A joint absorbing boundary for the multiple-relaxation-time lattice Boltzmann method in seismic acoustic wavefield modeling

Conventional seismic wave forward simulation generally uses mathematical means to solve the macroscopic wave equation,and then obtains the corresponding seismic wavefield.Usually,when the subsurface structure is finely constructed and the continuity of media is poor,this strategy is difficult to meet the requirements of accurate wavefield calculation.This paper uses the multiple-relaxation-time lattice Boltzmann method(MRT-LBM)to conduct the seismic acoustic wavefield simulation and verify its computational accuracy.To cope with the problem of severe reflections at the truncated boundaries,we analogize the viscous absorbing boundary and perfectly matched layer(PML)absorbing boundary based on the single-relaxation-time lattice Boltzmann(SRT-LB)equation to the MRT-LB equation,and further,propose a joint absorbing boundary through comparative analysis.We give the specific forms of the modified MRT-LB equation loaded with the joint absorbing boundary in the two-dimensional(2D)and three-dimensional(3D)cases,respectively.Then,we verify the effects of this absorbing boundary scheme on a 2D homogeneous model,2D modified British Petroleum(BP)gas-cloud model,and 3D homogeneous model,respectively.The results reveal that by comparing with the viscous absorbing boundary and PML absorbing boundary,the joint absorbing boundary has the best absorption performance,although it is a little bit complicated.Therefore,this joint absorbing boundary better solves the problem of truncated boundary reflections of MRT-LBM in simulating seismic acoustic wavefields,which is pivotal to its wide application in the field of exploration seismology.

A study of damping factors in perfectly matched layers for the numerical simulation of seismic waves

When simulating seismic wave propagation in free space, it is essential to introduce absorbing boundary conditions to eliminate reflections from artificially trtmcated boundaries. In this paper, a damping factor referred to as the Gaussian dmping factor is proposed. The Gaussian damping factor is based on the idea of perfectly matched layers （PMLs）. This work presents a detailed analysis of the theoretical foundations and advantages of the Gaussian damping factor. Additionally, numerical experiments for the simulation of seismic waves are presented based on two numerical models： a homogeneous model and a multi-layer model. The results show that the proposed factor works better. The Gaussian damping factor achieves a higher Signal-to-Noise Ratio （SNR） than previously used factors when using same number of PMLs, and requires less PMLs than other methods to achieve an identical SNR.

Digital earth, Virtual Reality and urban seismic disaster simulation

US Vice President Al Gore's vision of Digital Earth applies us with prospects for brand-new ways of solving problems the earth is facing such as seismic disaster. ms paper first briefly introduces the concept of Digital Earth. Then in the context of Digital Earth. the Origin, concept and application of Virtual Reality technology are reviewed. After that we present in detail our preliminary case study--CVR-USD (Computer Virtual Reality for Urban Seismic Disaster Simulation) System which aims to simulate and manage seismic disaster through integrating RS, GIS and VR technologies. For this system, we've built USD subsystem, developed SMVR software to implement CVR. and also developed a Spatial Dare Analysis Package to handle spatial data related to earthquake disaster.

A new integration scheme for application to seismic hybrid simulation

Hybrid simulation is a powerful test method for evaluating the seismic performance of structural systems. This method makes it feasible that only critical components of a structure be experimentally tested. This paper presents a newly proposed integration algorithm for seismic hybrid simulation which is aimed to extend its capabilities to a wide range of systems where existing methods encounter some limitations. In the proposed method, which is termed the variable time step （VTS） integration method, an implicit scheme is employed for hybrid simulation by eliminating the iterative phase on experimental element, the phase which is necessary in regular implicit applications. In order to study the effectiveness of the VTS method, a series of numerical investigations are conducted which show the successfulness of the VTS method in obtaining accurate, stable and converged responses. Then, in a comparative approach, the improved accuracy of the VTS method over commonly used integration methods is demonstrated. The stability of the VTS method is also studied and the results show that it provides conditional stability; however, its stability limit is well beyond the accuracy limit. The effect of time delay on the VTS method results is also investigated and it is shown that the VTS method is quite successful in handling this experimental error.

3D elastic wave equation forward modeling based on the precise integration method

The Finite Difference （FD） method is an important method for seismic numerical simulations. It helps us understand regular patterns in seismic wave propagation, analyze seismic attributes, and interpret seismic data. However, because of its discretization, the FD method is only stable under certain conditions. The Arbitrary Difference Precise Integration （ADPI） method is based on the FD method and adopts an integration scheme in the time domain and an arbitrary difference scheme in the space domain. Therefore, the ADPI method is a semi-analytical method. In this paper, we deduce the formula for the ADPI method based on the 3D elastic equation and improve its stability. In forward modeling cases, the ADPI method was implemented in 2D and 3D elastic wave equation forward modeling. Results show that the travel time of the reflected seismic wave is accurate. Compared with the acoustic wave field, the elastic wave field contains more wave types, including PS- and PP- reflected waves, transmitted waves, and diffracted waves, which is important to interpretation of seismic data. The method can be easily applied to elastic wave equation numerical simulations for eoloical models.

Simulation of multi-support depth-varying earthquake ground motions within heterogeneous onshore and offshore sites

This paper presents a novel approach to model and simulate the multi-support depth-varying seismic motions（MDSMs） within heterogeneous offshore and onshore sites.Based on 1 D wave propagation theory,the three-dimensional ground motion transfer functions on the surface or within an offshore or onshore site are derived by considering the effects of seawater and porous soils on the propagation of seismic P waves.Moreover,the depth-varying and spatial variation properties of seismic ground motions are considered in the ground motion simulation.Using the obtained transfer functions at any locations within a site,the offshore or onshore depth-varying seismic motions are stochastically simulated based on the spectral representation method（SRM）.The traditional approaches for simulating spatially varying ground motions are improved and extended to generate MDSMs within multiple offshore and onshore sites.The simulation results show that the PSD functions and coherency losses of the generated MDSMs are compatible with respective target values,which fully validates the effectiveness of the proposed simulation method.The synthesized MDSMs can provide strong support for the precise seismic response prediction and performance-based design of both offshore and onshore large-span engineering structures.

MathematicalsimulationofmoderateandstrongearthquakesequenceinZhujiangDeltaanditssurroundingareasinth

With the orthogonal design and the finite element methods, the outside stresses acting on the boundary and the inside tectonic stress field before the 1911 Honghai Bay earthquake are obtained. Under these stress fields, the dislocation patterns of the faults are consistent with the observed ones. Using the softening unstabilization model for elastoplastic media to simulate the process of the earthquake occurrence, 5 moderate and strong earthquakes in these areas in this century are simulated. The results show that the moderate or strong earthquake happened only at the sections of the faults whose fault safety degree is zero. According to the present distribution of the fault safety degree, the authors predict the seismic risk zones there.

Comparison between staggered grid finite difference method and stochastic method in simulating strong ground motions

Strong ground motion of an earthquake is simulated by using both staggered grid finite difference method (FDM) and stochastic method, respectively. The acceleration time histories obtained from the both ways and their response spectra are compared. The result demonstrates that the former is adequate to simulate the low-frequency seismic wave; the latter is adequate to simulate the high-frequency seismic wave. Moreover, the result obtained from FDM can better reflect basin effects.

The manufacture of a three-dimensional transducer used in laboratory

Since the development of ultrasonic pulse technique seismologists can study the seismic problems by simulation experiments in laboratries. In the 1950s Oliver (1954) conducted two-dimensional seismic model experimental study. Henceforth geophysical model experiments have been conducted widly all over the world. In 1958 Zhao et al. of Peking University built the apparatures for seismic model experiments and did various model experiments (Zhao, 1986). In the 1960s, Birch (1960) measured the velocity of seismic waves in rocks under high pressure and first used the ultrasonic technique in the measurement of physical properties of rocks under high pressure. Since the end of the 1960s people paid attention to wave velocity anomaly as a seismic precursor, and simulation experiments of wave velocity anomoly have been developed (Nur, 1969; Liu and Lai, 1986; Liu, 1989). In the 1980s the developments of three-dimensional AE loation technique provided the conditions for study of seismic source mechanism in the laboratory (Kusunose, et al., 1981 ). All the experimental studies mentioned above used one-dimensional transducers. But the experiments require three-dimensional transducers with high precision to get accurate experimental data. We have manufactured three-dimensional transducers used in the laboratory,and they are able to stand high temperature and high pressure. By using the three-dimensional transducer in the laboratory the shape and the arrival times of longitudinal wave (P) and transverse wave in two polarization directions (S1, S2) can be measured simulataneously. Therefore, in the measurement of parameters of physical properties, the velocities, attenuation properties and frequency spectra of longitudinal wave (P) and transverse waves (S1, S2) can be measured with the same sample in the same experiemnt. Thus the problem caused by the difference in conditions of two experiments can be avoided. These trnasducers can also be used in model experiments and acoustic-wave position location, and under high temperature and high pressure conditions.

Simulation and characteristics analysis of a wavefield in a thermoelastic medium adopting the rotated staggered-grid pseudospectral method and L-S theory

The simulation of wave propagation in high-temperature media requires thermoelastic theory.In this paper,we apply the rotated-staggered-grid pseudo-spectral method(RSG-PSM)to solving thermoelastic governing equations based on L-S theory.A time splitting method is used to solve the stiffness problem of the equations,and we introduce the rotated staggered pseudo-spectral operator and centered pseudo-spectral operator to compute the first-order spatial derivatives and second-order spatial derivatives,respectively.In the case of the heterogeneous-medium model,the Crank-Nicolson explicit method is used instead of the pseudo-spectral method to compute the wavefield.The properties and propagation of the thermal coupled wavefield are discussed,and we compare the simulation results obtained using the pseudo-spectral method,staggered-grid pseudo-spectral method,and RSG-PSM.In the case of an isotropic homogeneous medium,we obtain stable and highly accurate results using the time splitting method combined with the RSG-PSM.However,the algorithm cannot be applied with a large time step when the thermal conductivity changes dramatically,and the algorithm is unstable when the reference temperature has a gradient distribution.The optimal combined application of the mesh generation mode and numerical algorithm is explored,laying a foundation for the extension of these methods to thermoporoelasticity,thermoviscoelasticity,and anisotropy.