The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is mod...The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.展开更多
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 r...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.展开更多
Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesi...Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.展开更多
Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the...Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.展开更多
A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating...A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating a reference perforated plate about its origin point according to the parabolic equation y=-x2 A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s （1976） method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.展开更多
The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicula...The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicular to its hole and the other to its side wall. Until now, there has not been a program to calculate the input impedance or its equivalent electromagnetic parameters for the later case. In this paper, an approach for analyzing the reflection characteristics of the impregnated honeycomb when its side wall faces the incident plane wave is proposed. Experiments prove it an effective, accurate and fast solution to this subject.展开更多
The present work analyzes the interaction of oblique waves by a porous flexible breakwater in the presence of a step-type bottom.The physical models for both scattering and trapping cases are considered and developed ...The present work analyzes the interaction of oblique waves by a porous flexible breakwater in the presence of a step-type bottom.The physical models for both scattering and trapping cases are considered and developed within the framework of small amplitude water-wave theory.Darcy’s law is used to model the wave interaction with the porous medium.It is assumed that the varying bottom extends over a finite interval,connected by a finite length of uniform bottom near an impermeable wall,and a semi-infinite length of bottom in the open water region.The boundary value problem is solved using the eigenfunction expansion method in the uniform bottom regions,while a modified mild-slope equation(MMSE)is used for the region with the varying bottom.Additionally,a mass-conserving jump condition is employed to handle the solution at slope discontinuities in the bottom.A system of equations is derived by matching the solutions at interfaces.The reflection coefficient and force on the breakwater and impermeable wall are plotted and analyzed for various parameters,such as the length of the varying bottom,depth ratio,angle of incidence,and flexural rigidity.It is observed that moderate values of flexural rigidity and depth ratio significantly contribute to an optimum reflection coefficient and reduce the wave force on the wall and breakwater.Remarkably,the outcomes of this study are assumed to be applicable in the construction of this type of breakwater in coastal regions.展开更多
The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four s...The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.展开更多
Although the ambiguity of seismic inversion is widely recognized in both theory and practice, so far as a concrete inversion example is concerned, there is not any objective, controllable method or any standard for ho...Although the ambiguity of seismic inversion is widely recognized in both theory and practice, so far as a concrete inversion example is concerned, there is not any objective, controllable method or any standard for how to evaluate and determine its ambiguity and reliability, especially for the high frequency components beyond the effective seismic frequency band. Taking log-constrained impedance inversion as an example, a new appraisal method is proposed on the basis of analyzing a simple geological model. Firstly, the inverted impedance model is transformed to a reflection coefficient series. Secondly, the maximum effective frequency of the real seismic data is chosen as a cutoff point and the reflection coefficient series is decomposed into two components by low-pass and high-pass filters. Thirdly, the geometrical reflection characteristics of the high-frequency components and that of the real seismic data are compared and analyzed. Then, the reliability of the inverted impedance model is appraised according to the similarity of geometrical characteristics between the high-frequency components and the real seismic data. The new method avoids some subjectivity in appraising the inverted result, and helps to enhance the reliability of reservoir prediction by impedance inversion technology.展开更多
Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (...Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO_(2)) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.展开更多
An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked por...An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.展开更多
In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant dep...In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant depth, whereas the third wall is impermeable. The wave–structure interaction and flow behavior of this type of breakwater arrangement are complicated and must be analyzed before breakwaters can be appropriately designed. To study the hydrodynamic breakwater performance, we developed a mathematical model based on the eigenfunction expansion method and a least squares technique for predicting wave interaction with three rows of vertical slotted wall breakwaters. We theoretically examined the wave transmission, reflection, energy loss, wave runup, and wave force under normal regular waves. Comparisons with experimental measurements show that the mathematical model results adequately reproduce most of the important features. The results of this investigation provide a better understanding of the hydrodynamic performance of triple-row vertical slotted wall breakwaters.展开更多
The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an...The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an approximation for the free surface, and the lower one was bounded below by an impermeable bottom surface having a small deformation; the channel was unbounded in the horizontal directions. Assuming irrotational motion, the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green＇s integral theorem suitably with the introduction of appropriate Green＇s functions. Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape ftmction c（x） representing the bottom deformation. Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem. Two special examples of bottom deformation were considered to validate the results. Consideration of a patch of sinusoidal ripples （having the same wave number） shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large. Similar results were observed for a patch of sinusoidal ripples having different wave numbers. It was also observed that for small angles of incidence, the reflected energy is greater compared to other angles of incidence up to π/ 4. These theoretical observations are supported by graphical results.展开更多
In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric ...In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.展开更多
The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is a...The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.展开更多
In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular...In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.展开更多
Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investi...Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.展开更多
The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of...The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.展开更多
The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. U...The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.展开更多
This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes seco...This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.展开更多
文摘The seismic reflection and transmission characteristics of a single layer sandwiched between two dissimilar poroelastic solids saturated with two immiscible viscous fluids are investigated. The sandwiched layer is modeled as a porous solid with finite thickness. The propagation of waves is represented with potential functions. The displacements of particles in different phases of the aggregate are defined in terms of these potential functions. Due to the presence of viscosity in pore fluids, the reflected and transmitted waves are inhomogeneous in nature, i.e., with different directions of propagation and attenuation. The closed-form analytical expressions for reflection and transmission coefficients are derived theoretically for appropriate boundary conditions. These expressions are calculated as a non-singular system of linear algebraic equations and depend on the various parameters involved in this non-singular system. Hence,numerical examples are studied to determine the effects of various properties of the sandwich layer on reflection and transmission coefficients. The essential features of layer thickness, incident direction, wave frequency, liquidsaturation and capillary pressure of the porous layer on reflection and transmission coefficients are depicted graphically and discussed. The analysis shows that reflection and transmission coefficients are strongly associated with incident direction and various properties of the porous layer.
文摘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.
基金the sponsorship of the National 973 Program of China (2013CB228604)the National Grand Project for Science and Technology (2011ZX05030-004-002, 2011ZX05019-003 and 2011ZX05006-002) for funding this research+2 种基金the support of the Australian and Western Australian Governments and the North West Shelf Joint Venture Partnersthe Western Australian Energy Research Alliance (WA:ERA)Foundation from Geophysical Key Lab of SINOPEC (WTYJYWX2013-04-01)
文摘Linearized approximations of reflection and transmission coefficients set a foundation for amplitude versus offset（AVO） analysis and inversion in exploration geophysics.However,the weak properties contrast hypothesis of those linearized approximate equations leads to big errors when the two media across the interface vary dramatically.To extend the application of AVO analysis and inversion to high contrast between the properties of the two layers,we derive a novel nonlinearized high-contrast approximation of the PP-wave reflection coefficient,which establishes the direct relationship between PPwave reflection coefficient and P-wave velocities,S-wave velocities and densities across the interface.（A PP wave is a reflected compressional wave from an incident compressional wave（P-wave）.） This novel approximation is derived from the exact reflection coefficient equation with Taylor expansion for the incident angle.Model tests demonstrate that,compared with the reflection coefficients of the linearized approximations,the reflection coefficients of the novel nonlinearized approximate equation agree with those of the exact PP equation better for a high contrast interface with a moderate incident angle.Furthermore,we introduce a nonlinear direct inversion method utilizing the novel reflection coefficient equation as forward solver,to implement the direct inversion for the six parameters including P-wave velocities,S-wave velocities,and densities in the upper and lower layers across the interface.This nonlinear inversion algorithm is able to estimate the inverse of the nonlinear function in terms of model parameters directly rather than in a conventional optimization way.Three examples verified the feasibility and suitability of this novel approximation for a high contrast interface,and we still could estimate the six parameters across the interface reasonably when the parameters in both media across the interface vary about 50%.
基金Project 40574058 Supported by the National Natural Science Foundation of China
文摘Although the Zoeppritz equation is suitable for a single interface in a thick deposit, it has some limitations for composite reflection waves from both the floor and the roof of coal seams. Based on the ray model, the relationship of the overall reflection coefficient of composite reflection P waves, from coal seam versus incidence angle (AVO), is dis- cussed. The result shows that: 1) the overall reflection coefficient of composite reflection waves from coal seams is a negative value and is determined mainly by the lithology of roof and floor, which is different from the reflection coeffi- cient of a single interface; 2) if the incidence angle ranges from 0° to 6°, the reflection coefficient of composite waves of a coal seam does not change with the incidence angle and 3) if the incidence angle ranges from 6–60° , the reflection coefficient increases monotonically.
文摘A set of experiments is carried out in a towing tank to study the effects of the curvature of perforated plates on the wave reflection coefficient （Cr）. The curvature of a perforated plate can be changed by rotating a reference perforated plate about its origin point according to the parabolic equation y=-x2 A plunger-type wave maker is used to generate regular waves. The reflection coefficients are calculated using Goda and Suzuki’s （1976） method. The results are compared with those of vertical or sloped passive wave absorbers. The comparison shows that a perforated plate with a curved profile is highly efficient in terms of reducing the wave reflection coefficient. A correlation is established to estimate the reflection coefficient of curved perforated plates as a function of both flow and geometry characteristics.
文摘The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicular to its hole and the other to its side wall. Until now, there has not been a program to calculate the input impedance or its equivalent electromagnetic parameters for the later case. In this paper, an approach for analyzing the reflection characteristics of the impregnated honeycomb when its side wall faces the incident plane wave is proposed. Experiments prove it an effective, accurate and fast solution to this subject.
文摘The present work analyzes the interaction of oblique waves by a porous flexible breakwater in the presence of a step-type bottom.The physical models for both scattering and trapping cases are considered and developed within the framework of small amplitude water-wave theory.Darcy’s law is used to model the wave interaction with the porous medium.It is assumed that the varying bottom extends over a finite interval,connected by a finite length of uniform bottom near an impermeable wall,and a semi-infinite length of bottom in the open water region.The boundary value problem is solved using the eigenfunction expansion method in the uniform bottom regions,while a modified mild-slope equation(MMSE)is used for the region with the varying bottom.Additionally,a mass-conserving jump condition is employed to handle the solution at slope discontinuities in the bottom.A system of equations is derived by matching the solutions at interfaces.The reflection coefficient and force on the breakwater and impermeable wall are plotted and analyzed for various parameters,such as the length of the varying bottom,depth ratio,angle of incidence,and flexural rigidity.It is observed that moderate values of flexural rigidity and depth ratio significantly contribute to an optimum reflection coefficient and reduce the wave force on the wall and breakwater.Remarkably,the outcomes of this study are assumed to be applicable in the construction of this type of breakwater in coastal regions.
文摘The effect of porosity on surface wave scattering by a vertical porous barrier over a rectangular trench is studied here under the assumption of linearized theory of water waves.The fluid region is divided into four subregions depending on the position of the barrier and the trench.Using the Havelock’s expansion of water wave potential in different regions along with suitable matching conditions at the interface of different regions,the problem is formulated in terms of three integral equations.Considering the edge conditions at the submerged end of the barrier and at the edges of the trench,these integral equations are solved using multi-term Galerkin approximation technique taking orthogonal Chebyshev’s polynomials and ultra-spherical Gegenbauer polynomial as its basis function and also simple polynomial as basis function.Using the solutions of the integral equations,the reflection coefficient,transmission coefficient,energy dissipation coefficient and horizontal wave force are determined and depicted graphically.It was observed that the rate of convergence of the Galerkin method in computing the reflection coefficient,considering special functions as basis function is more than the simple polynomial as basis function.The change of porous parameter of the barrier and variation of trench width and height significantly contribute to the change in the scattering coefficients and the hydrodynamic force.The present results are likely to play a crucial role in the analysis of surface wave propagation in oceans involving porous barrier over submarine trench.
基金supported by the Major Basic Research Development Program of China’s 973 Project(grant No.2007CB209608)the Science and Technology Innovation Foundation of CNPC(grant No.2010D-5006-0301)
文摘Although the ambiguity of seismic inversion is widely recognized in both theory and practice, so far as a concrete inversion example is concerned, there is not any objective, controllable method or any standard for how to evaluate and determine its ambiguity and reliability, especially for the high frequency components beyond the effective seismic frequency band. Taking log-constrained impedance inversion as an example, a new appraisal method is proposed on the basis of analyzing a simple geological model. Firstly, the inverted impedance model is transformed to a reflection coefficient series. Secondly, the maximum effective frequency of the real seismic data is chosen as a cutoff point and the reflection coefficient series is decomposed into two components by low-pass and high-pass filters. Thirdly, the geometrical reflection characteristics of the high-frequency components and that of the real seismic data are compared and analyzed. Then, the reliability of the inverted impedance model is appraised according to the similarity of geometrical characteristics between the high-frequency components and the real seismic data. The new method avoids some subjectivity in appraising the inverted result, and helps to enhance the reliability of reservoir prediction by impedance inversion technology.
基金National Natural Science Foundation of China(42174139,41974119,42030103)Laoshan Laboratory Science and Technology Innovation Program(LSKJ202203406)Science Foundation from Innovation and Technology Support Program for Young Scientists in Colleges of Shandong Province and Ministry of Science and Technology of China(2019RA2136).
文摘Monitoring the change in horizontal stress from the geophysical data is a tough challenge, and it has a crucial impact on broad practical scenarios which involve reservoir exploration and development, carbon dioxide (CO_(2)) injection and storage, shallow surface prospecting and deep-earth structure description. The change in in-situ stress induced by hydrocarbon production and localized tectonic movements causes the changes in rock mechanic properties (e.g. wave velocities, density and anisotropy) and further causes the changes in seismic amplitudes, phases and travel times. In this study, the nonlinear elasticity theory that regards the rock skeleton (solid phase) and pore fluid as an effective whole is used to characterize the effect of horizontal principal stress on rock overall elastic properties and the stress-dependent anisotropy parameters are therefore formulated. Then the approximate P-wave, SV-wave and SH-wave angle-dependent reflection coefficient equations for the horizontal-stress-induced anisotropic media are proposed. It is shown that, on the different reflectors, the stress-induced relative changes in reflectivities (i.e., relative difference) of elastic parameters (i.e., P- and S-wave velocities and density) are much less than the changes in contrasts of anisotropy parameters. Therefore, the effects of stress change on the reflectivities of three elastic parameters are reasonably neglected to further propose an AVO inversion approach incorporating P-, SH- and SV-wave information to estimate the change in horizontal principal stress from the corresponding time-lapse seismic data. Compared with the existing methods, our method eliminates the need for man-made rock-physical or fitting parameters, providing more stable predictive power. 1D test illustrates that the estimated result from time-lapse P-wave reflection data shows the most reasonable agreement with the real model, while the estimated result from SH-wave reflection data shows the largest bias. 2D test illustrates the feasibility of the proposed inversion method for estimating the change in horizontal stress from P-wave time-lapse seismic data.
文摘An aim of current study is to analyze the contribution of reflected longitudinal waves to wave-induced fluid flow(WIFF) in the cracked porous solid.Initially,we investigate the time harmonic plane waves in cracked porous solid by employing the mathematical model proposed by Zhang et al.(2019).The solution is obtained in form of the Christoffel equations.The solution of the Christoffel equations indicates that there exist four(three dilatational and one shear) waves.These waves are attenuated in nature due to their complex and frequency-dependent velocities.The reflection coefficients are calculated at the sealed pore stress-free surface of cracked porous solid for the incidence of P1 and SV waves.It is found that three longitudinal waves contribute to WIFF and the contribution of these waves to the induced fluid in the cracked porous solid is analyzed using the reflection coefficients of these longitudinal waves.We analytically show that the fluid flow induced by these longitudinal waves is linked directly to their respective reflection coefficients.Finally,a specific numerical example is considered to discuss and to depict the impact of various parameters on the characteristics of propagation like phase velocity/attenuation,reflection coefficients and WIFF of longitudinal waves.
基金King Abdul-Aziz City for Science and Technology,General Directorate of Research Grants Programs(LGP-35-287)
文摘In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant depth, whereas the third wall is impermeable. The wave–structure interaction and flow behavior of this type of breakwater arrangement are complicated and must be analyzed before breakwaters can be appropriately designed. To study the hydrodynamic breakwater performance, we developed a mathematical model based on the eigenfunction expansion method and a least squares technique for predicting wave interaction with three rows of vertical slotted wall breakwaters. We theoretically examined the wave transmission, reflection, energy loss, wave runup, and wave force under normal regular waves. Comparisons with experimental measurements show that the mathematical model results adequately reproduce most of the important features. The results of this investigation provide a better understanding of the hydrodynamic performance of triple-row vertical slotted wall breakwaters.
文摘The problem of oblique wave （internal wave） propagation over a small deformation in a channel flow consisting of two layers was considered. The upper fluid was assumed to be bounded above by a rigid lid, which is an approximation for the free surface, and the lower one was bounded below by an impermeable bottom surface having a small deformation; the channel was unbounded in the horizontal directions. Assuming irrotational motion, the perturbation technique was employed to calculate the first-order corrections of the velocity potential in the two fluids by using Green＇s integral theorem suitably with the introduction of appropriate Green＇s functions. Those functions help in calculating the reflection and transmission coefficients in terms of integrals involving the shape ftmction c（x） representing the bottom deformation. Three-dimensional linear water wave theory was utilized for formulating the relevant boundary value problem. Two special examples of bottom deformation were considered to validate the results. Consideration of a patch of sinusoidal ripples （having the same wave number） shows that the reflection coefficient is an oscillatory function of the ratio of twice the x-component of the wave number to the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and the interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large. Similar results were observed for a patch of sinusoidal ripples having different wave numbers. It was also observed that for small angles of incidence, the reflected energy is greater compared to other angles of incidence up to π/ 4. These theoretical observations are supported by graphical results.
基金supported by the Program for New Century Excellent Talents in University(No.NCET-05-0575)the Education Science Foundation of Jiangxi Province(No.Z-03510)
文摘In this study, the propagation of electromagnetic waves in one-dimensional plasma photonic crystals （PPCs）, namely, superlattice structures consisting alternately of a homogeneous unmagnetized plasma and dielectric material, is simulated numerically using the finite-difference time-domain （FDTD） algorithm. A perfectly matched layer （PML） absorbing technique is used in this simulation. The reflection and transmission coefficients of electromagnetic （EM） waves through PPCs are calculated. The characteristics of the photonic band gap （PBG） are discussed in terms of plasma density, dielectric constant ratios, number of periods, and introduced layer defect. These may provide some useful information for designing plasma photonic crystal devices.
基金Partially Supported by a Research from Department of Science and Technology(DST),India under Grant No.SB/FTP/MS-003/2013
文摘The interaction of oblique incident water waves with a small bottom deformation on a porous ocean-bed is examined analytically here within the framework of linear water wave theory. The upper surface of the ocean is assumed to be covered by an infinitely extended thin uniform elastic plate, while the lower surface is bounded by a porous bottom surface having a small deformation. By employing a simplified perturbation analysis, involving a small parameter c^（〈〈l ）, which measures the smallness of the deformation, the governing Boundary Value Problem （BVP） is reduced to a simpler BVP for the first-order correction of the potential function. This BVP is solved using a method based on Green＇s integral theorem with the introduction of suitable Green＇s function to obtain the first-order potential, and this potential function is then utilized to calculate the first-order reflection and transmission coefficients in terms of integrals involving the shape function c（x） representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number propagating just below the elastic plate and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the surface below the elastic plate. Again, for small angles of incidence, the reflected wave energy is more as compared to the other angles of incidence. It is also observed that the reflected wave energy is somewhat sensitive to the changes in the flexural rigidity of the elastic plate, the porosity of the bed and the ripple wave numbers. The main advantage of the present study is that the results for the values of reflection and transmission coefficients obtained are found to satisfy the energy-balance relation almost accurately.
基金Partially Supported by the Department of Science and Technology Through a Research Grant to RG(No.SR/FTP/MS-020/2010)
文摘In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.
文摘Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.
文摘The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape fimction. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed.
基金partially supported by a research grant from Department of Science and Technology(DST),India(No.SB/FTP/MS-003/2013)
文摘The scattering of oblique incident surface waves by the edge of a small cylindrical deformation on a porous bed in an ocean of finite depth, is investigated here within the framework of linearized water wave theory. Using perturbation analysis, the corresponding problem governed by modified Helmholtz equation is reduced to a boundary value problem for the first-order correction of the potential function. The first-order potential and, hence, the reflection and transmission coefficients are obtained by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function. Consideration of a patch of sinusoidal ripples shows that when the quotient of twice the component of the incident field wave number along x-direction and the ripple wave number approaches one, the theory predicts a resonant interaction between the bed and the free-surface, and the reflection coefficient becomes a multiple of the number of ripples. Again, for small angles of incidence, the reflected energy is more as compared to the other angles of incidence. It is also observed that the reflected energy is somewhat sensitive to the changes in the porosity of the ocean bed. From the derived results, the solutions for problems with impermeable ocean bed can be obtained as particular cases.
文摘This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.
