Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual wo...Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual work principles, three boundary integral equations which fit for arbitrary shapes, loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods.展开更多
Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time mi...Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice.展开更多
<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensio...<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient <em>θ </em>= <em>b/a =</em><em></em><span></span> 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. </div>展开更多
The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement wi...The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.展开更多
AVO (Amplitude variation with offset) technology is widely used in gas hydrate research. BSR (Bottom simulating reflector), caused by the huge difference in wave impedance between the hydrate reservoir and the underly...AVO (Amplitude variation with offset) technology is widely used in gas hydrate research. BSR (Bottom simulating reflector), caused by the huge difference in wave impedance between the hydrate reservoir and the underlying free gas reservoir, is the bottom boundary mark of the hydrate reservoir. Analyzing the AVO attributes of BSR can evaluate hydrate reservoirs. However, the Zoeppritz equation which is the theoretical basis of conventional AVO technology has inherent problems: the Zoeppritz equation does not consider the influence of thin layer thickness on reflection coefficients;the approximation of the Zoeppritz equation assumes that the difference of wave impedance between the two sides of the interface is small. These assumptions are not consistent with the occurrence characteristics of natural gas hydrate. The Brekhovskikh equation, which is more suitable for thin-layer reflection coefficient calculation, is used as the theoretical basis for AVO analysis. The reflection coefficients calculated by the Brekhovskikh equation are complex numbers with phase angles. Therefore, attributes of the reflection coefficient and its phase angle changing with offset are used to analyze the hydrate reservoir's porosity, saturation, and thickness. Finally, the random forest algorithm is used to predict the reservoir porosity, hydrate saturation, and thickness of the hydrate reservoir. In the synthetic data, the inversion results based on the four attributes of the Brekhovskikh equation are better than the conventional inversion results based on the two attributes of Zoeppritz, and the thickness can be accurately predicted. The proposed method also achieves good results in the application of Blake Ridge data. According to the method proposed in this paper, the hydrate reservoir in the area has a high porosity (more than 50%), and a medium saturation (between 10% and 20%). The thickness is mainly between 200m and 300m. It is consistent with the previous results obtained by velocity analysis.展开更多
In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in ste...In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.展开更多
煤层顶板砂岩富水性预测是有待解决的重要问题。以实际测井曲线数据为输入,利用Gassmann方程和AVO(Amplitude Variation with Offset)技术探讨煤层顶板砂岩富水性的预测方法。首先,利用实际测井曲线计算顶板砂岩的纵波速度、孔隙度和泥...煤层顶板砂岩富水性预测是有待解决的重要问题。以实际测井曲线数据为输入,利用Gassmann方程和AVO(Amplitude Variation with Offset)技术探讨煤层顶板砂岩富水性的预测方法。首先,利用实际测井曲线计算顶板砂岩的纵波速度、孔隙度和泥质含量;其次,以Han经验公式为基础,曲面拟合纵波速度、孔隙度和泥质含量间的关系式,并导出砂岩骨架纵波速度;再次,利用Castagna经验公式计算砂岩骨架的横波速度,并建立14种顶板砂岩模型;最后,利用Gassmann方程进行流体替换,计算各模型的纵横波速度和密度,从而正演模拟顶板砂岩的AVO响应。结合理论分析和实例预测,发现截距–梯度交会图可以区分砂岩孔隙度和干湿性,是顶板砂岩富水性预测的一种有效手段。展开更多
文摘Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual work principles, three boundary integral equations which fit for arbitrary shapes, loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates. It provides the fundamental theories for the application of BEM. A numerical example is given for clamped, simply supported and free boundary conditions. The results obtained are satisfactory as compared with the analytical methods.
基金supported by the Important National Science&Technology Specific Projects(No.2011ZX05019-003)the New Method and Technology Research Project of Geophysical Exploration of CNPC(No.2014A-3612)
文摘Stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter x_（eff） are correlated in the PS-converted-wave（PS-wave） anisotropic prestack Kirchhoff time migration（PKTM） velocity model and are thus difficult to independently determine.We extended the simplified two-parameter（stacking velocity V_（C2） and anisotropic parameter k_（eff）） moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter（stacking velocity V_（C2）,vertical velocity ratio γ_0,effective velocity ratio γ_（eff）,and anisotropic parameter k_（eff）） PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified twoparameter moveout equation.In the proposed method,first,the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters;then,the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration.The vertical velocity ratio γ_0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration.The initial effective velocity ratio γ_（eff） is calculated using the Thomsen（1999） equation in combination with the P-wave velocity analysis;ultimately,the final velocity model of the effective velocity ratio γ_（eff） is obtained by percentage scanning migration.This method simplifies the PS-wave parameter estimation in high-quality imaging,reduces the uncertainty of multiparameter estimations,and obtains good imaging results in practice.
文摘<div style="text-align:justify;"> The ellipse and the superellipse are both planar closed curves with a double axis of symmetry. Here we show the isoconcentration contour of the simplified two-dimensional advection-diffusion equation from a stable line source in the center of a wide river. A new two-parameter heteromorphic elliptic equation with a single axis of symmetry is defined. The values of heights, at the point of the maximum width and that of the centroid of the heteromorphic ellipse, are derived through mathematical analysis. Taking the compression coefficient <em>θ </em>= <em>b/a =</em><em></em><span></span> 1 as the criterion, the shape classification of H-type, Standard-type and W-type for heteromorphic ellipse have been given. The area formula, the perimeter theorem, and the radius of curvature of heteromorphic ellipses, and the geometric properties of the rotating body are subsequently proposed. An illustrative analysis shows that the inner contour curve of a heteromorphic elliptic tunnel has obvious advantages over the multiple- arc splicing cross section. This work demonstrates that the heteromorphic ellipses have extensive prospects of application in all categories of tunnels, liquid transport tanks, aircraft and submarines, bridges, buildings, furniture, and crafts. </div>
文摘The n-power two-parameter universal equation for rotational spectra which we deduced recently is appliedto the description of the rotational bands of several diatomic and tetra-atomic molecules. Excellent agreement withexperimental data can be obtained with small n values. The relation between our equation and the famous Dunhamformula is discussed.
基金The research is funded by the National Natural Science Foundation of China(No.12171455)the Original Innovation Research Program of the Chinese Academy of Sciences(CAS)under grant number ZDBS-LY-DQC003the Key Research Programs IGGCAS-2019031.
文摘AVO (Amplitude variation with offset) technology is widely used in gas hydrate research. BSR (Bottom simulating reflector), caused by the huge difference in wave impedance between the hydrate reservoir and the underlying free gas reservoir, is the bottom boundary mark of the hydrate reservoir. Analyzing the AVO attributes of BSR can evaluate hydrate reservoirs. However, the Zoeppritz equation which is the theoretical basis of conventional AVO technology has inherent problems: the Zoeppritz equation does not consider the influence of thin layer thickness on reflection coefficients;the approximation of the Zoeppritz equation assumes that the difference of wave impedance between the two sides of the interface is small. These assumptions are not consistent with the occurrence characteristics of natural gas hydrate. The Brekhovskikh equation, which is more suitable for thin-layer reflection coefficient calculation, is used as the theoretical basis for AVO analysis. The reflection coefficients calculated by the Brekhovskikh equation are complex numbers with phase angles. Therefore, attributes of the reflection coefficient and its phase angle changing with offset are used to analyze the hydrate reservoir's porosity, saturation, and thickness. Finally, the random forest algorithm is used to predict the reservoir porosity, hydrate saturation, and thickness of the hydrate reservoir. In the synthetic data, the inversion results based on the four attributes of the Brekhovskikh equation are better than the conventional inversion results based on the two attributes of Zoeppritz, and the thickness can be accurately predicted. The proposed method also achieves good results in the application of Blake Ridge data. According to the method proposed in this paper, the hydrate reservoir in the area has a high porosity (more than 50%), and a medium saturation (between 10% and 20%). The thickness is mainly between 200m and 300m. It is consistent with the previous results obtained by velocity analysis.
基金Foundation item: Hubei University Youngth Foundations (099206).
文摘In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the non-Lipschitz conditions. We use a martingale formula in stead of Ito formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.
文摘煤层顶板砂岩富水性预测是有待解决的重要问题。以实际测井曲线数据为输入,利用Gassmann方程和AVO(Amplitude Variation with Offset)技术探讨煤层顶板砂岩富水性的预测方法。首先,利用实际测井曲线计算顶板砂岩的纵波速度、孔隙度和泥质含量;其次,以Han经验公式为基础,曲面拟合纵波速度、孔隙度和泥质含量间的关系式,并导出砂岩骨架纵波速度;再次,利用Castagna经验公式计算砂岩骨架的横波速度,并建立14种顶板砂岩模型;最后,利用Gassmann方程进行流体替换,计算各模型的纵横波速度和密度,从而正演模拟顶板砂岩的AVO响应。结合理论分析和实例预测,发现截距–梯度交会图可以区分砂岩孔隙度和干湿性,是顶板砂岩富水性预测的一种有效手段。
