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.

复杂裂隙岩体统计断裂本构关系与变形参数研究

Rock mass is widely recognized as a kind of geologic body which consists of rock blocks and discontinuities. The deformation and failure of rock mass is not only determined by rock block，but also by discontinuity which is virtually more important. Mutual cutting and combination of discontinuities controlled mechanical property of rock mass. The complex cutting of discontinuities determine the intense anisotropy on mechanical property of rock mass，especially under the effect of ground stress. Engineering practice has show that the brittle failure of hard rock always occurs when its working stress is far lower than the yield strength and compressive strength，the failure always directly related to the fracture propagation of discontinuities. Fracture propagation of discontinuities is the virtue of hard rock’s failure. We can research the rock mass discontinuous mechanical properties precisely by the methods of statistical analysis of discontinuities and Fracture Mechanics. According to Superposition Principle in Fracture Mechanics，A Problem or C Problem could be chosen to research. Problem A mainly calculates the crack-tip stress field and displacement field on internal discontinuities by numerical method. Problem C calculate the crack-tip stress field and displacement field under the assumption of that the mainly rock mass stress field has been known. So the Problem C avoid the complex mutual interference of stress fields of discontinuities，which is called crack system problem in Fracture Mechanics. To solve Problem C, field test on stress field in the rock mass is needed. The linear Superposition of discontinuities strain energies are Scientific and Rational. The difference of Fracture Mechanics between rock mass and other materials can mostly expression as：other materials Fracture Mechanics mostly face the problem A，and can’t avoid multi-crack puzzle, while the Rock mass Fracture Mechanics answer to the Problem C. Problem C can avoid multi-discontinuities mutual interference puzzle via the ground stress test. On the basis of Problem C, Fracture Mechanics could be used conveniently in rock mass. The rock mass statistics fracture constitutive relations, which introduced in this article, are based on the Problem C and the Discontinuity Strain Energy linear superposition. This constitutive relation has several merits: first, it is physical constitutive relation rather than empirical; second, it is very fit to describe the rock mass anisotropy properties; third, it elaborates the exogenous factors such as ground stress. The rock mass statistics fracture constitutive relation is the available approach to answer to the physical, anisotropic and ground stress impacted rock mass problems. This article stand on the foundation of predecessor’s statistics fractures constitutive relation, and improved the discontinuity distributive function. This article had derived the limitation of negative exponential distribution in the course of regression analysis, and advocated to using the two parameter negative exponential distribution for instead. In order to solve the problems of two-dimension stability on engineering key cross-sectional view in rock mass, this article derived the rock mass planar flexibility tensor, and established rock mass two-dimension penetrate statistics fracture constitutive relation on the basis of penetrate fracture mechanics. Based on the crack tip plasticity research production of penetrate fracture, for example the Irwin plasticity equifinality crack, this article established the way to deal with the discontinuity stress singularity and plastic yielding problem at discontinuity tip. The research on deformation parameters is always the high light region of rock mass mechanics field. After the dam foundation excavation of XiaoWan hydroelectric power station, dam foundation rock mass upgrowthed a great deal of unload cracks, rock mass mechanical property gotten intricacy and strong anisotropy. The dam foundation rock mass mostly upgrowthed three group discontinuities： the decantation discontinuity, the steep pitch discontinuity, and the schistosity plane. Most of the discontinuities have got partial unload looseness. In accordance with ground stress field data, the dam foundation stress field greatly non-uniform, which felled under the great impaction of tectonic stress field, self-weight stress field, excavation geometric boundary condition, and excavation, unload. The discontinuity complexity and stress field heterogeneity, created the rock mass mechanical property of dam foundation intricacy and levity. The research on the rock mass mechanics, if not take every respected influencing factor into consideration as best as we can, major errors likely to be created. This article calculated the rock mass elastic modulus that after Xiao Wan hydroelectric power station dam foundation gutter excavation finished. The calculation region covered possession monolith of Xiao Wan concrete double-curvature arch dam. Different monolith were adopted the penetrate fracture statistics constitutive relation or bury fracture statistics constitutive relation selectively. Statistics fracture constitutive relation is fit for the intensity anisotropy and heterogeneity rock mass of Xiao Wan hydroelectric power station dam foundation. This article had contrastive analysis the statistics fracture constitutive relation result with the inclined plane load test actual measurement elastic modulus and RMR method estimated elastic modulus, and find that the three methods elastic modulus have got greatly comparability. So, the statistics fracture constitutive relations are qualified for trust. Generally speaking，this article had finished following works based on predecessors job: “Argumentation the C Problems of superposition principle in Fracture Mechanics, establish two-dimension penetrate statistics fracture constitutive relation of rock mass, argue the negative exponential distribution limitation and improve it, improve of the three-dimension berry statistics fracture constitutive relation of rock mass, discontinuity-tip plastic zone isoeffect calculation, calculate the rock mass elastic modulus on two-dimension cross-sectional view”. The whole research clue of this article inherited from the “statistics rock mass mechanics” of Wu Faquan（1992）.

地震波场模拟及叠前深度偏移的李群方法

The processes of seismic wave propagation in phase space and one way wave extrapolation in frequency-space domain, if without dissipation, are essentially transformation under the action of one parameter Lie groups. Consequently, the numerical calculation methods of the propagation ought to be Lie group transformation too, which is known as Lie group method. After a fruitful study on the fast methods in matrix inversion, some of the Lie group methods in seismic numerical modeling and depth migration are presented here. Firstly the Lie group description and method of seismic wave propagation in phase space is proposed, which is, in other words, symplectic group description and method for seismic wave propagation, since symplectic group is a Lie subgroup and symplectic method is a special Lie group method. Under the frame of Hamiltonian, the propagation of seismic wave is a symplectic group transformation with one parameter and consequently, the numerical calculation methods of the propagation ought to be symplectic method. After discrete the wave field in time and phase space, many explicit, implicit and leap-frog symplectic schemes are deduced for numerical modeling. Compared to symplectic schemes, Finite difference (FD) method is an approximate of symplectic method. Consequently, explicit, implicit and leap-frog symplectic schemes and FD method are applied in the same conditions to get a wave field in constant velocity model, a synthetic model and Marmousi model. The result illustrates the potential power of the symplectic methods. As an application, symplectic method is employed to give synthetic seismic record of Qinghai foothills model. Another application is the development of Ray+symplectic reverse-time migration method. To make a reasonable balance between the computational efficiency and accuracy, we combine the multi-valued wave field & Green function algorithm with symplectic reverse time migration and thus develop a new ray+wave equation prestack depth migration method. Marmousi model data and Qinghai foothills model data are processed here. The result shows that our method is a better alternative to ray migration for complex structure imaging. Similarly, the extrapolation of one way wave in frequency-space domain is a Lie group transformation with one parameter Z and consequently, the numerical calculation methods of the extrapolation ought to be Lie group methods. After discrete the wave field in depth and space, the Lie group transformation has the form of matrix exponential and each approximation of it gives a Lie group algorithm. Though Pade symmetrical series approximation of matrix exponential gives a extrapolation method which is traditionally regarded as implicit FD migration, it benefits the theoretic and applying study of seismic imaging for it represent the depth extrapolation and migration method in a entirely different way. While, the technique of coordinates of second kind for the approximation of the matrix exponential begins a new way to develop migration operator. The inversion of matrix plays a vital role in the numerical migration method given by Pade symmetrical series approximation. The matrix has a Toepelitz structure with a helical boundary condition and is easy to inverse with LU decomposition. A efficient LU decomposition method is spectral factorization. That is, after the minimum phase correlative function of each array of matrix had be given by a spectral factorization method, all of the functions are arranged in a position according to its former location to get a lower triangular matrix. The major merit of LU decomposition with spectral factorization (SF Decomposition) is its efficiency in dealing with a large number of matrixes. After the setup of a table of the spectral factorization results of each array of matrix, the SF decomposition can give the lower triangular matrix by reading the table. However, the relationship among arrays is ignored in this method, which brings errors in decomposition method. Especially for numerical calculation in complex model, the errors is fatal. Direct elimination method can give the exact LU decomposition But even it is simplified in our case, the large number of decomposition cost unendurable computer time. A hybrid method is proposed here, which combines spectral factorization with direct elimination. Its decomposition errors is 10 times little than that of spectral factorization, and its decomposition speed is quite faster than that of direct elimination, especially in dealing with a large number of matrix. With the hybrid method, the 3D implicit migration can be expected to apply on real seismic data. Finally, the impulse response of 3D implicit migration operator is presented.

ω循环型预条件矩阵及其应用

In this paper, we apply the preconditioned conjugate gradient method to the solution of positive-definite Toeplitz systems, especially we introduce a new kind of co-circulant preconditioners Pn[ca] by the use of embedding method. We have also discussed the properties of these new preconditioners and proved that many of former preconditioners can be considered as some special cases of Pn[co\. Because of the introduction of co-circulant preconditioners pn[a>], we can greatly overcome the singularity caused by circulant preconditioners. We have discussed the oo-circulant series and functions. We compare the ordinary circularity with the co-circularity, showing that the latter one can be considered as the extended form of the former one; correspondingly, many methods and theorems of the ordinary circularity can be extended. Furthermore, we present the co-circulant decompositional method. By the use of this method, we can divide any co-circulant signal into a summation of many sub-signals; especially among those sub-signals, there are many subseries of which their period is just equal to 1, which are actually the frequency elements of the original co-circulant signal. In this way, we can establish the relationship between the signal and its frequency elements, that is, the frequency elements hi the frequency domain are actually signals with the period of 1 in the spatial domain. We have also proved that the co-circulant has already existed in the traditional Fourier theory. By the use of different criteria for constructing preconditioners, we can get many different preconditioned systems. From the preconditioned systems PN[conditioned systems instead of the given Toeplitz systems to get some approximate solutions. Theoretical analysis and actually numerical experiments have already proved the effectiveness of this approximation. By combining the co-circulant with the boundary condition, we can overcome end effects efficiently. We have also presented the co-circulant boundary condition and compared it with the helix boundary condition. Furthermore, we can also get another new boundary condition: the mixed boundary condition. Numerical experiments have proved that the co-circulant boundary condition is better than the mixed one while the helix boundary condition is the worst among them.

地震偏移宽角吸收边界条件和Toeplitz矩阵反演中的边界效应研究

The content of this paper is based on the research work while the author took part in the key project of NSFC and the key project of Knowledge Innovation of CAS. The whole paper is expanded by introduction of the inevitable boundary problem during seismic migration and inversion. Boundary problem is a popular issue in seismic data processing. At the presence of artificial boundary, reflected wave which does not exist in reality comes to presence when the incident seismic wave arrives at the artificial boundary. That will interfere the propagation of seismic wave and cause alias information on the processed profile. Furthermore, the quality of the whole seismic profile will decrease and the subsequent work will fail.This paper has also made a review on the development of seismic migration, expatiated temporary seismic migration status and predicted the possible break through. Aiming at the absorbing boundary problem in migration, we have deduced the wide angle absorbing boundary condition and made a compare with the boundary effect of Toepiitz matrix fast approximate computation.During the process of fast approximate inversion computation of Toepiitz system, we have introduced the pre-conditioned conjugate gradient method employing co circulant extension to construct pre-conditioned matrix. Especially, employment of combined preconditioner will reduce the boundary effect during computation.Comparing the boundary problem in seismic migration with that in Toepiitz matrix inversion we find that the change of boundary condition will lead to the change of coefficient matrix eigenvalues and the change of coefficient matrix eigenvalues will cause boundary effect. In this paper, the author has made an qualitative analysis of the relationship between the coefficient matrix eigenvalues and the boundary effect. Quantitative analysis is worthy of further research.

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations.

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

Application of enthalpy method for moving boundary problem in laser surface melting

A numerical analysis was carried out to study the moving boundary problem in the physical process of pulsed Nd-YAG laser surface melting prior to vaporization. The enthalpy method was applied to solve this two-phase axisymmetrical melting problem Computational results of temperature fields were obtained, which provide useful information to practical laser treatment processing. The validity of enthalpy method in solving such problems is presented.

Direct Numerical Simulation of a Spatially Evolving Supersonic Turbulent Boundary Layer at Ma=6

Direct numerical simulation is carried out for a spatially evolving supersonic turbulent boundary layer at free-stream Mach number 6. To overcome numerical instability, the seventh-order WENO scheme is used for the convection terms of Navier-Stokes equations, and fine mesh is adopted to minimize numerical dissipation. Compressibilty effects on the near-wall turbulent kinetic energy budget are studied. The cross-stream extended self-similarity and scaling exponents including the near-wall region are studied. In high Mach number flows, the coherence vortex structures are arranged to be smoother and streamwised, and the hair-pin vortices are less likely to occur.

Boundary knot method for 2D and 3D Helmholtz and convection-diffusion problems under complicated geometry

The boundary knot method (BKM) of very recent origin is an inherently meshless, integration-free, boundary-type, radial basis function collocation technique for the numerical discretization of general partial differential equation systems. Unlike the method of fundamental solutions, the use of non-singular general solution in the BKM avoids the unnecessary requirement of constructing a controversial artificial boundary outside the physical domain. The purpose of this paper is to extend the BKM to solve 2D Helmholtz and convection-diffusion problems under rather complicated irregular geometry. The method is also first applied to 3D problems. Numerical experiments validate that the BKM can produce highly accurate solutions using a relatively small number of knots. For inhomogeneous cases, some inner knots are found necessary to guarantee accuracy and stability. The stability and convergence of the BKM are numerically illustrated and the completeness issue is also discussed.

Experimental Study on Vortex-Induced Vibrations of a Pipeline Near a Plane Boundary in Steady Flow

对单向水流作用下近壁管道横向涡激振动进行了实验模拟,重点探讨了管道与壁面间隙比(e/D)对管道涡激振动幅值和涡激振动频率响应特性的影响规律.实验结果表明,管道与壁面间隙宽度对管道涡激振动特性有较明显影响.在较大间隙比(e/D＞0.66)下,管道振幅随着Vr数的增大先快速增长到最大值,然后平缓下降;在振动初期(即Vr数较小时),管道振动频率变化基本符合Strouhal规律;在振动中后期(即Vr数较大时),管道振动频率变化不符合Strouhal规律,而在管道固有频率附近缓慢增长.在较小间隙比(e/D＜0.30)下,管道振幅随Vr数的增大先平缓上升到最大值,随后较快速下降;在振动初期,管道振动频率变化不遵循Strouhal规律;在整个振动范围内,与较大间隙比情况相比,随着Vr数增加,管道振动频率增长幅度明显较大.

Acoustic Emission Experiments of Rock Failure under Load Simulating the Hypocenter Condition

A series of acoustic emission (AE) experiments of rock failure have been conducted under cyclic load in tri-axial stress tests. To simulate the hypocenter condition the specimens are loaded by the combined action of a constant stress, intended to simulate

Heat-Transfer Study of External Superheater of CFB Incinerator

The heat transfer coefficients for horizontally immersed tubes have been studied in model internally circulating fluidized bed (ICFB) and pilot ICFB incinerators. The characteristics in the ICFB were found to be significantly different from those in a bubbling bed. In ICFB, there is a flowing zone with high velocity, a heat exchange zone, and a moving zone with low velocity. The controllable heat transfer coefficients in ICFB strongly depend on the fluidized velocity in the flowing zone, and also the flow condition in the moving zone. The heat exchange process and suitable bed temperature can be well controlled according to this feature. Based on the results of experiments, a formulation for heat transfer coefficient has been developed. These results were applied to an external superheater of a CFB incinerator with a 450 degreesC steam outlet in a waste-to-energy pilot cogeneration plant of 12 MW in Jiaxing City, China.

Some characteristics of low-speed streaks under sheared air-water interfaces

The characteristics of low-speed fluid streaks occurring under sheared air-water interfaces were examined by means of hydrogen bubble visualization technique. A critical shear condition under which the streaky structure first appears was determined to be u(tau) approximate to 0.19 cm/s. The mean spanwise streak spacing increases with distance from the water surface owing to merging and bursting processes, and a linear relationship describing variation of non-dimensional spacing <(+)over bar> versus y(+) was found essentially independent of shear stress on the interface. Values of <(+)over bar>, however, are remarkably smaller than their counterparts in the near-wall region of turbulent boundary layers. Though low-speed streaks occur randomly in time and space, the streak spacing exhibits a lognormal probability distribution behavior. A tentative explanation concerning the formation of streaky structure is suggested, and the fact that <(+)over bar> takes rather smaller values than that in wall turbulence is briefly discussed.

Influence of grain boundary on melting

The temperature behaviour of an Al bicrystal with surfaces consisting of (110) and (111) crystals is simulated using molecular dynamics. The result shows that the (110) crystal losses its crystalline order at 820K, whereas the disorder does not propagate through the (111) crystal at this temperature. Instead, some disordered atoms are recrystallized into the (111) crystal and the initial grain boundary changes into a stable order-disorder interface. Thus, it was discovered that at a temperature near its melting point, the (111) crystal grew and obstructed the propagation of disorder. Such an obstruction is helpful for understanding melting.