Numerical simulation of seismic wave propagation in complex media by convolu-tional differentiator

We apply the forward modeling algorithm constituted by the convolutional Forsyte polynomial differentiator pro-posed by former worker to seismic wave simulation of complex heterogeneous media and compare the efficiency and accuracy between this method and other seismic simulation methods such as finite difference and pseudospec-tral method. Numerical experiments demonstrate that the algorithm constituted by convolutional Forsyte polyno-mial differentiator has high efficiency and accuracy and needs less computational resources, so it is a numerical modeling method with much potential.

Mesh Size Effect in Numerical Simulation of Blast Wave Propagation and Interaction with Structures

Numerical method is popular in analysing the blast wave propagation and interaction with structures.However,because of the extremely short duration of blast wave and energy trans-mission between different grids,the numerical results are sensitive to the finite element mesh size.Previous numerical simulations show that a mesh size acceptable to one blast scenario might not be proper for another case,even though the difference between the two scenarios is very small,indicating a simple numerical mesh size convergence test might not be enough to guarantee accu-rate numerical results.Therefore,both coarse mesh and fine mesh were used in different blast scenarios to investigate the mesh size effect on numerical results of blast wave propagation and interaction with structures.Based on the numerical results and their comparison with field test re-sults and the design charts in TM5-1300,a numerical modification method was proposed to correct the influence of the mesh size on the simulated results.It can be easily used to improve the accu-racy of the numerical results of blast wave propagation and blast loads on structures.

Propagation simulation and attenuation law analysis of seismic wave in elastoplastic tunnel rock medium

The energy caused by the dynamic impact in mining engineering forth release and spread by the way of seismic waves, monitoring is an effective way for forecasting mine dynamical disasters, such as rockburst and coal and gas outburst. Three-dimensional dynamic model was built to simulate the propagating progress of seismic waves in the elastoplastic tunnel rock and analyzed the propagating law of perturbation acceleration around tunnel, based on the finite element dynamic analysis software ANSYS/L S-DYNA. The simulation results indicate that： （1） The propagation attenuation of seismic wave is a negative index relationship; （2） The acceleration amplitude of seismic wave decays rapidly in near-field and decays slowly in far-field; （3） When the perturbation is generated in the dead ahead of tunnel, the acceleration of seismic wave become smaller and smaller away from the roadway-rib;（4） The elastic and plastic stress state of tunnel rock is also an important factor for propagation process of wave, the energy of seismic wave is mainly consumed for geometric spreading and plastic deformation in propagation in the elastoplastic medium model.

Finite element equations and numerical simulation of elastic wave propagation in two-phase anisotropic media

Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotropic media are derived in this paper.Numerical solution of finite element equations is given.Finally,Properties of elastic wave propagation are observed and analyzed through FEM modeling.

Effect of Blasting Stress Wave on Dynamic Crack Propagation

Stress waves affect the stress field at the crack tip and dominate the dynamic crack propagation.Therefore,evaluating the influence of blasting stress waves on the crack propagation behavior and the mechanical characteristics of crack propagation is of great significance for engineering blasting.In this study,ANSYS/LS-DYNA was used for blasting numerical simulation,in which the propagation characteristics of blasting stress waves and stress field distribution at the crack tip were closely observed.Moreover,ABAQUS was applied for simulating the crack propagation path and calculating dynamic stress intensity factors(DSIFs).The universal function was calculated by the fractalmethod.The results show that:the compressive wave causes the crack to close and the reflected tensile wave drives the crack to initiate and propagate,and failure mode is mainly tensile failure.The crack propagation velocity varies with time,which increases at first and then decreases,and the crack arrest occurs due to the attenuation of stress waves and dissipation of the blasting energy.In addition,crack arrest toughness is smaller than the crack initiation toughness,applied pressure waveforms(such as the peak pressure,duration,waveforms,wavelengths and loading rates)have a great influence on DSIFs.It is conducive to our deep understanding or the study of blasting stress waves dominated fracture,suggesting a broad reference for the further development of rock blasting in engineering practice.

Numerical Simulation of Bubble Plumes and an Analysis of Their Seismic Attributes

To study the bubble plume's seismic response characteristics,the model of a plume water body has been built in this article using the bubble-contained medium acoustic velocity model and the stochastic medium theory based on an analysis of both the acoustic characteristics of a bubble-contained water body and the actual features of a plume.The finite difference method is used for forward modelling,and the single-shot seismic record exhibits the characteristics of a scattered wave field generated by a plume.A meaningful conclusion is obtained by extracting seismic attributes from the pre-stack shot gather record of a plume.The values of the amplitude-related seismic attributes increase greatly as the bubble content goes up,and changes in bubble radius will not cause seismic attributes to change,which is primarily observed because the bubble content has a strong impact on the plume's acoustic velocity,while the bubble radius has a weak impact on the acoustic velocity.The above conclusion provides a theoretical reference for identifying hydrate plumes using seismic methods and contributes to further study on hydrate decomposition and migration,as well as on distribution of the methane bubble in seawater.

A Comparative Study of Numerical Models for Wave Propagation and Setup on Steep Coral Reefs

Complex factors including steep slopes, intense wave breaking, large bottom friction and remarkable wave setup should be considered while studying wave propagation over coral reefs, and how to simulate wave propagation and setup on coral reefs efficiently has become a primary focus. Several wave models can be used on coral reefs as have been published, but further testing and comparison of the reliability and applicability of these models are needed. A comparative study of four numerical wave models (i.e., FUNWAVE-TVD, Coulwave, NHWAVE and ZZL18) is carried out in this paper. These models’ governing equations and numerical methods are compared and analyzed firstly to obtain their differences and connections;then the simulation effects of the four wave models are tested in four representative laboratory experiments. The results show that all four models can reasonably predict the spectrum transformation. Coulwave, NHWAVE and ZZL18 can predict the wave height variation more accurately;Coulwave and FUNWAVE-TVD tend to underestimate wave setup on the reef top induced by spilling breaker, while NHWAVE and ZZL18 can predict wave setup relatively accurately for all types of breakers;NHWAVE and ZZL18 can predict wave reflection by steep reef slope more accurately. This study can provide evidence for choosing suitable models for practical engineering or establishing new models.

Basin Structure and Numerical Simulation for the Mechanisms of Seismic Disasters

In the present study seismic wave propagation in heterogeneous media is numerically simulated by using the pseudospectral method with the staggered grid RFFT differentiation in order to clarify the cause for the complicated distribution characteristics of strong ground motion in regions with basin structure. The results show that the maximum amplitudes of simulated ground acceleration waveforms are closely related to the basin structure. Interference of seismic waves in the basin strongly affects the distribution of maximum seismic waveforms, which may result in peak disasters during earthquakes. Peak disasters might be away from basin boundaries or earthquake faults. Seismic energy transmitted into the basin from the bedrock can hardly penetrate the bottom of the basin and then travel back into the bedrock region. The seismic energy is absorbed by basin media, and transferred into the kinematical energy of seismic waves with great amplitude in the basin. Seismic waves between basins may result in serious damage to buildings over the basin. This is significant for aseismatic research. Geological surveys in and around urban areas would benefit aseismatic research and mitigation of seismic disasters of a city. Such geological surveys should involve seismic velocity structure in the media above the bedrock besides such subjects as active faults and geological structure.

Parallel Simulation of 3D Wave Propagation by Domain Decomposition

In order to perform large scale numerical simulation of wave propagation in 3D heterogeneous multiscale viscoelastic media, Finite Difference technique and its parallel implementation based on domain decomposition is used. A couple of typical statements of borehole geophysics are dealt with—sonic log and cross well measurements. Both of them are essentially multiscales, which claims to take into account heterogeneities of very different sizes in order to provide reliable results of simulations. Locally refined spatial grids help us to avoid the use of redundantly tiny grid cells in a target area, but cause some troubles with uniform load of Processor Units involved in computations. We present results of scalability tests together with results of numerical simulations for both statements performed for some realistic models.

Spatial-temporal characterization of the San Andreas Fault by fault-zone trapped waves at seismic experiment site,Parkfield,California

In this article,we review our previous research for spatial and temporal characterizations of the San Andreas Fault(SAF)at Parkfield,using the fault-zone trapped wave(FZTW)since the middle 1980s.Parkfield,California has been taken as a scientific seismic experimental site in the USA since the 1970s,and the SAF is the target fault to investigate earthquake physics and forecasting.More than ten types of field experiments(including seismic,geophysical,geochemical,geodetic and so on)have been carried out at this experimental site since then.In the fall of 2003,a pair of scientific wells were drilled at the San Andreas Fault Observatory at Depth(SAFOD)site;the main-hole(MH)passed a~200-m-wide low-velocity zone(LVZ)with highly fractured rocks of the SAF at a depth of~3.2 km below the wellhead on the ground level(Hickman et al.,2005;Zoback,2007;Lockner et al.,2011).Borehole seismographs were installed in the SAFOD MH in 2004,which were located within the LVZ of the fault at~3-km depth to probe the internal structure and physical properties of the SAF.On September 282004,a M6 earthquake occurred~15 km southeast of the town of Parkfield.The data recorded in the field experiments before and after the 2004 M6 earthquake provided a unique opportunity to monitor the co-mainshock damage and post-seismic heal of the SAF associated with this strong earthquake.This retrospective review of the results from a sequence of our previous experiments at the Parkfield SAF,California,will be valuable for other researchers who are carrying out seismic experiments at the active faults to develop the community seismic wave velocity models,the fault models and the earthquake forecasting models in global seismogenic regions.

Study on Physical Models of In-Seam Seismic Wave

The propagation laws of in-seam seismic wave in coal seam in differeut situations are studied by means of in-seam seismic simulatiou tests. Some valuable conclusions are obtained, which are signiricant in guiding in-seam seismic prospecting in the future.

A mathematical model of calculating local tsunami wave source constraints and propagation

This paper presents a local tsunami simulation, including the initial displacement field model of tsunami source and tsunami wave propagation model. We deduced the tsunami wave equation; applied the matching of interior and exterior solutions method and water mass method to determine the initial displacement field in different bottom topography. Tsunami wave propagation model was based on the Boussinesq equation. Difference format was based on the ADI method which discretized in alternating direction in the form of implicit scheme. The open boundary of ADI had been revised considering the influence of wave propagation in the equation of motion. The local tsunami mathematical model was used in the simulation of 2011 Japan tsunami, and the results and the observation data match well.

The Application of a Numerical Model to Coastal Surface Water Waves

Based on the Navier-Stokes Equations (NSE), numerical simulation with fine grids is conducted to simulate the coastal surface wave changes, including wave generation, propagation, transformation and interactions between waves and structures. This numerical model has been tested for the generation of the desired incident waves, including both regular and random waves. Some numerical results of this model are compared with available experimental data. In order to apply this model to actual cases, boundary conditions are considered in detail for different shoreline types (beach or breakwater, slope or vertical wall, etc. ). Finally, the utility of the model to a real coastal area is shown by applying it to a fishing port located in Shidao, Rongcheng, Shandong Province, P.R. China.

Study on the Propagation Law of Shock Wave Pressure in Tunnels with Different Materials

The propagation of shock wave pressure in the tunnel is greatly affected by the tunnel structure,shape,material and other factors,and there are great differences in the propagation law of shock wave pressure in different kinds of tunnels.In order to study the propagation law of shock wave pressure in tunnels with different materials,taking the long straight tunnel with the square section as an example,the AUTODYN software is used to simulate the explosion of TNT in the concrete,steel and granite tunnel,and study on the variation law of shock wave pressure in tunnels with different materials.By using dimensional analysis and combined with the results of numerical simulation,a mathematical model of the propagation law of shock wave pressure in the tunnel is established,and the effectiveness of the mathematical model is verified by making the explosion test of the warhead in the reinforce concrete tunnel.The results show that the same mass of TNT explodes in the tunnel with different materials,and the shock wave overpressure peak at the same measuring point is approximate in the near field.However,there is a significant difference in the middle-far fields from the explosion center,the shock wave overpressure peak in the steel tunnel is 20.76%and 34.82%higher than that of the concrete and the granite tunnel respectively,and the shock wave overpressure peak in the concrete tunnel is 24.91%higher than that in the granite tunnel.Through the experimental verification,getting the result that the maximum relative deviation between the measured value and the calculated value of the shock wave overpressure peak is 11.85%.Therefore,it is proved that the mathematical model can be used to predict the shock wave overpressure peak in the tunnel with different materials,and it can provide some reference for the power evaluation of warhead explosion in the tunnel.

Numerical simulation scattered imaging in deep mines

Conventional seismic exploration,mostly based on reflection theory,hardly has accurate imaging results for disaster geologic bodies which have small scale,steep dip,or complex structure.In this paper,we design two typical geologic models for analyzing the characteristics of scattered waves in mines for forward modeling by finite difference and apply the equivalent offset migration（EOM）and EOM-based interference stack migration methods to mine prospecting.We focus on the analysis of scatted imaging’s technological superiority to reflection imaging.Research shows：1）scattered imaging can improve fold and make the best of weak scattered information,so it shows better results than post-stack migration imaging and 2）it can utilize the diffraction stack migration method-based ray path theory for mine seismic advanced prediction,so it provides an new efficient imaging method for improving resolution of mine seismic exploration.

Comparative analysis of the characteristics of global seismic wave propagation excited by the M_w 9.0 Tohoku earthquake using numerical simulation

Giant earthquakes generate rich signals that can be used to explore the characteristics of the hierarchical structure of the Earth’s interior associated with the eigenfrequencies of the Earth.We employ the spectral element method,incorporated with large-scale parallel computing technology,to investigate the characteristics of global seismic wave propagation excited by the2011 Mw9.0 Tohoku earthquake.The transversely isotropic PREM model is employed as a prototype of our numerical global Earth model.Topographic data and the effect of the oceans are taken into consideration.Wave propagation processes are simulated by solving three-dimensional elastic wave governing equations with the seismic moment tensor obtained from the Global Centroid Moment Tensor Catalog.Three-dimensional visualization of our computing results displays the nature of the global seismic wave propagation.Comparative analysis of our calculations with observations obtained from the Incorporated Research Institutions for Seismology demonstrates the reliability and feasibility of our numerical results.We compare synthetic seismograms with incorporated and unincorporated ocean models.First results show that the oceans have obvious effects on the characteristics of seismic wave propagation.The peak displacement and peak velocity of P waves become relatively small under the effect of the ocean.However,the effect of the ocean on S-waves is complex.The displacement and velocity of S waves decrease rapidly over time using an unincorporated ocean model.Therefore,the effects of the ocean should be incorporated when undertaking quantitative earthquake hazard assessments on coastal areas.In addition,we undertake comparative analysis on the characteristics of the Earth’s oscillation excited by the 2004 Sumatra-Andaman,2008 Wenchuan,and 2011Tohoku earthquakes that incorporate the effect of the Earth’s gravitational potential.A comparison of the amplitude spectra of the numerical records indicates that energy released by the three big earthquakes is different.Our comparative analysis realizes that the computing results can accurately reproduce some eigenfrequencies of the Earth,such as toroidal modes 0T2 to 0T13and spheroidal modes 0S7 to 0S31.These results demonstrate that numerical simulations can be successfully used to investigate the Earth’s oscillations.We propose that numerical simulations can be used as one of the major tools to further reveal how the Earth’s lateral heterogeneities affect the Earth’s oscillations.

SIMULATION OF BOUNDARY LAYER EFFECTS ON A HEAVY RAINFALL EVENT CAUSED BY A MESOSCALE CONVECTIVE SYSTEM OVER THE YELLOW RIVER MIDSTREAM AREA

A heavy rainfall event caused by a mesoscale convective system(MCS),which occurred over the Yellow River midstream area during 7-9 July 2016,was analyzed using observational,high-resolution satellite,NCEP/NCAR reanalysis,and numerical simulation data.This heavy rainfall event was caused by one mesoscale convective complex(MCC)and five MCSs successively.The MCC rainstorm occurred when southwesterly winds strengthened into a jet.The MCS rainstorms occurred when low-level wind fields weakened,but their easterly components in the lower and boundary layers increased continuously.Numerical analysis revealed that there were obvious differences between the MCC and MCS rainstorms,including their three-dimensional airflow structure,disturbances in wind fields and vapor distributions,and characteristics of energy conversion and propagation.Formation of the MCC was related to southerly conveyed water vapor and energy to the north,with obvious water vapor exchange between the free atmosphere and the boundary layer.Continuous regeneration and development of the MCSs mainly relied on maintenance of an upward extension of a positive water vapor disturbance.The MCC rainstorm was triggered by large range of convergent ascending motion caused by a southerly jet,and easterly disturbance within the boundary layer.While a southerly fluctuation and easterly disturbance in the boundary layer were important triggers of the MCS rainstorms.Maintenance and development of the MCC and MCSs were linked to secondary circulation,resulting from convergence of Ekman non-equilibrium flow in the boundary layer.Both intensity and motion of the convergence centers in MCC and MCS cases were different.Clearly,sub-synoptic scale systems in the middle troposphere played a leading role in determining precipitation distribution during this event.Although mesoscale systems triggered by the sub-synoptic scale system induced the heavy rainfall,small-scale disturbances within the boundary layer determined its intensity and location.

The Response of a Shear Beam as 1D Medium to Seismic Excitations Dependent on the Boundary Conditions

We study response of a shear beam to seismic excitations at its base. The research is conducted using computer simulation of the wave propagation on a numerical model. The wave equation is solved using the method of finite differences （FD） where the spatial and temporal derivatives are approximated with FD. We used formulation of the wave equation via the particle velocities, strains, mid stresses. Integrating particle velocities in time, we obtained displacements at spatial points. The main goal in this research is to study phenomena occurring due to three different types of boundary conditions, Dirichlet, Neumann, and moving boundary when simple half-sine pulse propagates through 1D medium modeled as a shear beam.

Numerical simulation of nonlinear propagation of sound waves in a finite horn

Nonlinear acoustic propagation generated by a piston in a finite horn is numerically studied. A quasi-one-dimensional nonlinear model with varying cross-section uses high-order low-dispersion numerical schemes to solve the governing equation. Because of the nonlinear wave distortion and reflected sound waves at the mouth, broadband time-domain impedance boundary conditions are employed. The impedance approximation can be optimized to identify the complex-conjugate pole-residue pairs of the impedance functions, which can be calculated by fast and efficient recursive convolution. The numerical results agree very well with experi- mental data in the situations of weak nonlinear wave propagation in an exponential horn, it is shown that the model can describe the broadband characteristics caused by nonlinear distortion. Moreover, finite-amplitude acoustic propagation in types of horns is simulated, including hyperbolic, conical, exponential and sinusoidal horns. It is found that sound pressure levels at the horn mouth are strongly affected by the horn profiles, the driving velocity and frequency of the piston. The paper also discusses the influence of the horn geometry on nonlinear waveform distortion.