Fracture system plays a very important role in the enrichment and accumulation of oil and gas in the reservoirs. Based on scattering wave information, Fracture Orientation Function （FOF） was built, which can be used...Fracture system plays a very important role in the enrichment and accumulation of oil and gas in the reservoirs. Based on scattering wave information, Fracture Orientation Function （FOF） was built, which can be used to predict the fracture orientations. However, this method has only been verified by physical experiments without studies on the application scope. In this study, based on the linear sliding theory, F0F of the scattering wave was applied to the numerical simulation and the application scope was further studied according to fracture flexibility tensor. According to the fractures filled with gas and liquid, numerical simulation was conducted on the models with various fracture flexibilities. Numerical simulation results were used to inverse fracture orientation with the aid of the FOF of the scattering wave. The results show that it is workable to predict the vertical fracture orientation with the F0F of the scattering wave. Application of this method is more effective when the fractures are filled with gas than liquid. Moreover, the application scope can be predicted by the fracture flexibility.展开更多
Fractures play a crucial role in various fields such as hydrocarbon exploration,groundwater resources management,and earthquake research.The determination of fracture location and the estimation of parameters such as ...Fractures play a crucial role in various fields such as hydrocarbon exploration,groundwater resources management,and earthquake research.The determination of fracture location and the estimation of parameters such as fracture length and dip angle are the focus of geophysical work.In borehole observation system,the short distance between fractures and detectors leads to weak attenuation of elastic wave energy,and high-frequency source makes it easier to identify small-scale fractures.Compared to traditional monopole logging methods,dipole logging method has advantage of exciting pure shear waves sensitive to fractures,so its application is becoming increasingly widespread.However,since the reflected shear waves and scattered shear waves of fractures correspond to different fracture properties,how to distinguish and analyze these two kinds of waves is crucial for accurately characterizing the fracture parameters.To address this issue,numerical simulation of wave responses by a single fracture near a borehole in rock formation is performed,and the generation mechanism and characteristics of shear waves scattered by fractures are investigated.It is found that when the dip angle of the fracture surpasses a critical threshold,the S-wave will propagate to both endpoints of the fracture and generate scattered S-waves,resulting in two distinct scattered wave packets on the received waveform.When the polarization direction of the acoustic source is parallel to the strike of the fracture,the scattered SH-waves always have larger amplitude than the scattered SV-waves regardless of changing the fracture dip angle.Unlike SV-waves,the SH-waves scattered by the fracture do not have any mode conversion.Additionally,propagation of S-waves to a short length fracture can induce dipole mode vibration of the fracture within a wide frequency range.The phenomena of shear waves reflected and scattered by the fracture are further illustrated and verified by two field examples,thus showing the potential of scattered waves for fracture evaluation and characterization with borehole observation system.展开更多
In conventional fi nite diff erence numerical simulation of seismic waves,regular grids in Cartesian coordinates are used to divide the calculated region.When simulating seismic wave fi elds under an irregular surface...In conventional fi nite diff erence numerical simulation of seismic waves,regular grids in Cartesian coordinates are used to divide the calculated region.When simulating seismic wave fi elds under an irregular surface,such grids are unsuitable to realize the free boundary condition.They also easily generate false scattered waves at the corners of the grids owing to the approximation of the stepped grids.These issues affect the simulation accuracy.This study introduces an orthogonal body-fitted grid generation technique in computational fl uid dynamics for generating grids in transversely isotropic(TI)media under an irregular surface.The fi rst-order velocity-stress equation in curvilinear coordinates is calculated using the optimized nonstaggered grids finite difference method.The point oscillation generated by the nonstaggered grids difference is eliminated by selective filtering.The orthogonal body-fitted grids can accurately describe the irregular surface.Further,the orthogonality of the grids allows the implementation of free boundary conditions without complicated coordinate transformation and interpolation operations.Numerical examples show that the numerical solutions obtained by this method agree well with the analytical solutions.By comparing the simulation results of the proposed method with those of the regular grid difference method,the proposed method can eff ectively eliminate the false scattered waves caused by the stepped grids under the condition of the same grid spacing.Thus,the accuracy of the numerical simulation is improved.In addition,the simulation results of the three-layer TI media model on an irregular surface show that the proposed method is also suitable for complex models.展开更多
This study proposes a numerically efficient technique for computing the far-field scattered by a spherical target placed near the seabed.The bottom is supposed to be a homogeneous liquid attenuating half-space.The tra...This study proposes a numerically efficient technique for computing the far-field scattered by a spherical target placed near the seabed.The bottom is supposed to be a homogeneous liquid attenuating half-space.The transmitter and receiver are situated at different points of a homogeneous water half-space.The distances between the transmitter,receiver,and object of interest are assumed to be much larger than the acoustic wavelength in water.The scattered far-field is ascertained using Hackman and Sammelmann’s general approach.The arising scattering coefficients of a sphere are assessed using the steepest descent approach.The branch cut contribution is also considered.The obtained formulas for the form-function can be used for acoustically rigid or soft scatterers,as well as elastic targets or spherical elastic shells.Numerical simulations are conducted for an acoustically rigid sphere.Asymptotic expressions for the scattering coefficients allow a decrease in the number of summands in the formula for the target strength and a significant reduction in computational time.展开更多
Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an a...Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.展开更多
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 typ...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.展开更多
A Boundary Element Method(BEM) is;described to compute the scattering of elastic waves by an axisymmetric inclusion in an infinite elastic medium. The boundary loads applied to the inclusion is expanded in terms of Fo...A Boundary Element Method(BEM) is;described to compute the scattering of elastic waves by an axisymmetric inclusion in an infinite elastic medium. The boundary loads applied to the inclusion is expanded in terms of Fourier series in an infinite space. The boundary integral equation is solved in the general direction of the axisymmetric inclusion by BEM The problem of the 3-D scattering of elastic waves is reduced to a 1-D one. According to the geometric features of the axisymmetric inclusion the ring shell elements are adopted in this method. A comparison is made with other BEM methods. The numerical results show this method can reduce the amount of calculation and enhance the speed of convergence.展开更多
The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed...The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed first, which is the solution of displacement fields for elastic half space with circle canyon under output plane harmonic line loading at horizontal surface. Then the integral equation for determining the unknown forces in the problem can be changed into the algebraic one and solved numerically so that crack DSIF can be determined. Last when the medium parameters are altered, the influence on the crack DSIF is discussed partially with the displacement between circle canyon and crack.展开更多
In this paper, a computer visualization approach is proposed for electromagnetic wave interaction with structures by mains of finite difference-time doain method (F-D) and computer graphics. By visualization of FDTD, ...In this paper, a computer visualization approach is proposed for electromagnetic wave interaction with structures by mains of finite difference-time doain method (F-D) and computer graphics. By visualization of FDTD, Phenomena such as wave propagation, penetration through structures, renection and absorption by structures are observed. Visualization of electromagnetic wave interactions with two wing-shaped structures is demonstrated. These examples indicate that the approach describe in the paper offers an effective way for investigating electromagnetic wave phenomena and is helpful to the engineers in controlling radar signature of the targets.展开更多
The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteris...The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb＇s singular solutions, i.e., the integral solutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed..展开更多
Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of...Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.展开更多
The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped,...The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.展开更多
Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress...Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.展开更多
The reflection and transmission characteristics of an anisotropic half-space medium normally illuminated by a plane wave are analyzed by kDB coordination. The general formula of reflection coefficient at the air-mediu...The reflection and transmission characteristics of an anisotropic half-space medium normally illuminated by a plane wave are analyzed by kDB coordination. The general formula of reflection coefficient at the air-medium interface is given, and its validity is also discussed. The possible propagating modes in different mediums and the effect of medium parameters on these modes are emphatically studied. This work provides the theoretical preparations for the parameter reconstruction of an anisotropic material.展开更多
Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane ...Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.展开更多
The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral ...The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.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
Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated so...Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.展开更多
The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investi...The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.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
基金supported by the National Basic Research Program of China ( No. 2014CB239104 and No. 2012CB214800)National Science and Technology Major Project of the Ministry of Science and Technology of China ( No. 2011ZX05066-002)
文摘Fracture system plays a very important role in the enrichment and accumulation of oil and gas in the reservoirs. Based on scattering wave information, Fracture Orientation Function （FOF） was built, which can be used to predict the fracture orientations. However, this method has only been verified by physical experiments without studies on the application scope. In this study, based on the linear sliding theory, F0F of the scattering wave was applied to the numerical simulation and the application scope was further studied according to fracture flexibility tensor. According to the fractures filled with gas and liquid, numerical simulation was conducted on the models with various fracture flexibilities. Numerical simulation results were used to inverse fracture orientation with the aid of the FOF of the scattering wave. The results show that it is workable to predict the vertical fracture orientation with the F0F of the scattering wave. Application of this method is more effective when the fractures are filled with gas than liquid. Moreover, the application scope can be predicted by the fracture flexibility.
基金supported by Scientific Research and Technology Development Project of CNPC(2024ZG38,2024ZG42)the CNPC Innovation Fund(2022DQ02-0307).
文摘Fractures play a crucial role in various fields such as hydrocarbon exploration,groundwater resources management,and earthquake research.The determination of fracture location and the estimation of parameters such as fracture length and dip angle are the focus of geophysical work.In borehole observation system,the short distance between fractures and detectors leads to weak attenuation of elastic wave energy,and high-frequency source makes it easier to identify small-scale fractures.Compared to traditional monopole logging methods,dipole logging method has advantage of exciting pure shear waves sensitive to fractures,so its application is becoming increasingly widespread.However,since the reflected shear waves and scattered shear waves of fractures correspond to different fracture properties,how to distinguish and analyze these two kinds of waves is crucial for accurately characterizing the fracture parameters.To address this issue,numerical simulation of wave responses by a single fracture near a borehole in rock formation is performed,and the generation mechanism and characteristics of shear waves scattered by fractures are investigated.It is found that when the dip angle of the fracture surpasses a critical threshold,the S-wave will propagate to both endpoints of the fracture and generate scattered S-waves,resulting in two distinct scattered wave packets on the received waveform.When the polarization direction of the acoustic source is parallel to the strike of the fracture,the scattered SH-waves always have larger amplitude than the scattered SV-waves regardless of changing the fracture dip angle.Unlike SV-waves,the SH-waves scattered by the fracture do not have any mode conversion.Additionally,propagation of S-waves to a short length fracture can induce dipole mode vibration of the fracture within a wide frequency range.The phenomena of shear waves reflected and scattered by the fracture are further illustrated and verified by two field examples,thus showing the potential of scattered waves for fracture evaluation and characterization with borehole observation system.
基金supported by the National Key Research and Development Program of China (Grant No.2023YFC3206501 and 2022YFFO802600)the National Natural Science Foundation of China (Grant No.52369003,42262010 and 42374166)+6 种基金the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No.2023LHMS04011 and2022MS04009)the Application Technology Research and Development Project of Jungar Banner (Grant No.2023YY-18 and 2023YY-19)the First-class Academic Subjects Special Research Project of the Education Department of Inner Mongolia Autonomous Region (Grant No.YLXKZX-NND-010)the Inner Mongolia Autonomous Region Science and Technology Leading Talent Team (Grant No.2022LJRC0007)the Inner Mongolia Agricultural University Basic Research Project(BR22-12-04)the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No.NMGIRT2313)the Basic Scientific Research Project of Institutions of Higher(Grant No.JY20230090)。
文摘In conventional fi nite diff erence numerical simulation of seismic waves,regular grids in Cartesian coordinates are used to divide the calculated region.When simulating seismic wave fi elds under an irregular surface,such grids are unsuitable to realize the free boundary condition.They also easily generate false scattered waves at the corners of the grids owing to the approximation of the stepped grids.These issues affect the simulation accuracy.This study introduces an orthogonal body-fitted grid generation technique in computational fl uid dynamics for generating grids in transversely isotropic(TI)media under an irregular surface.The fi rst-order velocity-stress equation in curvilinear coordinates is calculated using the optimized nonstaggered grids finite difference method.The point oscillation generated by the nonstaggered grids difference is eliminated by selective filtering.The orthogonal body-fitted grids can accurately describe the irregular surface.Further,the orthogonality of the grids allows the implementation of free boundary conditions without complicated coordinate transformation and interpolation operations.Numerical examples show that the numerical solutions obtained by this method agree well with the analytical solutions.By comparing the simulation results of the proposed method with those of the regular grid difference method,the proposed method can eff ectively eliminate the false scattered waves caused by the stepped grids under the condition of the same grid spacing.Thus,the accuracy of the numerical simulation is improved.In addition,the simulation results of the three-layer TI media model on an irregular surface show that the proposed method is also suitable for complex models.
基金Supported by the Ministry of Science and Higher Education of the Russian Federation as a part of World-class Research Center Program:Advanced Digital Technologies(contract No.075-15-2022-312 dated 20 April 2022).
文摘This study proposes a numerically efficient technique for computing the far-field scattered by a spherical target placed near the seabed.The bottom is supposed to be a homogeneous liquid attenuating half-space.The transmitter and receiver are situated at different points of a homogeneous water half-space.The distances between the transmitter,receiver,and object of interest are assumed to be much larger than the acoustic wavelength in water.The scattered far-field is ascertained using Hackman and Sammelmann’s general approach.The arising scattering coefficients of a sphere are assessed using the steepest descent approach.The branch cut contribution is also considered.The obtained formulas for the form-function can be used for acoustically rigid or soft scatterers,as well as elastic targets or spherical elastic shells.Numerical simulations are conducted for an acoustically rigid sphere.Asymptotic expressions for the scattering coefficients allow a decrease in the number of summands in the formula for the target strength and a significant reduction in computational time.
基金supported by the National Key R&D Program of China(Grant No.2022YFC3003601)Joint Funds of the National Natural Science Foundation of China Project on Earthquake Science(Grant No.U2239252)the program of the Innovative Research Team in China Earthquake Administration.
文摘Surface irregularities,such as hills and ridges,can significantly amplify ground motion caused by earthquakes.Therefore,in this study,we propose an analytical solution model to investigate the interaction between an asymmetric triangular hill on Earth and SH waves.Firstly,based on the development of wave functions and regional matching techniques,we introduce a semi-circular artificial auxiliary boundary,dividing the solution model into a semi-infinite body containing a semi-circular depression and an asymmetric fan-shaped region.Secondly,we derive the domain function form applicable to solving asymmetric problems.Utilizing the theory of complex variables,we establish a well-posed matrix for solving domain functions within the same coordinate system.Numerical results demonstrate that the scattering of SH waves by a protuberance is jointly influenced by the geometric parameters of the hill and the angle of incidence.Additionally,the frequency of the incident wave also has a certain degree of impact on the displacement amplitude.This study elucidates the scattering mechanism of SH waves by complex boundaries,providing a theoretical reference for building site selection and seismic design.In practical problems,the asymmetric assumption is more applicable than the symmetry assumption.
基金supported financially by the National Key Project(Grant No.2008ZX05035)the 973 Program(Grant No. 2009CB219603 and 2007CB209406)the National Natural Science Foundation of China(Grant No.50974081)
文摘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.
基金Foundation of Ph.D Program of State Education Commission of China.
文摘A Boundary Element Method(BEM) is;described to compute the scattering of elastic waves by an axisymmetric inclusion in an infinite elastic medium. The boundary loads applied to the inclusion is expanded in terms of Fourier series in an infinite space. The boundary integral equation is solved in the general direction of the axisymmetric inclusion by BEM The problem of the 3-D scattering of elastic waves is reduced to a 1-D one. According to the geometric features of the axisymmetric inclusion the ring shell elements are adopted in this method. A comparison is made with other BEM methods. The numerical results show this method can reduce the amount of calculation and enhance the speed of convergence.
文摘The dynamic stress intensity factor (DSIF) and the scattering of SH wave by circle canyon and crack are studied with Green's function. In order to solve the problem, a suitable Green's function is constructed first, which is the solution of displacement fields for elastic half space with circle canyon under output plane harmonic line loading at horizontal surface. Then the integral equation for determining the unknown forces in the problem can be changed into the algebraic one and solved numerically so that crack DSIF can be determined. Last when the medium parameters are altered, the influence on the crack DSIF is discussed partially with the displacement between circle canyon and crack.
文摘In this paper, a computer visualization approach is proposed for electromagnetic wave interaction with structures by mains of finite difference-time doain method (F-D) and computer graphics. By visualization of FDTD, Phenomena such as wave propagation, penetration through structures, renection and absorption by structures are observed. Visualization of electromagnetic wave interactions with two wing-shaped structures is demonstrated. These examples indicate that the approach describe in the paper offers an effective way for investigating electromagnetic wave phenomena and is helpful to the engineers in controlling radar signature of the targets.
基金Science Council Under Grant No.NSC98-2221-E-027-057-MY2)
文摘The diffraction of elastic waves by a sedimentary valley in a homogeneous elastic half-space is studied in this paper. The sediment-filled valley is composed of a fluid layer over a soft soil deposit whose characteristics may be significant and should be carefully considered when designing long span bridges with high piers. The method of analysis adopted in the paper is to decompose the problem into an interior region and an exterior region. In the exterior region, the scattered wave fields are constructed with the linear combinations of two independent sets of Lamb＇s singular solutions, i.e., the integral solutions for two concentrated surface loads in two directions; and their derivatives are used to represent the scattered wave fields. A technique is proposed to calculate the integrals in the wave-number domain based on the method of steepest descent. For the interior region, the wave fields for the fluid layer and soft soil deposit are expressed in terms of wave functions which satisfy the equation of motion. The continuity condition at the interface of the media is satisfied in the least square sense. The effects of geometric topography, soil amplification and fluid layer subject to different types of incident harmonic plane waves are analyzed and discussed..
文摘Half-space Green's function due to a spatially harmonic line load has been expressed as a sum of the full-space Green's functions and a 2-D integral representation of the reflected waves by the free surface of the half-space.By using the obtained half-space Green's function,an integral rep- resentation of the scattered waves by a cylindrical obstacle is then derived.Finally,by analyzing the far-zone behavior of the integrands of the integral representation.the far-field pattern of the scattered waves in a half-space obtained.
文摘The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.
基金The project supported by the National Natural Science Foundation of China
文摘Using the complex variable method and conformal mapping,scat- tering of flexural waves and dynamic stress concentrations in Mindlin's thick plates with a cutout have been studied.The general solution of the stress problem of the thick plate satisfying the boundary conditions on the contour of cutouts is obtained. Applying the orthogonal function expansion technique,the dynamic stress problem can be reduced into the solution of a set of infinite algebraic equations.As examples, numerical results for the dynamic stress concentration factor in Mindlin's plates with a circular,elliptic cutout are graphically presented in sequence.
文摘The reflection and transmission characteristics of an anisotropic half-space medium normally illuminated by a plane wave are analyzed by kDB coordination. The general formula of reflection coefficient at the air-medium interface is given, and its validity is also discussed. The possible propagating modes in different mediums and the effect of medium parameters on these modes are emphatically studied. This work provides the theoretical preparations for the parameter reconstruction of an anisotropic material.
基金National Natural Science Foundation of China under Grant Nos.51578373 and 51578372
文摘Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.
基金Project supported by the Research Fund for Doctors of Hebei Province China (No. B2001213).
文摘The scattering of SH wave by a cylindrical piezoelectric inclusion partially debonded from its surrounding piezoelectric material is investigated using the wave function expansion method and singular integral equation technique. The debonding regions are modeled as mul- tiple arc-shaped interface cracks with non-contacting faces. By expressing the scattered ?elds as wave function expansions with unknown coe?cients, the mixed boundary value problem is ?rstly reduced to a set of simultaneous dual series equations. Then dislocation density functions are introduced as unknowns to transform these dual series equations into Cauchy singular integral equations of the ?rst type, which can be numerically solved easily. The solution is valid for arbi- trary number and size of the debonds. Finally, numerical results of the dynamic stress intensity factors are presented for the cases of one debond and two debonds. The e?ects of incidence direc- tion, crack con?guration and various material parameters on the dynamic stress intensity factors are respectively discussed. The solution of this problem is expected to ?nd applications in the investigation of dynamic fracture properties of piezoelectric materials with cracks.
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Projects(50969007,51269021) supported by the National Natural Science Foundation of ChinaProjects(20114BAB206012,20133ACB20006) supported by the Natural Science Foundation of Jiangxi Province of China
文摘Based on Biot’s theory and considering the properties of a cavity,the boundary integral equations for the numerical simulation of wave scattering around a cavity with a circular cross-section embedded in saturated soil are obtained using integral transform methods.The Cauchy type singularity of the boundary integral equation is discussed.The effectiveness of the properties of soil mass and incident field on the dynamic stress concentration and pore pressure concentration around a cavity is analyzed.Our results are in good agreement with the existing solution.The numerical results of this work show that the dynamic stress concentration and pore pressure concentration are influenced by the degree of fluid–solid coupling as well as the pore compressibility and water permeability of saturated soil.With increased degree of fluid–solid coupling,the dynamic stress concentration improves from 1.87 to 3.42 and the scattering becomes more significant.With decreased index of soil mass compressibility,the dynamic stress concentration increases and its maximum reaches 3.67.The dynamic stress concentration increases from 1.64 to 3.49 and pore pressure concentration improves from 0.18 to 0.46 with decreased water permeability of saturated soil.
基金The work was partially supported bythe Nanyang Technological University,Singapore(Grant No.SUG03/07)partially supported by RGC,Hong Kong,China(Grant No.DAG03/04.EG39)
文摘The adoption of slotted breakwaters can be an ideal option in the protection of very large near-shore floating struc-trees that may extend offshore to a considerable water depth. In this paper, we experimently investigated the behaviour of wave transmission and reflection coefficients of double slotted barriers in the presence of a steady opposing current. The experimental results show that opposing currents have only minor effects on wave reflection, but can significantly reduce the wave transmission through double slotted barriers. The experimental results suggest that coastal currents should be taken into consideration for an economical design of slotted breakwaters.
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.
