Application to the fault zone structure of the Mozumi-Sukenobu fault, central Japan—

Fault zone waves have the potential to be a powerful tool to reveal the fine structure of a fault zone down to the seismogenic depth. Seismic fault zone waves include head waves, trapped waves and direct body waves propagating in the fault zone. 3-D numerical simulation is necessary to interpret the waveforms in the presence of low-velocity zones with relatively complex fault structure. We computed finite difference (FD) synthetic seismograms to fit the seismograms of explosions, which contain frequencies up to 25 Hz, recorded by a linear seismometer array across the Mozumi-Sukenobu fault, central Japan. We find fault zone head waves, direct P waves propagating within the low-velocity zone and wave trains following the direct P waves associated with the fault for both observed and synthetic waveforms. Thus, modelling of fault zone waves is expected to determine details of complex fault zone structure.

Earthquakes and Eruptions: Temporal and Spatial Display of Earthquake Hypocenters, Seismic‐wave Paths, and Volcanic Eruptions

Alan Jones and the Smithsonian Institution have come up with another educational software product that many of us have thought of but never had the time or skills to develop. Jones wrote the original programs, and the Smithsonian Institution put together a user‐friendly interface and an updating mechanism. The result is a CD‐ROM‐based product that shows all the earthquakes and volcanic eruptions on Earth since 1960, plus a seismic wave simulation program and a small photo gallery

Differentiation operation in the wave equation for the pseudospectral method with a staggered mesh

In the present analysis we introduced a calculation strategy of the staggered grid differentiation by using the real value FFT and real inverted FFT for the pseudospectral method and applied the technique to seismic wave simulation. The calculation method introduced here is one third faster on average than the traditional differentiation method by using the complex FFT. The introduced differentiation strategy is very efficient in economy. For example we apply the staggered grid differentiation by real valued FFT to the simulation of seismic wave propagation in inhomogeneous medium. The results show the validity of the present method.

Energy balance and fundamental relations in dynamic anisotropic poro-viscoelasticity

An energy balance equation and fundamental relations are obtained for wave motion in anisotropic poro‐viscoelastic media. The balance of energy identifies the strain and kinetic energy densities, and the dissipated energy densities due to viscoelastic and viscodynamic effects. The relations allow the calculation of these energies in terms of the Umov‐Poynting vector and kinematic variables. The energy balance is obtained for time‐harmonic fields, while the following relations are valid for inhomogeneous body waves. (i) The magnitude of the phase velocity is equal to the projection of the energy velocity vector onto the propagation direction. (ii) The time‐average of the dissipated energy density is obtained from the projection of the average power‐flow vector onto the attenuation direction. (iii) The time‐average energy density (kinetic plus strain) is obtained from the projection of the average power‐flow vector onto the propagation direction. (iv) The strain energy equals the kinetic energy when the medium is lossless. These relations are shown to be valid for anisotropic poro‐viscoelasticity at all frequency ranges. An example of ultrasonic wave propagation in an orthorhombic medium (human femoral bone saturated with water) illustrates the theory. Measurable quantities, like the attenuation factor and the energy velocity, can easily be interpreted in terms of microstructural properties such as tortuosity and permeability.

Staggered‐Grid High‐Order Differencemethod for the First‐Order Elastic Wave Equations

AbstractAll numerical methods of seismic wave simulation have the aim to improve their computational accuracy and efficiency. Through converting the odd high‐order temporal derivatives of velocity(or stress) to spatial derivatives of stress(or velocity), we use the high‐order difference method which has any order of the temporal and spatial difference accuracy and the staggered‐grid technique in calculations of the first‐order elastic wave equations expressed with velocity and stress. The snapshots and the simulated results of a realistic model show that this method is more accurate and less dispersive than conventional FD methods. Mean‐while bigger spatial grids and temporal steps can be used to raise computational efficiency.

Composite absorbing boundaries for the numerical simulation of seismic waves

AbstractComposite absorbing boundary methods are developed for the numerical simulation of seismic waves. These methods combine low-angle absorbing boundary conditions, based on the characteristic analysis of one-dimensional wave equations, with either of two novel wave field modification approaches, namely the anisotropic filters and the one-way sponge filters. The anisotropic filter method adjusts the propagation direction of the waves, so that they reach the boundary at normal angles. The one-way sponge filter method endows the transition zone with a dissipation mechanism that selectively damps the incoming waves. These methods absorb not only the body waves but also the surface waves. A narrow transition zone adjacent to a computational boundary is introduced whose width is smaller than in the sponge filter approach. Numerical examples illustrate the effectiveness of these methods in absorbing the artificial reflections.

A three-dimensional simulation of seismic waves in the Santa Clara Valley, California, from a Loma Prieta aftershock

Abstract The finite-difference method is used to propagate elastic waves through a 3-D model of the Santa Clara Valley, an alluvium-filled basin that underlies the city of San Jose, California. The model was based on depth to bedrock information from water wells in the area. The simulation corresponded to a region 30 (east-west) by 22 (north-south) by 6 (depth) km and contained about 4 million grid points. Synthetic seismograms from the simulation are accurate at frequencies up to 1 Hz. Motions from a magnitude 4.4 aftershock of the Loma Prieta earthquake were modeled. Snapshots of ground motion and synthetic seismograms from the simulation are presented. The simulation illustrates S -to-surface-wave conversion at the edges of the basin and the large amplitude and long duration of ground motion in the basin compared to the surrounding rock. Love waves produced at the edge of the basin are the largest arrivals in the transverse synthetics. Because of the slow group velocity of the Love waves, sites near the center of the basin have longer durations of significant motions than basin sites near the valley edges. Sites near the center of the basin also show larger peak amplitudes on the transverse component. Array analysis of the synthetic seismograms indicates that Love waves tend to propagate parallel to the eastern and western edges of the valley. Rayleigh waves are produced along the southern margin of the basin from incident S waves. Large radial motions occur where a Rayleigh wave impinges on the northeast margin of the valley. Some Rayleigh waves travel westward across the basin, after being scattered from the eastern edge of the valley. Synthetic seismograms from the simulation have similar peak amplitudes as seismograms recorded by the Sunnyvale dense array for this aftershock, although the duration of the tranverse component is not matched by the synthetic seismogram, using this basin model. The simulation indicates that the Love waves observed on the actual seismograms were produced by conversion of incident S waves at the southern margin of the Santa Clara Valley. 2-D simulations show how the S -to-Love-wave conversion is affected by the angle of incidence of the S wave and the sharpness of the velocity transition between the alluvium and bedrock. As more accurate basin models are developed, 3-D simulations should become valuable for predicting ground motions in sedimentary basins for future large earthquakes.