Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away fr...Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away from the borehole. Remote acoustic logging uses phase-controlled array-transmitting and long sound probes that increase the depth of investigation. The interpretation of logging data with respect to fractures is typically guided by practical experience rather than theory and is often ambiguous. We use remote acoustic reflection logging data and high-order finite-difference approximations in the forward modeling and prestack reverse-time migration to image fractures. First, we perform forward modeling of the fracture responses as a function of the fracture-borehole wall distance, aperture, and dip angle. Second, we extract the energy intensity within the imaging area to determine whether the fracture can be identified as the formation velocity is varied. Finally, we evaluate the effect of the fracture-borehole distance, fracture aperture, and dip angle on fracture identification.展开更多
Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI me...Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI media）. This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer （PML） absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.展开更多
Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelo...Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.展开更多
As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elim...Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting （GESP） method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.展开更多
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobiell...A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.展开更多
The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo se...The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.展开更多
The standard and high-order Gaussian beam solutions for gravitational wave is obtained in the linear approximation of vacuum Einstein equation under harmonic conditions.
A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified w...A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.展开更多
The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuo...The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.展开更多
基金supported by National Petroleum Major Project(Grant No.2011ZX05020-008)
文摘Fracture identification is important for the evaluation of carbonate reservoirs. However, conventional logging equipment has small depth of investigation and cannot detect rock fractures more than three meters away from the borehole. Remote acoustic logging uses phase-controlled array-transmitting and long sound probes that increase the depth of investigation. The interpretation of logging data with respect to fractures is typically guided by practical experience rather than theory and is often ambiguous. We use remote acoustic reflection logging data and high-order finite-difference approximations in the forward modeling and prestack reverse-time migration to image fractures. First, we perform forward modeling of the fracture responses as a function of the fracture-borehole wall distance, aperture, and dip angle. Second, we extract the energy intensity within the imaging area to determine whether the fracture can be identified as the formation velocity is varied. Finally, we evaluate the effect of the fracture-borehole distance, fracture aperture, and dip angle on fracture identification.
基金supported by the National Natural Science Foundation of China(No.41674118)the national science and technology major project(No.2016ZX05027-002)
文摘Based on the pure quasi-P wave equation in transverse isotropic media with a vertical symmetry axis （VTI media）, a quasi-P wave equation is obtained in transverse isotropic media with a tilted symmetry axis （TTI media）. This is achieved using projection transformation, which rotates the direction vector in the coordinate system of observation toward the direction vector for the coordinate system in which the z-component is parallel to the symmetry axis of the TTI media. The equation has a simple form, is easily calculated, is not influenced by the pseudo-shear wave, and can be calculated reliably when δ is greater than ε. The finite difference method is used to solve the equation. In addition, a perfectly matched layer （PML） absorbing boundary condition is obtained for the equation. Theoretical analysis and numerical simulation results with forward modeling prove that the equation can accurately simulate a quasi-P wave in TTI medium.
文摘Using trial equation method, abundant exact envelope traveling wave solutions of high-order dispersive cubic-quintic nonlinear Schr6dinger equation, which include envelope soliton solutions, triangular function envelope solutions, and Jacobian elliptic function envelope solutions, are obtained. To our knowledge, all of these results are new. In particular, our proposed method is very simple and can be applied to a lot of similar equations.
文摘As an improved version of trial equation method, a new trial equation method is proposed. Using this method, abundant new exact traveling wave solutions to a high-order KdV-type equation are obtained.
基金supported by China State Key Science and Technology Project on Marine Carbonate Reservoir Characterization (No. 2008ZX05004-006)
文摘Frequency domain wave equation forward modeling is a problem of solving large scale linear sparse systems which is often subject to the limits of computational efficiency and memory storage. Conventional Gaussian elimination cannot resolve the parallel computation of huge data. Therefore, we use the Gaussian elimination with static pivoting （GESP） method for sparse matrix decomposition and multi-source finite-difference modeling. The GESP method does not only improve the computational efficiency but also benefit the distributed parallel computation of matrix decomposition within a single frequency point. We test the proposed method using the classic Marmousi model. Both the single-frequency wave field and time domain seismic section show that the proposed method improves the simulation accuracy and computational efficiency and saves and makes full use of memory. This method can lay the basis for waveform inversion.
基金National Natural Science Foundation of China under Grant Nos 10472063 and 10772110
文摘A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.
文摘The aim of this paper is to obtain the approximate analytical solution of a fractional Zakharov-Kuznetsov equation by using homotopy perturbation method (HPM). The fractional derivatives are described in the Caputo sense. Several examples are given and the results are compared to exact solutions. The results reveal that the method is very effective and simple.
文摘The standard and high-order Gaussian beam solutions for gravitational wave is obtained in the linear approximation of vacuum Einstein equation under harmonic conditions.
基金supported by the National Natural Science Foundation of China(Grant Nos.11032006,11072094,and 11121202)the Ph.D.Program Foundation of Ministry of Education of China(Grant No.20100211110022)+2 种基金the National Key Project of Magneto-Constrained Fusion Energy Development Program(Grant No.2013GB110002)the Fundamental Research Funds for the Central Universities(Grant No.lzujbky-2013-1)the Scholarship Award for Excellent Doctoral Student granted by the Lanzhou University
文摘A wavelet method is proposed to solve the Burgers’equation.Following this method,this nonlinear partial differential equation is first transformed into a system of ordinary differential equations using the modified wavelet Galerkin method recently developed by the authors.Then,the classical fourth-order explicit Runge–Kutta method is employed to solve the resulting system of ordinary differential equations.Such a wavelet-based solution procedure has been justified by solving two test examples:results demonstrate that the proposed method has a much better accuracy and efficiency than many other existing numerical methods,and whose order of convergence can go up to 5.Most importantly,our results also indicate that the present wavelet method can readily deal with those fluid dynamics problems with high Reynolds numbers.
基金supported by the National Natural Science Foundation of China under Grant Nos.10671184 and 10971203
文摘The standard finite elements of degree p over the rectangular meshes are applied to solve a kind of nonlinear viscoelastic wave equations with nonlinear boundary conditions, and the superclose property of the continuous Galerkin approximation is derived without using the nonclassical elliptic projection of the exact solution of the model problem. The global superconvergence of one order higher than the traditional error estimate is also obtained through the postprocessing technique.
