高阶广义屏波动方程叠前深度偏移

Attaining sufficient accuracy and efficiency of generalized screen propagator and improving the quality of input gathers are often problems　of wave equation presack depth migration,　in this paper,a high order formula of generalized screen propagator　for one-way wave equation is proposed by using the asymptotic expansion of single-square-root operator. Based on the formula，a new generalized screen propagator is developed ,which is composed of split-step Fourier propagator and high order correction terms，the new generalized screen propagator not only improving calculation precision without sharply increasing the quantity of computation，facilitates the suitability of generalized screen propagator to the media with strong lateral velocity variation.　As wave-equation prestack depth migration is sensitive to the quality of input gathers, which greatly affect the output，and the available seismic data processing system has inability to obtain traveltimes corresponding to the multiple arrivals, to estimate of great residual statics， to merge seismic datum from different projects and to design inverse Q filter, we establish　difference equations with an embodiment of Huygens’s principle for obtaining traveltimes corresponding to the multiple arrivals,bring forward a time variable matching filter for seismic datum merging by using the fast algorithm called Mallat tree for wavelet transformations， put forward a method for estimation of residual statics by applying the optimum model parameters estimated by iterative inversion with three organized algorithm,i.e,the CMP intertrace cross-correlation algorithm,the Laplacian image edge extraction algorithm,and the DFP algorithm, and present phase-shift inverse Q filter based on Futterman’s amplitude and phase-velocity dispersion formula and wave field extrapolation theory. All of their numerical and real data calculating results shows that our theory and method are practical and efficient. Key words: prestack depth migration, generalized screen propagator, residual statics，inverse Q filter ,traveltime，3D seismic datum mergence

层析静校正技术研究和应用

Static correction is one of the indispensable steps in the conventional onshore seismic data processing, particularly in the western part of China; it is theoretically and practically significant to resolve the issue of static correction. Conventional refraction static correction is put forward under the assumption that layered medium is horizontal and evenly distributed. The complicated nature of the near surface from western part of China is far from the assumption. Therefore, the essential way to resolve the static correction problem from the complex area is to develop a new theory. In this paper, a high-precision non-linear first arrival tomography is applied to solve the problem, it moved beyond the conventional refraction algorithm based on the layered medium and can be used to modeling the complex near surface. Some of the new and creative work done is as follows: One. In the process of first arrival tomographic image modeling, a fast high-order step algorithm is used to calculate the travel time for first arrival and ray path and various factors concerning the fast step ray tracing algorithm is analyzed. Then the second-order and third-order differential format is applied to the step algorithm which greatly increased the calculation precision of the ray tracing and there is no constraint to the velocity distribution from the complex areas. This method has very strong adaptability and it can meet the needs of great velocity variation from the complicated areas. Based on the numerical calculation, a fast high-order step is a fast, non-conditional and stable high-precision tomographic modeling algorithm. Two, in the tomographic inversion, due to the uneven fold coverage and insufficient information, the inversion result is unstable and less reliable. In the paper, wavelet transform is applied to the tomographic inversion which has achieved a good result. Based on the result of the inversion from the real data, wavelet tomographic inversion has increased the reliability and stability of the inversion. Three. Apply the constrained high-precision wavelet tomographic image to the static correction processing from the complex area. During tomographic imaging, by using uphole survey, refraction shooting or other weathering layer method, weathering layer can be identified before the image. Because the group interval for the shot first arrival is relatively big, there is a lack of precision for the near surface inversion. In this paper, an inversion method of the layer constraint and well constraint is put forward, which can be used to compensate the shallow velocity of the inversion for the shot first arrival and increase the precision of the tomographic inversion. Key words: Tomography ，Fast marching method，Wavelet transform, Static corrections, First break

基于广义正交多项式迭积微分算子的地震波场数值模拟研究

Seismic Numerical Modeling is one of bases of the Exploratory Seismology and Academic Seismology, also is a research field in great demand. Essence of seismic numerical modeling is to assume that structure and parameters of the underground media model are known, simulate the wave-field and calculate the numerical seismic record that should be observed. Seismic numerical modeling is not only a means to know the seismic wave-field in complex inhomogeneous media, but also a test to the application effect by all kinds of methods. There are many seismic numerical modeling methods, each method has its own merits and drawbacks. During the forward modeling, the computation precision and the efficiency are two pivotal questions to evaluate the validity and superiority of the method. The target of my dissertation is to find a new method to possibly improve the computation precision and efficiency, and apply the new forward method to modeling the wave-field in the complex inhomogeneous media. Convolutional Forsyte polynomial differentiator (CFPD) approach developed in this dissertation is robust and efficient, it shares some of the advantages of the high precision of generalized orthogonal polynomial and the high speed of the short operator finite-difference. By adjusting the operator length and optimizing the operator coefficient, the method can involve whole and local information of the wave-field. One of main tasks of the dissertation is to develop a creative, generalized and high precision method. The author introduce convolutional Forsyte polynomial differentiator to calculate the spatial derivative of seismic wave equation, and apply the time staggered grid finite-difference which can better meet the high precision of the convolutional differentiator to substitute the conventional finite-difference to calculate the time derivative of seismic wave equation, then creating a new forward method to modeling the wave-field in complex inhomogeneous media. Comparing with Fourier pseudo-spectral method, Chebyshev pseudo-spectral method, staggered- grid finite difference method and finite element method, convolutional Forsyte polynomial differentiator (CFPD) method has many advantages: 1. Comparing with Fourier pseudo-spectral method. Fourier pseudo-spectral method (FPS) is a local operator, its results have Gibbs effects when the media parameters change, then arose great errors. Therefore, Fourier pseudo-spectral method can not deal with special complex and random heterogeneous media. But convolutional Forsyte polynomial differentiator method can cover global and local information. So for complex inhomogeneous media, CFPD is more efficient. 2. Comparing with staggered-grid high-order finite-difference method, CFPD takes less dots than FD at single wave length, and the number does not increase with the widening of the studying area. 3. Comparing with Chebyshev pseudo-spectral method (CPS). The calculation region of Chebyshev pseudo-spectral method is fixed in , under the condition of unchangeable precision, the augmentation of calculation is unacceptable. Thus Chebyshev pseudo-spectral method is inapplicable to large area. CFPD method is more applicable to large area. 4. Comparing with finite element method (FE), CFPD can use lager grids. The other task of this dissertation is to study 2.5 dimension (2.5D) seismic wave-field. The author reviews the development and present situation of 2.5D problem, expatiates the essentiality of studying the 2.5D problem, apply CFPD method to simulate the seismic wave-field in 2.5D inhomogeneous media. The results indicate that 2.5D numerical modeling is efficient to simulate one of the sections of 3D media, 2.5D calculation is much less time-consuming than 3D calculation, and the wave dispersion of 2.5D modeling is obviously less than that of 3D modeling. Question on applying time staggered-grid convolutional differentiator based on CFPD to modeling 2.5D complex inhomogeneous media was not studied by any geophysicists before, it is a fire-new creation absolutely. The theory and practices prove that the new method can efficiently model the seismic wave-field in complex media. Proposing and developing this new method can provide more choices to study the seismic wave-field modeling, seismic wave migration, seismic inversion, and seismic wave imaging.

离散裂缝诱导各向异性粘弹性地震波模拟与特征分析

The real media always attenuate and distort seismic waves as they propagate in the earth. This behavior can be modeled with a viscoelastic and anisotropic wave equation. The real media can be described as fractured media. In this thesis, we present a high-order staggered grid finite-difference scheme for 2-D viscoelastic wave propagation in a medium containing a large number of small finite length fractures. We use the effective medium approach to compute the anisotropic parameters in each grid cell. By comparing our synthetic seismogram by staggered-grid finite-difference with that by complex-ray parameter ray tracing method, we conclude that the high-order staggered-grid finite-difference technique can effectively used to simulate seismic propagation in viscoelastic-anisotropic media. Synthetic seismograms demonstrate that strong attenuation and significant frequency dispersion due to viscosity are important factors of reducing amplitude and delaying arrival time varying with incidence angle or offset. On the other hand, the amount of scattered energy not only provides an indicator of orientation of fracture sets, but can also provide information about the fracture spacing. Analysis of synthetic seismograms from dry- and fluid-filled fractures indicates that dry-filled fractures show more significant scattering on seismic wavefields than fluid-filled ones, and offset-variations in P-wave amplitude are observable. We also analyze seismic response of an anticlinal trap model that includes a gas-filled fractured reservoir with high attenuation, which attenuates and distorts the so-called bright spot.

全局优化的Fourier有限差分偏移方法研究

Seismic exploration is the main method of seeking oil and gas. With the development of seismic exploration, the target becomes more and more complex, which leads to a higher demand for the accuracy and efficiency in seismic exploration. Fourier finite-difference (FFD) method is one of the most valuable methods in complex structure exploration, which has obtained good effect. However, in complex media with wider angles, the effect of FFD method is not satisfactory. Based on the FFD operator, we extend the two coefficients to be optimized to four coefficients, then optimize them globally using simulated annealing algorithm. Our optimization method select the solution of one-way wave equation as the objective function. Except the velocity contrast, we consider the effects of both frequency and depth interval. The proposed method can improve the angle of FFD method without additional computation time, which can reach 75° in complex media with large lateral velocity contrasts and wider propagation angles. In this thesis, combinating the FFD method and alternative-direction-implicit plus interpolation(ADIPI） method, we obtain 3D FFD with higher accuracy. On the premise of keeping the efficiency of the FFD method, this method not only removes the azimuthal anisotropy but also optimizes the FFD mehod, which is helpful to 3D seismic exploration. We use the multi-parameter global optimization method to optimize the high order term of FFD method. Using lower-order equation to obtain the approximation effect of higher-order equation, not only decreases the computational cost result from higher-order term, but also obviously improves the accuracy of FFD method. We compare the FFD, SAFFD（multi-parameter simulated annealing globally optimized FFD）, PFFD, phase-shift method(PS）, globally optimized FFD （GOFFD）, and higher-order term optimized FFD method. The theoretical analyses and the impulse responses demonstrate that higher-order term optimized FFD method significantly extends the accurate propagation angle of the FFD method, which is useful to complex media with wider propagation angles.

指数矩阵近似计算在地震波场延拓中的应用

Seismic wave field numerical modeling and seismic migration imaging based on wave equation have become useful and absolutely necessarily tools for imaging of complex geological objects. An important task for numerical modeling is to deal with the matrix exponential approximation in wave field extrapolation. For small value size matrix exponential, we can approximate the square root operator in exponential using different splitting algorithms. Splitting algorithms are usually used on the order or the dimension of one-way wave equation to reduce the complexity of the question. In this paper, we achieve approximate equation of 2-D Helmholtz operator inversion using multi-way splitting operation. Analysis on Gauss integral and coefficient of optimized partial fraction show that dispersion may accumulate by splitting algorithms for steep dipping imaging. High-order symplectic Pade approximation may deal with this problem, However, approximation of square root operator in exponential using splitting algorithm cannot solve dispersion problem during one-way wave field migration imaging. We try to implement exact approximation through eigenfunction expansion in matrix. Fast Fourier Transformation (FFT) method is selected because of its lowest computation. An 8-order Laplace matrix splitting is performed to achieve a assemblage of small matrixes using FFT method. Along with the introduction of Lie group and symplectic method into seismic wave-field extrapolation, accurate approximation of matrix exponential based on Lie group and symplectic method becomes the hot research field. To solve matrix exponential approximation problem, the Second-kind Coordinates (SKC) method and Generalized Polar Decompositions (GPD) method of Lie group are of choice. SKC method utilizes generalized Strang-splitting algorithm. While GPD method utilizes polar-type splitting and symmetric polar-type splitting algorithm. Comparing to Pade approximation, these two methods are less in computation, but they can both assure the Lie group structure. We think SKC and GPD methods are prospective and attractive in research and practice.

工作幸福感的结构、测量及作用机制

With the emergence and development of positive psychology, happiness has been the focus of academia and business. However, there is no uniform measure of happiness, because of many different theories of happiness, which are not compatible with others. It bounds the further development of happiness theory. It is also the same with the research of work well-being, which refers to the emotional experience and quality of psychological functioning of employee in the workplace. Subjective well-being (SWB) and psychological well-being (PWB) are two major theories of happiness. Prior research has demonstrated the integration of these two theories theoretically, but still needs more empirical support. Besides, in line with the development of positive psychology, a body of knowledge about positive leadership is advocated. Transformational leadership is treated as one kind of positive leadership, since it emphasizes the leader’s motivational and elevating effect on followers. But the extent to which the transformational leadership can enhance work well-being, and what the mechanism is, these are the questions need to be explored. Based on the integration of SWB and PWB, this research tried to investigate the structure, measurement and mechanism of work well-being, and combining with the theory of transformational leadership, this study also tried to investigate the relationship between transformational leadership and work well-being. The structure and measurement of work well-being, the relationships between work well-being and job characteristics (including job resources and job demands), the relationships among transformational leadership, job resources, work well-being and corresponding outcomes, the relationships among transformational leadership, job demands, work well-being and corresponding outcomes, and the relationships among transformational leadership, group job characteristics, group work well-being and corresponding group outcomes were explored by using content analysis, Subject Matter Experts (SMEs) discussion, and structural questionnaire surveys. More than 7000 subjects were surveyed, and Explore Factor Analysis (EFA), Confirm Factor Analysis (CFA), Structural Equation Modeling (SEM), Hierarchical Linear Modeling (HLM) and other statistics methods were used. The following is the major conclusions. Firstly, work well-being is a two high-order factors structure, which includes affective well-being (AWB) and cognitive well-being (CWB). AWB is similar to SWB, and CWB is similar to PWB. Besides, the construct of AWB includes sub-dimensions of positive emotional experience and negative emotional experience. And the construct of CWB consists of work autonomy, personal growth, work competent, and work significance. Secondly, the relationships between job characteristics and AWB and CWB are different. On one hand job demands are directly related to AWB, and are indirectly related to CWB through the full mediation of AWB, on the other job resources are directly related to CWB, and are indirectly related to AWB through the full mediation of CWB, which means AWB and CWB reciprocally influences each other in the model of job demands-resources. These results were concluded as the process model of work well-being. Thirdly, AWB and CWB are positively related to many workplace outcomes, including job satisfaction, group satisfaction, organizational commitment, turnover intention, job performance, organizational citizenship behavior (OCB), and general psychological health and general physiological health. Fourthly, transformational leadership is indirectly related to CWB through the full mediation of job resources, and is related to AWB through the partial mediation of job demands. Meanwhile, transformational leadership is related to many workplace outcomes through the mediation of job characteristics and work well-being. These results implied that transformational leadership is indeed one kind of positive leadership. Fifthly, in the group level, transformational leadership is indirectly related to group CWB through the full mediation of group job resources, and is related to group AWB through the full mediation of group job demands. Group AWB has positive influence on group CWB, but not vice versa. Group job characteristics and group work well-being fully mediate the relationships between transformational leadership and intragroup cooperation and group performance.

Multistep Methods for Integrating the Solar System

High order multistep methods, run at constant stepsize, are very effective for integrating the Newtonian solar system for extended periods of time. I have studied the stability and error growth of these methods when applied to harmonic oscillators and two-body systems like the Sun-Jupiter pair. I have also tried to design better multistep integrators than the traditional Stormer and Cowell methods, and I have found a few interesting ones.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Predictions of the Pt(8)Ti phase in unexpected systems.

The binary A(8)B phase (prototype Pt(8)Ti) has been experimentally observed in 11 systems. A high-throughput search over all the binary transition intermetallics, however, reveals 59 occurrences of the A(8)B phase: Au(8)Zn(dagger), Cd(8)Sc(dagger), Cu(8)Ni(dagger), Cu(8)Zn(dagger), Hg(8)La, Ir(8)Os(dagger), Ir(8)Re, Ir(8)Ru(dagger), Ir(8)Tc, Ir(8)W(dagger), Nb(8)Os(dagger), Nb(8)Rh(dagger), Nb(8)Ru(dagger), Nb(8)Ta(dagger), Ni(8)Fe, Ni(8)Mo(dagger)*, Ni(8)Nb(dagger)*, Ni(8)Ta*, Ni(8)V*, Ni(8)W, Pd(8)Al(dagger), Pd(8)Fe, Pd(8)Hf, Pd(8)Mn, Pd(8)Mo*, Pd(8)Nb, Pd(8)Sc, Pd(8)Ta, Pd(8)Ti, Pd(8)V*, Pd(8)W*, Pd(8)Zn, Pd(8)Zr, Pt(8)Al(dagger), Pt(8)Cr*, Pt(8)Hf, Pt(8)Mn, Pt(8)Mo, Pt(8)Nb, Pt(8)Rh(dagger), Pt(8)Sc, Pt(8)Ta, Pt(8)Ti*, Pt(8)V*, Pt(8)W, Pt(8)Zr*, Rh(8)Mo, Rh(8)W, Ta(8)Pd, Ta(8)Pt, Ta(8)Rh, V(8)Cr(dagger), V(8)Fe(dagger), V(8)Ir(dagger), V(8)Ni(dagger), V(8)Pd, V(8)Pt, V(8)Rh, and V(8)Ru(dagger) ((dagger) = metastable, * = experimentally observed). This is surprising for the wealth of new occurrences that are predicted, especially in well-characterized systems (e.g., Cu-Zn). By verifying all experimental results while offering additional predictions, our study serves as a striking demonstration of the power of the high-throughput approach. The practicality of the method is demonstrated in the Rh-W system. A cluster-expansion-based Monte Carlo model reveals a relatively high order-disorder transition temperature.

The M/M/1 queue with mass exodus and mass arrivals when empty

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate {αr; r≥ 1} when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

[Review] M. Feistauer, J. Felcman, I. Straskbraba, Mathematical and Computational Methods for Compressible Flow, Oxford Science Publication, Oxford, ISBN 0198505884, 2004 (535pp.)

The growth of computer power allows the solution of complex problems related to compressible flow, which is an important class of problems in modern day CFD. Over the last 15 years or so, many review works on CFD have been published. This book concerns both mathematical and numerical methods for compressible flow. In particular, it provides a clear cut introduction as well as in depth treatment of modern numerical methods in CFD. This book is organised in two parts. The first part consists of Chapters 1 and 2, and is mainly devoted to theoretical discussions and results. Chapter 1 concerns fundamental physical concepts and theoretical results in gas dynamics. Chapter 2 describes the basic mathematical theory of compressible flow using the inviscid Euler equations and the viscous Navier–Stokes equations. Existence and uniqueness results are also included. The second part consists of modern numerical methods for the Euler and Navier–Stokes equations. Chapter 3 is devoted entirely to the finite volume method for the numerical solution of the Euler equations and covers fundamental concepts such as order of numerical schemes, stability and high-order schemes. The finite volume method is illustrated for 1-D as well as multidimensional Euler equations. Chapter 4 covers the theory of the finite element method and its application to compressible flow. A section is devoted to the combined finite volume–finite element method, and its background theory is also included. Throughout the book numerous examples have been included to demonstrate the numerical methods. The book provides a good insight into the numerical schemes, theoretical analysis, and validation of test problems. It is a very useful reference for applied mathematicians, numerical analysts, and practice engineers. It is also an important reference for postgraduate researchers in the field of scientific computing and CFD.

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Effect of relativistic plasma on extreme-ultraviolet harmonic emission from intense laser-matter interactions

Experiments were performed in which intense laser pulses (up to 9x10(19) W/cm(2)) were used to irradiate very thin (submicron) mass-limited aluminum foil targets. Such interactions generated high-order harmonic radiation (greater than the 25th order) which was detected at the rear of the target and which was significantly broadened, modulated, and depolarized because of passage through the dense relativistic plasma. The spectral modifications are shown to be due to the laser absorption into hot electrons and the subsequent sharply increasing relativistic electron component within the dense plasma.