Statistical distribution of depth-integrated local horizontal momentum for second-order random ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth- integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

波动方程模拟与偏移的实用化方法研究

Along with the widespread and in-depth applications in petroleum prospecting and development, the seismic modeling and migration technologies are proposed with a higher requirement by oil industrial, and the related practical demand is getting more and more urgent. Based on theories of modeling and migration methods for wave equation, both related with velocity model, I thoroughly research and develop some methods for the goal of highly effective and practical in this dissertation. In the first part, this dissertation probes into the layout designing by wave equations modeling, focusing on the target-oriented layout designing method guided by wave equation modeling in complicated structure areas. It is implemented by using the fourth order staggered grid finite difference (FD) method in velocity-stress 2D acoustic wave equations plus perfectly matched layer (PML) absorbing boundary condition. To design target-oriented layout: (a) match the synthetic record on the surface with events of subsurface structures by analyzing the snapshots of theoretical model; (b) determine the shot-gather distance by tracking the events of target areas and measuring the receiving range when it reaches the surface; (c) restrict the range of valid shot-gather distance by drawing seismic windows in single shot records; (d) choose the best trace distance by comparing the resolution of prospecting targets from the simulated records with different trace distance. Eventually, we obtained the observation system parameters, which achieve the design requirements. In the second part, this dissertation presents the practical method to improve the 3D Fourier Finite Difference (FFD) migration, and carefully analyzes all the factors which influence 3D FFD migration’s efficiency. In which, one of the most important parameters of migration is the extrapolating step. This dissertation presents an efficient 3D FFD migration algorithm, which use FFD propagator to extrapolate wavefields over big layers, and use Born-Kirchhoff interpolator to image wavefields over small layers between the big ones. Finally, I show the effectiveness of this hybrid migration method by comparing migration results from 3D SEG/EAGE model with different methods.

复杂介质中地震波场数值模拟研究——基于广义正交多项式迭积微分算子法

In this paper, we propose a new numerical modeling method – Convolutional Forsyte Polynomial Differentiator (CFPD), aimed at simulating seismic wave propagation in complex media with high efficiency and accuracy individually owned by short-scheme finite differentiator and general convolutional polynomial method. By adjusting the operator length and optimizing the operator coefficient, both global and local informations can be easily incorporated into the wavefield which is important to invert the undersurface geological structure. The key issue in this paper is to introduce the convolutional differentiator based on Forsyte generalized orthogonal polynomial in mathematics into the spatial differentiation of the first velocity-stress equation. To match the high accuracy of the spatial differentiator, this method in the time coordinate adopts staggered grid finite difference instead of conventional finite difference to model seismic wave propagation in heterogeneous media. To attenuate the reflection artifacts caused by artificial boundary, Perfectly Matched Layer (PML) absorbing boundary is also being considered in the method to deal with boundary problem due to its advantage of automatically handling large-angle emission. The PML formula for acoustic equation and first-order velocity-stress equation are also derived in this paper. There is little difference to implement the PML boundary condition in all kind of wave equations, but in Biot media, special attenuation factors should be taken. Numerical results demonstrate that the PML boundary condition is better than Cerjan absorbing boundary condition which makes it more suitable to hand the artificial boundary reflection. Based on the theories of anisotropy, Biot two-phase media and viscous-elasticity, this paper constructs the constitutive relationship for viscous-elastic and two-phase media, and further derives the first-order velocity-stress equation for 3D viscous-elastic and two-phase media. Numerical modeling using CFPD method is carried out in the above-mentioned media. The results modeled in the viscous-elastic media and the anisotropic pore elastic media can better explain wave phenomena of the true earth media, and can also prove that CFPD is a useful numerical tool to study the wave propagation in complex media.

复杂介质边界元法数值模拟研究

A major impetus to study the rough surface and complex structure in near surface model is because accuracy of seismic observation and geophysical prospecting can be improved. Wave theory study about fluid-satuated porous media has important significance for some scientific problems, such as explore underground resources, study of earth's internal structure, and structure response of multi-phase porous soil under dynamic and seismic effect. Seismic wave numerical modeling is one of the effective methods which understand seismic propagation rules in complex media. As a numerical simulation method, boundary element methods had been widely used in seismic wave field study. This paper mainly studies randomly rough surface scattering which used some approximation solutions based on boundary element method. In addition, I developed a boundary element solution for fluid saturated porous media. In this paper, we used boundary element methods which based on integral expression of wave equation to study the free rough surface scattering effects of Kirchhoff approximation method, Perturbation approximation method, Rytov approximation method and Born series approximation method. Gaussian spectrum model of randomly rough surfaces was chosen as the benchmark model. The approximation methods result were compared with exact results which obtained by boundary element methods, we study that the above approximation methods were applicable how rough surfaces and it is founded that this depends on and ( here is the wavenumber of the incident field, is the RMS height and is the surface correlation length ). In general, Kirchhoff approximation which ignores multiple scatterings between any two surface points has been considered valid for the large-scale roughness components. Perturbation theory based on Taylor series expansion is valid for the small-scale roughness components, as and are .Tests with the Gaussian topographies show that the Rytov approximation methods improves the Kirchhoff approximation in both amplitude and phase but at the cost of an extra treatment of transformation for the wave fields. The realistic methods for the multiscale surfaces come with the Born series approximation and the second-order Born series approximation might be sufficient to guarantee the accuracy of randomly rough surfaces. It could be an appropriate choice that a complex rough surface can be divided into large-, medium-, and small-scale roughness components with their scattering features be studied by the Kirchhoff or Rytov phase approximations, the Born series approximation, and the perturbation theory, respectively. For this purpose, it is important to select appropriate parameters that separate these different scale roughness components to guarantee the divided surfaces satisfy the physical assumptions of the used approximations, respectively. In addition, in this paper, the boundary element methods are used for solving the porous elastic wave propagation and carry out the numerical simulation. Based on the fluid-saturated porous model, this paper analyses and presents the dynamic equation of elastic wave propagation and boundary integral equation formulation of fluid saturated porous media in frequency domain. The fundamental solutions of the elastic wave equations are obtained according to the similarity between thermoelasticity and poroelasticity. At last, the numerical simulation of the elastic wave propagation in the two-phase isotropic media is carried out by using the boundary element method. The results show that a slow quasi P-wave can be seen in both solid and fluid wave-field synthetic seismograms. The boundary element method is effective and feasible.

Wave dynamic processes induced by a supersonic projectile discharging from a shock tube

A numerical study on wave dynamic processes occurring in muzzle blast flows, which are created by a supersonic projectile released from the open-end of a shock tube into ambient air, is described in this paper. The Euler equations, assuming axisymmetric flows, are solved by using a dispersion-controlled scheme implemented with moving boundary conditions. Three test cases are simulated for examining friction effects on the muzzle flow. From numerical simulations, the wave dynamic processes, including two blast waves, two jet flows, the bow shock wave and their interactions in the muzzle blasts, are demonstrated and discussed in detail. The study shows that the major wave dynamic processes developing in the muzzle flow remain similar when the friction varies, but some wave processes, such as shock-shock interactions, shock-jet interactions and the contact surface instability, get more intensive, which result in more complex muzzle blast flows.

Three-Dimensional Propagation of the Transmitted Shock Wave in a Square Cross-Sectional Chamber

An investigation into the three-dimensional propagation of the transmitted shock wave in a square cross-section chamber was described in this paper, and the work was carried out numerically by solving the Euler equations with a dispersion-controlled scheme. Computational images were constructed from the density distribution of the transmitted shock wave discharging from the open end of the square shock tube and compared directly with holographic interferograms available for CFD validation. Two cases of the transmitted shock wave propagating at different Mach numbers in the same geometry were simulated. A special shock reflection system near the corner of the square cross-section chamber was observed, consisting of four shock waves: the transmitted shock wave, two reflection shock waves and a Mach stem. A contact surface may appear in the four-shock system when the transmitted shock wave becomes stronger. Both the secondary shock wave and the primary vortex loop are three-dimensional in the present case due to the non-uniform flow expansion behind the transmitted shock.

Dust-Cloud Structures behind a Shock Wave Moving Over a Deposited Layer of Fine Particles

The present paper investigates dispersed-phase flow structures of a dust cloud induced by a normal shock wave moving at a constant speed over a flat surface deposited with fine particles. In the shock-fitted coordinates, the general equations of dusty-gas

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

A generalized wave action conservative equation for the dissipative dynamical system in the nearshore region

To describe the various complex mechanisms of the dissipative dynamical system between waves, currents, and bottoms in the nearshore region that induce typically the wave motion on large-scale variation of ambient currents, a generalized wave action equation for the dissipative dynamical system in the nearshore region is developed by using the mean-flow equations based on the Navier-Stokes equations of viscous fluid, thus raising two new concepts: the vertical velocity wave action and the dissipative wave action, extending the classical concept, wave action, from the ideal averaged flow conservative system into the real averaged flow dissipative system (that is, the generalized conservative system). It will have more applications.

Upwind compact scheme with dispersion control for aerodynamic equations

A compact upwind scheme with dispersion control is developed using a dissipation analogy of the dispersion term. The term is important in reducing the unphysical fluctuations in numerical solutions. The scheme depends on three free parameters that may be used to regulate the size of dissipation as well as the size and direction of dispersion. A coefficient to coordinate the dispersion is given. The scheme has high accuracy, the method is simple, and the amount of computation is small. It also has a good capability of capturing shock waves. Numerical experiments are carried out with two-dimensional shock wave reflections and the results are very satisfactory.

Perturbational finite volume scheme for the one-dimensional Navier-Stokes equations

Starting from the second-order finite volume scheme,though numerical value perturbation of the cell facial fluxes, the perturbational finite volume (PFV) scheme of the Navier-Stokes (NS) equations for compressible flow is developed in this paper. The central PFV scheme is used to compute the one-dimensional NS equations with shock wave.Numerical results show that the PFV scheme can obtain essentially non-oscillatory solution.

instability of standing wave, global existence and blowup for the klein-gordon-zakharov system with different-degree nonlinearities

This paper discusses the Klein–Gordon–Zakharov system with different-degree nonlinearities in two and three space dimensions. Firstly, we prove the existence of standing wave with ground state by applying an intricate variational argument. Next, by introducing an auxiliary functional and an equivalent minimization problem, we obtain two invariant manifolds under the solution flow generated by the Cauchy problem to the aforementioned Klein–Gordon–Zakharov system. Furthermore, by constructing a type of constrained variational problem, utilizing the above two invariant manifolds as well as applying potential well argument and concavity method, we derive a sharp threshold for global existence and blowup. Then, combining the above results, we obtain two conclusions of how small the initial data are for the solution to exist globally by using dilation transformation. Finally, we prove a modified instability of standing wave to the system under study.

Four-wave mixing self-stability based on photonic crystal fiber and its applications on erbium-doped fiber lasers

The analytic solutions of coupled-mode equations of four-wave mixings (FWMs) are achieved by means of the undepleted approximation and the perturbation method. The self-stability mechanism of the FWM processes is theoretically proved and is applicable to design a new kind of triple-wavelength erbium-doped fiber lasers. The proposed fiber lasers with excellent stability and uniformity are demonstrated by using a flat-near-zero-dispersion high-nonlinear photonic-crystal-fiber. The significant excellence is analyzed in theory and is proved in experiment. Our fiber lasers can stably lase three waves with the power ripple of less than 0.4 dB. (c) 2005 Elsevier B.V. All rights reserved.

Choice of calibration equations of the TSM method

For the reciprocal-test fixtures, there are six independent S-parameters to. be determined, and the thru-short-match (TSM) calibration can provide eight calibration equations. In this paper, the relation of calibration equations is investigated. It has been shown that the four equations obtained from the measurement with a transmission standard can be used simultaneously in the calibration. Experimental results show that the different choice of equations will lead to quite different solution, and the calibration accuracy can be improved by taking advantages of the established relation among the calibration equations and properly choosing calibration equations.

Third-order Stokes wave solutions for interfacial internal waves in a three-layer density-stratified fluid

Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular method, and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. as expected, the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves. The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.