Application of Gaussian Beam Summation Migration in Reflected In-seam Wave Imaging

The geological conditions for coal mining in China are complex,with various structural issues such as faults and collapsed columns seriously compromising the safety of coal mine production.In-seam wave exploration is an effective technique for acquiring detailed information on geological structures in coal seam working faces.However,the existing reflected in-seam wave imaging technique can no longer meet the exploration precision requirements,making it imperative to develop a new reflected in-seam wave imaging technique.This study applies the Gaussian beam summation(GBS)migration method to imaging coal seams'reflected in-seam wave data.Firstly,with regard to the characteristics of the reflected in-seam wave data,methods such as wavefield removal and enveloped superposition are employed for the corresponding wavefield separation,wave train compression and other processing of reflected in-seam waves.Thereafter,imaging is performed using the GBS migration technique.The feasibility and effectiveness of the proposed method for reflected in-seam wave imaging are validated by conducting GBS migration tests on 3D coal-seam fault models with different dip angles and throws.By applying the method to reflected in-seam wave data for an actual coal seam working face,accurate imaging of a fault structure is obtained,thereby validating its practicality.

Wave Reflection by Rectangular Breakwaters for Coastal Protection

In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.

A Three-Point Method for Separating Incident and Reflected Waves over A Sloping Bed

This study presents a three-point method for separating incident and reflected waves to explain normally incident waves' propagating over a sloping bed. linear wave shoaling is used to determine changes in wave amplitude and phase in response to variations of bathymetry. The wave reflection coefficient and incident amplitude are estimated from wave heights measured at three fixed wave gauges with unequal spacing. Sensitivity analysis demonstrates that the proposed method can predict the reflection and amplitude of waves over a sloping bed more accurately than the two-point method.

Experimental investigating on the reflected waves from the caisson-type vertical porous seawalls

The hydrodynamic efficiencies of caisson-type vertical porous seawalls used for protecting coastal areas were calculated in this study. Physical models were developed to compare the wave reflection from vertical plane, semi-porous, and porous seawalls caused by both regular and random waves. Tests were carried out for a wide range of wave heights, wave periods, and different water depths (d=0.165, 0.270 and 0.375 m). The performance regarding the reflected waves from porous and semi-porous seawalls showed improvement when compared with those from the plane seawall. The reflection coefficients of the porous and semi-porous seawalls were calculated as 0.6 and 0.75, respectively, while the coefficient for the fully reflecting plane vertical wall was significantly higher (0.9). It was also observed that the reflection coefficient decreases with increase in wave steepness and relative water depth. In addition, the reduction in the reflection coefficient of porous and semi-porous seawalls, as compared to that of a plane seawall, was observed for both regular and random waves. New equations were also proposed to calculate the reflection coefficient of different types of seawalls with the aid of laboratory experiments. By verifying the developed equations using some other experimental data, it was validated that the equations could be used for practical situations. The results of the present study can be applied to optimize the design of vertical seawalls and for coastal protecting schemes.

Estimating Directional Distribution for Co-Existent Field of Incident and Reflected Waves

In the nearshore, the wave field contains reflected and incident waves in which there is correlation between their phases due to the effect of reflection by some obstacles. Based on the extended eigenvector method (EEV) derived by Guan et al., a modified method (MEEV) is proposed as a general and practical approach to estimating directional spectra for the co-existent field of incident and reflected waves and a formula is given for direct calculation of the reflection coefficient. The results of numerical simulations show that MEEV is superior to EEV in resolution power, and the computed reflection coefficient agrees well with the real value within a certain range of incident angle.

Numerical Simulated Study on the Separation of Oblique Incident and Reflected Waves

The Goda's method of separating the frequency spectrum of the unidirectional incident and reflected waves is improved. The proposed method can be applied to the separation of oblique incident and reflected waves and the two wave gauges can be arranged in an arbitrary angle in front of a structure. When the projected distance of the two probes on the incident wave direction is the multiple ofthe half length of the incident waves, the singular problem will emerge by using the method. It is advised that when the projected distance of the two measured points on the incident wave direction is 0.05～0.45 times the wave length of peak frequency wave, good results can be obtained. The simulated resultant waves are separated by the method of numerical simulation and the separated wave spectra are basically corresponding to the target spectra input. The wave trains calculated by the separated incident and reflected wave frequency spectrum are approximated to the input wave trains and the reflected coefficient can be derived correctly. Therefore, the method proposed in this paper is reliable.

Anomalous behaviours of terahertz reflected waves transmitted from GaAs induced by optical pumping

Femtosecond pump-terahertz probe studies of carrier dynamics in semi-insulating CaAs have been investigated in detail for various pump powers. It is observed that, at high pump powers, the reflection peaks flip to the opposite polarity and dramatically enhance as the pump arrival time approaches the reflected wave of the terahertz pulse. The abnormal polarity-flip and enhancement can be interpreted by the pump-induced enhancement in the photoconductivity of GaAs and half-wave loss. Moreover, the carrier relaxation processes and surface states filling in GaAs are also studied in these measurements.

Upgraded Force on a Wall from Reflected Surface Gravity Waves

During reflection from a solid vertical wall, surface gravity waves produce a steady force on the wall, which was calculated earlier by the momentum method. Recently the linear momentum of these waves has been estimated to be twice as large as deduced from the classical Stokes drift formula. Therefore, the magnitude of the reflected wave force has been doubled here and the algebraic form of the equation is converted to be more understandable physically. Wave force equals fluid density times the square of the particle’s orbital speed and a numerical constant. Observations are welcomed to compare with the theory.

Fault detection by reflected surface waves based on ambient noise interferometry

Detecting subsurface fault structure is important for evaluating potential earthquake risks associated with active faults.In this study,we propose a new method to detect faults using reflected surface waves observed in ambient noise cross correlation functions.Ambient noise tomography using direct surface waves obtained from ambient noise interferometry has been widely used to characterize active fault zones.In cases where a strong velocity contrast exists across the fault interface,fault-reflected surface waves are expected.We test this idea using a linear array deployed in the Suqian segment of Tanlu fault zone in Eastern China.The fault-reflected surface waves can be clearly seen in the cross-correlation functions of the ambient noise data,and the spatial position of the fault on the surface is close to the stations where the reflected signals first appear.Potentially reflected surface waves could also be used to infer the dip angle,fault zone thickness and the degree of velocity contrast across the fault by comparing synthetic and observed waveforms.

Reflection coefficients of P-SV waves in weak anisotropic media

We introduce the Thomsen anisotropic parameters into the approximate linear reflection coefficient equation for P-SV wave in weakly anisotropic HTI media. From this we get a new, more effective, and practical reflection coefficient equation. We performed forward modeling to AVO attributes, obtaining excellent results. The combined AVO attribute analysis of PP and PS reflection data can greatly reduce ambiguity, obtain better petrophysical parameters, and improve parameter accuracy.

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.

Experimental Researches on Reflective and Transmitting Performances of Quarter Circular Breakwater Under Regular and Irregular Waves

A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater （QCB） in comparison with those of semi-circular breakwater （SCB）. Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.

Bragg Reflection of Waves by Different Shapes of Artificial Bars

Experiments are performed in a wave flume to demonstrate the Bragg reflection of linear gravity waves by artificial bars. Three different artificial bars with rectangular, triangular and rectified cosinoidal shapes are placed discretely on the seabed for measurement of the Bragg reflection. A series of experimental conditions including the number of bars, the periodic bar spacing, the water depth and various wave conditions are tested. Key parameters influencing the Bragg resonances are investigated. The experimental data are compared with the values from both theoretical and numerical models. Some key parameters have proved to be effective in describing the primary resonances. Predictive equations of the characteristics for the Bragg reflection are proposed in this paper.

Reflection and Transmission of Regular Waves from/Through Single and Double Perforated Thin Walls

In this paper, reflection and transmission coefficients of regular waves from/through perforated thin walls are investigated. Small scale laboratory tests have been performed in a wave flume firstly with single perforated thin Plexiglas plates of various porosities. The plate is placed perpendicular to the flume with the height from the flume bottom to the position above water surface. With this thin wall in the flume wave overtopping is prohibited and incident waves are able to transmit. The porosities of the walls are achieved by perforating the plates with circular holes. Model settings with double perforated walls parallel to each other forming so called chamber system, have been also examined. Several parameters have been used for correlating the laboratory tests’ results. Experimental data are also compared with results from the numerical model by applying the multi-domain boundary element method （MDBEM） with linear wave theory. Wave energy dissipation due to the perforations of the thin wall has been represented by a simple yet effective porosity parameter in the model. The numerical model with the MDBEM has been further validated against the previously published data.

Reflection and refraction of attenuated waves at boundary of elastic solid and porous solid saturated with two immiscible viscous fluids

The propagation of elastic waves is studied in a porous solid saturated with two immiscible viscous fluids. The propagation of three longitudinal waves is represented through three scalar potential functions. The lone transverse wave is presented by a vector potential function. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. It is shown that there exist three longitudinal waves and one transverse wave. The phenomena of reflection and refraction due to longitudinal and transverse waves at a plane interface between an elastic solid half-space and a porous solid half-space saturated with two immiscible viscous fluids are investigated. For the presence of viscosity in pore-fluids, the waves refracted to the porous medium attenuate in the direction normal to the interface. The ratios of the amplitudes of the reflected and refracted waves to that of the incident wave are calculated as a non- singular system of linear algebraic equations. These amplitude ratios are used to further calculate the shares of different scattered waves in the energy of the incident wave. The modulus of the amplitude and the energy ratios with the angle of incidence are computed for a particular numerical model. The conservation of the energy across the interface is verified. The effects of variations in non-wet saturation of pores and frequencies on the energy partition are depicted graphically and discussed,

Reflection and transmission of seismic waves at an interface betwen two saturated soils

Based on the modified Biot model for asturated soils, taking the compressibilities of the grains and the pore fluid as well as the viscous coupling into account, the reflection and transmission of seismic aves at an interface between two saturated soils are studied in this paper. A formula is derived for calculation of the amplitude reflection and transmission coefficients of various waves. A aumerical investigation of the dependence of the coefficients on the angle of incidence and the frequency is performed. This study is of a value for seismological studies and geophysical exploration.

Reflection of plane seismic waves at the surface of double-porosity dual-permeability materials

The present work deals with the reflection of plane seismic waves at the stress-free plane surface of double-porosity dualpermeability material. The incidence of two main waves（i.e., P1 and SV） is considered. As a result of the incident waves,four reflected（three longitudinal and one shear） waves are found in the medium. The expressions of reflection coefficients for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy for fully closed as well as perfectly open pores. Effect of incident direction on the partition of the incident energy is analyzed with the change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure. It has been confirmed from the numerical interpretation that during the reflection process, conservation of incident energy is obtained at each angle of incidence.

Reflection and refraction of plane waves at the boundary of an elastic solid and double-porosity dual-permeability materials

Phenomena of reflection and refraction of plane harmonic waves at a plane interface between an elastic solid and doubleporosity dual-permeability material are investigated. The elastic solid behaves non-dissipatively, while double-porosity dual-permeability materials behave dissipatively to wave propagation due to the presence of viscosity in pore fluids. All the waves(i.e., incident and reflected) in an elastic medium are considered as homogeneous(i.e., having the same directions of propagation and attenuation), while all the refracted waves in double-porosity dual-permeability materials are inhomogeneous(i.e., having different directions of propagation and attenuation). The coefficients of reflection and refraction for a given incident wave are obtained as a non-singular system of linear equations. The energy shares of reflected and refracted waves are obtained in the form of an energy matrix. A numerical example is considered to calculate the partition of incident energy among various reflected and refracted waves. The effect of incident direction on the partition of the incident energy is analyzed with a change in wave frequency, wave-induced fluid-flow, pore-fluid viscosity and double-porosity structure.It has been confirmed from numerical interpretation that during the reflection/refraction process, conservation of incident energy is obtained at each angle of incidence.

The reflection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.