The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,w...The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.展开更多
We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to...We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.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
An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum...An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0＆#176; to 22.5＆#176;. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.展开更多
The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the ...The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.展开更多
基金financially supported by the National Natural Science Foundation of China(Grant No.42104131)the Natural Science Foundation of Sichuan Province of China(Grant No.2022NSFSC1140)Open Fund(PLC20211101)of State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation
文摘The analysis technology of Amplitude Variation with Offset(AVO)is one of the important methods for oil and gas reservoir prediction.Zoeppritz equation and its approximations are the theoretical basis of AVO analysis,which assumes that the upper and lower media of a horizontal interface are single-phase media.Limited by this assumption,AVO analysis has limited prediction and identification accuracy for complex porous reservoirs.In view of this,the first-order approximate analytical expressions of oblique elastic wave at an interface of porous media are derived.Firstly,the incident and scattering characteristics of various waves at the interface of porous media are analyzed,and the displacement vectors generated by these elastic waves are described by exponential function.Secondly,the kinematic and dynamic boundary conditions at the interface of porous media are discussed.Thirdly,by substituting the displacement vectors of incident and scattered waves into boundary conditions,the exact analytical equation is derived.Then,considering the symmetry of scattering matrix in the equation,the exact analytical expressions of each scattered wave are obtained.Furthermore,under the assumptions of small incident angle,weak elasticity at an interface of porous media,and ignoring the second-and higherorder terms,the first-order approximate analytical expressions are derived.Establishing a model of sandstone porous media with different porosity in upper and lower media,the correctness of the approximate analytical expressions is verified,and the elastic wave response characteristics of lithology and pore fluids are analyzed.
基金Supported by the National Natural Science Foundation of China under Grant Nos 11474195,11274226,51478258 and 51405287
文摘We investigate the three-dimensional （3D） scattering problem of an incident plane shear horizontal wave by a partly through-thickness hole in an isotropic plate, in which the Lamb wave modes are also included due to the mode conversions by the scattering obstacle in the 3D problem. An analytical model is presented such that the wave fields are expanded in all of propagating and evanescent SH modes and Lamb modes, and the scattered far-fields of three fundamental guided wave modes are analyzed numerically for different sizes of the holes and frequencies. The numerical results are verified by comparing with those obtained by using the approximate Poisson/Mindlin plate model for small hole radius and low frequency. It is also found that the scattering patterns are different from those of the SO wave incidence. Our work is useful for quantitative evaluation of the plate-like structure by ultrasonic guided waves.
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Foundation item： Supported by the National Natural Science Foundation of China under Grant No. 51109032, and the National Natural Science Foundation of China under Grant No. 50921001.
文摘An experimental investigation of irregular wave forces on quasi-ellipse caisson structures is presented. Irregular waves were generated based on the Jonswap spectrum with two significant wave heights, and the spectrum peak periods range from 1.19 s to 1.81 s. Incident wave directions relative to the centre line of the multiple caissons are from 0＆#176; to 22.5＆#176;. The spacing between caissons ranges from 2 to 3 times that of the width of the caisson. The effects of these parameters on the wave forces of both the perforated and non-perforated caissons were compared and analyzed. It was found that the perforated caisson can reduce wave forces, especially in the transverse direction. Furthermore, the relative interval and incident wave direction have significant effects on the wave forces in the case of multiple caissons.
文摘The present study deals with the oblique wave trapping by a surface-piercing flexible porous barrier near a rigid wall in the presence of step-type bottoms under the assumptions of small amplitude water waves and the structural response theory in finite water depth.The modified mild-slope equation along with suitable jump conditions and the least squares approximation method are used to handle the mathematical boundary value problem.Four types of edge conditions,i.e.,clamped-moored,clamped-free,moored-free,and moored-moored,are considered to keep the barrier at a desired position of interest.The role of the flexible porous barrier is studied by analyzing the reflection coefficient,surface elevation,and wave forces on the barrier and the rigid wall.The effects of step-type bottoms,incidence angle,barrier length,structural rigidity,porosity,and mooring angle are discussed.The study reveals that in the presence of a step bottom,full reflection can be found periodically with an increase in(i)wave number and(ii)distance between the barrier and the rigid wall.Moreover,nearly zero reflection can be found with a suitable combination of wave and structural parameters,which is desirable for creating a calm region near a rigid wall in the presence of a step bottom.
