窄带和宽带双曲正割脉冲光束的解析传输式

从近轴波动方程出发推导了窄带和宽带双曲正割脉冲光束的解析传输公式。通过数值计算比较了分别采用复振幅包络(CAE)表示式和复解析信号(CAS)表示式得到的脉冲光束，得出了选择脉冲光束研究方法的条件。结果表明复振幅包络表示式得到的解会存在空间奇异性，使光束出现不符合物理意义的非光束行为。对于宽带光束，复振幅包络解的奇异点的位置距离轴中心较近，使复包络解不能正确表示脉冲光束，而对于奇异点位置远离轴中心的窄带光束，对脉冲光束产生的影响可以忽略。因此，窄带脉冲光束可以采用复振幅包络和复解析信号两种表示式来研究，而对

Análise de transição entre cabos coaxiais constituída por corrugações e desníveis angulares.

Esta dissertação apresenta um formalismo baseado no Método dos Elementos Finitos (MEF), adequado a análise de descontinuidades coaxiais com simetria axial, entre duas linhas coaxiais quaisquer, incluindo corrugações nos tubos internos e externos. Pelo método de Galerkin-Budnov deduz-se um operador integral bilinear, aplicado ao campo magnético, expandido em todo o domínio da estrutura, coaxial-descontinuidade-coaxial. As portas de entrada e saída da estrutura são posicionadas distantes da descontinuidade, de forma que nelas só haja o modo Transversal Eletromagnético (TEM). O campo magnético procurado e obtido pelo MEF. Os resultados encontrados; perdas de retorno, comportamento do campo magnético e as equi-fases nas portas de entrada e saída da estrutura, foram calculados e confrontados com as do Método de Casamento de Modos (MCM), com um alto grau de concordância.

Um estudo de caso envolvendo a retroanálise de tensões residuais de cravação.

As tensões residuais de cravação ocorrem quando a estaca e o solo não são totalmente descomprimidos após dissipação completa da energia transferida à estaca durante sua instalação. Este assunto tem merecido a atenção de vários pesquisadores, uma vez que a presença das tensões residuais na estaca causa uma alteração no seu comportamento quando carregada. A presente dissertação reuniu estudos anteriores que estabeleceram os principais fatores que influenciam as tensões residuais de cravação. Procurou-se executar uma série de simulações objetivando melhor entender o desenvolvimento das tensões residuais com a porcentagem de resistência de ponta, em continuidade aos estudos de Costa (1994). Costa (1994) observou que a porcentagem de carga na ponta é um fator relevante na avaliação das tensões residuais de cravação. Uma análise paramétrica efetuada confirmou estudos anteriores, verificando que a razão entre a carga residual na ponta em relação à capacidade de carga global cresce, a medida que a porcentagem de carga na ponta aumenta, chegando a um valor máximo para, em seguida, diminuir. Este comportamento é similar ao da curva de compactação do solo, quando, ao aumentar a umidade, o peso específico seco aumenta, até um valor máximo, correspondente à umidade ótima, para em seguida reduzir. Verificouse, ainda, semelhantemente ao aumento da energia de compactação, que vai transladando a curva para cima e para à esquerda do gráfico umidade x peso específico seco, que o aumento do comprimento da estaca apresenta um comportamento similar. O aumento do comprimento leva a curva para cima e para a esquerda. Finalmente, selecionou-se um caso de obra com condições propícias para o desenvolvimento de altas tensões residuais de cravação. Trata-se de um caso de estacas metálicas longas, embutidas em solo residual jovem, de elevada resistência, bem documentado com extensa instrumentação, por ocasião da instalação. A retroanálise de cinco estacas do banco de dados mostrou que as cargas residuais previstas, num programa de simulação de cravação, se aproximaram muito dos valores experimentais. Foi observado também que a profundidade do ponto neutro previsto e medido apresentou uma excelente concordância. O resultado mais relevante desta pesquisa foi quando os valores de porcentagem de ponta foram introduzidos no eixo das abscissas e os valores da razão entre a carga residual na ponta e a capacidade de carga global, no eixo das ordenadas, e se observou o aspecto da curva semelhante à de compactação. A dissertação ilustra ser possível e simples a previsão das tensões residuais de cravação através de uma análise pela equação da onda.

Trailing edge noise theory for rotating blades in uniform flow

This paper presents a new formulation for trailing edge noise radiation from rotating blades based on an analytical solution of the convective wave equation. It accounts for distributed loading and the effect of mean flow and spanwise wavenumber. A commonly used theory due to Schlinker and Amiet (1981) predicts trailing edge noise radiation from rotating blades. However, different versions of the theory exist; it is not known which version is the correct one and what the range of validity of the theory is. This paper addresses both questions by deriving Schlinker and Amiet's theory in a simple way and by comparing it to the new formulation, using model blade elements representative of a wind turbine, a cooling fan and an aircraft propeller. The correct form of Schlinker and Amiet's theory (1981) is identified. It is valid at high enough frequency, i.e. for a Helmholtz number relative to chord greater than one and a rotational frequency much smaller than the angular frequency of the noise sources.

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

Nonlinear wave equation for a one-dimensional anharmonic crystal lattice in terms of its microscopic parameters is obtained by means of a continuum approximation. Using a small time scale transformation, the nonlinear wave equation is reduced to a combined KdV equation and its single soliton solution yields the supersonic kink form of nonlinear elastic waves for the system.

Holographic dual of linear dilaton black hole in Einstein-Maxwell-dilaton-axion gravity

Motivated by the recently proposed Kerr/CFT correspondence, we investigate the holographic dual of the extremal and non-extremal rotating linear dilaton black hole in Einstein-Maxwell-Dilaton-Axion Gravity. For the case of extremal black hole, by imposing the appropriate boundary condition at spatial infinity of the near horizon extremal geometry, the Virasoro algebra of conserved charges associated with the asymptotic symmetry group is obtained. It is shown that the microscopic entropy of the dual conformal field given by Cardy formula exactly agrees with Bekenstein-Hawking entropy of extremal black hole. Then, by rewriting the wave equation of massless scalar field with sufficient low energy as the SLL(2, R) x SLR(2, R) Casimir operator, we find the hidden conformal symmetry of the non-extremal linear dilaton black hole, which implies that the non-extremal rotating linear dilaton black hole is holographically dual to a two dimensional conformal field theory with the non-zero left and right temperatures. Furthermore, it is shown that the entropy of non-extremal black hole can be reproduced by using Cardy formula.

Entropy of Kaluza-Klein black hole from Kerr/CFT correspondence

We extend the recently proposed Kerr/CFT correspondence to examine the dual conformal field theory of four-dimensional Kaluza-Klein black hole in Einstein-Maxwell-Dilaton theory. For the extremal Kaluza-Klein black hole, the central charge and temperature of the dual conformal field are calculated following the approach of Guica, Hartman, Song and Strominger. Meanwhile, we show that the microscopic entropy given by the Cardy formula agrees with Bekenstein-Hawking entropy of extremal Kaluza-Klein black hole. For the non-extremal case, by studying the near-region wave equation of a neutral massless scalar field, we investigate the hidden conformal symmetry of Kaluza-Klein black hole, and find the left and right temperatures of the dual conformal field theory. Furthermore, we find that the entropy of non-extremal Kaluza-Klein black hole is reproduced by Cardy formula. (C) 2010 Elsevier B.V. All rights reserved.

用波动方程建立蠕动爬行攻泥机器人海底土力学运动模型

针对目前国内海底蠕动爬行机器人攻打千斤洞的特点 ,在对海洋沉积土的工程性质进行分析的基础上 ,利用流变力学的理论 ,提出用波动方程来建立攻泥机器人周期性冲击土壤的力学模型 ,用后向差分法解波动方程 ,得到土壤的位移和变形公式 ,确定土壤对攻泥机的阻力 .通过对模型的仿真 ,证明了用该模型计算阻力的可行性 .

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

VTI各向异性叠前深度偏移及速度分析

Theoretical research, laboratory test and field observation show that most of sediment rock has anisotropic features. It will produce some notable errors when applying isotropic methods such as prestack depth migration and velocity analysis to dada acquired under anisotropic condition; it also has a bad effect on geologic interpretation. Generally speaking, the vertical transverse isotropic media is a good approximation to geologic structure, thus it has an important realistic meaning for anisotropic prestack depth migration theory researching and precise complex geologic imaging if considering anisotropic effect of seismic wave propagation. There are two indispensable parts in prestack depth migration of realistic records, one is proper prestack depth migration algorithm, and the other is velocity analysis using prestack seismic data. The paper consists of the two aspects. Based on implicit finite difference research proposed by Dietrich Ristow et al （1997） about VTI media prestack depth migration, the paper proposed split-step Fourier prestack depth migration algorithm （VTISSF） and Fourier finite difference algorithm （VTIFFD） based on wave equation for VTI media, program are designed and the depth migration method are tested using synthetic model. The result shows that VTISSF is a stable algorithm, it generally gets a good result if the reflector dip is not very steep, while undermigration phenomena appeared in steep dips case; the VTIFFD algorithm bring us better result in steep dips with lower efficiency and frequency dispersion. For anisotropic prestack depth migration velocity analysis of VTI media, The paper discussed the basic hypothesis of VTI model in velocity analysis algorithm, basis of anisotropic prestack depth migration velocity analysis and travel time table calculation of VTI media in integral prestack depth migration. Then , analyzed the P-wave common imaging gather in the case of homogeneous velocity and vertically variable velocity . studied the residual correction in common imaging gather produced by media parameter error, analyzed the condition of flat event and correct depth in common imaging gather . In this case, the anisotropic model parameter vector is , is vertical velocity of a point at top surface, is vertical velocity gradient, and are anisotropic parameter. We can get vertical velocity gradient from seismic data; then the P-wave common imaging gather of VTI media whose velocity varies in vertical and horizontal direction, the relationship between media parameter and event residual time shift of common image gather are studied. We got the condition of flattening common imaging gather with correct depth. In this case the anisotropic model parameter vector is , is velocity gradient in horizontal direction. As a result, the vertical velocity grads can be decided uniquely, but horizontal velocity grads and anisotropic parameter can’t be distinguished if no priori information available, our method is to supply parameter by velocity scanning; then, as soon as is supplied we can get another four parameters of VTI media from seismic data. Based on above analysis, the paper discussed the feasibility of migration velocity analysis in vertically and horizontally varied VTI media, synthetic record of three models are used to test the velocity analysis method . Firstly, anisotropic velocity analysis test is done using a simple model with one block, then we used a model with multiple blocks, thirdly, we analyzed the anisotropic velocity using a part of Marmousi model. The model results show that this velocity analysis method is feasible and correct.

东海陆架盆地复杂天然气藏地震勘探判别技术研究

Exploration study proves that East sea shelf basin embeds abundant hydrocarbon resources. However, the exploration knowledge of this area is very low. Many problems in exploration are encountered here. One of them is that the gas reservoir of this area, with rapid lateral variation, is deeply buried. Correlation of Impendence between sandstone, gas sand and shale is very poor. Another problem is that the S/N ratio of the seismic data is very low and multiples are relatively productive which seriously affect reservoir identification. Resolution of the seismic data reflected from 2500-3000 meter is rather low, which seriously affects the application of hydrocarbon direct identification (HDI) technology. This research established a fine geological & geophysical model based on drilling、well logging、geology&seismic data of East sea Lishui area. A Q value extraction method from seismic data is proposed. With this method, Q value inversion from VSP data and seismic data is performed to determine the subsurface absorption of this area. Then wave propagation and absorption rule are in control. Field acquisition design can be directed. And at the same time, with the optimization of source system, the performance of high resolution seismic acquisition layout system is enhanced. So the firm foundation is ensured for east sea gas reservoir exploration. For solving the multiple and amplitude preserving problems during the seismic data processing, wave equation pre-stack amplitude preservation migration and wave equation feedback iteratively multiple attenuation technologies are developed. Amplitude preservation migration technology can preserve the amplitude of imaging condition and wave-field extrapolation. Multiple removing technology is independent of seismic source wavelet and velocity model, which avoiding the weakness of Delft method. Aiming at the complicated formation condition of the gas reservoir in this area, with dissecting typical hydrocarbon reservoir, a series of pertinent advanced gas reservoir seismic identification technologies such as petrophysical properties analyzing and seismic modeling technology、pre-stack/post-stack joint elastic inversion, attribute extraction technology based on seismic non-stationary signal theory and formation absorption characteristic and so on are studied and developed. Integrated analysis of pre-stack/post-stack seismic data, reservoir information, rock physics and attribute information is performed. And finally, a suit of gas reservoir identification technology is built, according to the geological and geophysical characteristics of this area. With developed innovative technologies, practical application and intergrated interpretation appraisal researches are carried out in Lishui 36-1.The validity of these technologies is tested and verified. Also the hydrocarbon charging possibility and position of those three east sea gas exploration targets are clearly pointed out.

辽东湾隐蔽油气藏地球物理识别技术研究

In China and world, more than half the recent basin discovered reserves involve lithologic hydrocarbon reservoir reserves. The major target for further hydrocarbon basin exploration is the subtle reservoir. The Liaodong Bay prospect is much important in Bohai Sea, which includes Liaoxi low uplift, Liaodong uplift, Liaoxi sag and Liaozhong sag. After dozens years’ exploration in Liaodong Bay, few unexplored big-and-middle-sized favorable structural traps are remained and most of the stock structure targets are bad for fragmentary. Thus seeking for new prospect area and making a breakthrough, have become the unique way to relieve the severe exploration condition in Liaodong Bay. Technique Route Based on the petrophysical property of target area, the seismic forward inference of typical subtle trap model is expanded with analysis of logging, seismic and geologic data. According to petrophysical characteristics and forward inference and research on seismic response of actual seismic data in target area, the optimization of geophysical technique is used in subtle trap identification and the geophysical identification technique system of subtle reservoir is formed. The Key Research ① Petrophysical Model The petrophysical parameter is the basic parameter for seismic wave simulation. The seismic response difference of rocks bearing different fluids is required. With the crossplot of log data, the influence of petrophysical parameters on rock elastic properties of target area is analyzed, such as porosity, shale index, fluid property and saturation. Based on the current research on Biot-Gassmann and Kuster-Toksoz model, the petrophysical parameter calculator program which can be used for fluid substitution is established. ② S-wave evaluation based on conventional log data The shear velocity is needed during forward inference of AVO or other elastic wave field. But most of the recent conventional log data is lack of shear wave. Thus according to the research on petrophysical model, the rock S-wave parameter can be evaluated from conventional log data with probability inverse method. ③ AVO forward modeling based on well data For 6 wells in JZ31-6 block and 9 wells in LD22-1 block, the AVO forward modeling recording is made by log curve. The classification of AVO characteristics in objective interval is made by the lithologic information. ④ The 2D parameter model building and forward modeling of subtle hydrocarbon trap in target area. According to the formation interpretation of ESS03D seismic area, the 2D parameter model building and seismic wave field forward modeling are carried on the given and predicted subtle hydrocarbon trap with log curve. ⑤ The lithology and fluid identification of subtle trap in target area After study the seismic response characteristics of lithology and fluid in given target area, the optimization of geophysical technique is used for lithology identification and fluid forecast. ⑥The geophysical identification technique system of subtle reservoir The Innovative Points of this Paper ① Based on laboratory measurement and petrophysical model theory, the rock S-wave parameter can be evaluated from conventional log data with probability inverse method. Then the fluid substitution method based on B-G and K-T theory is provided. ② The method and workflow for simulating seismic wave field property of subtle hydrocarbon trap are established based on the petrophysical model building and forward modeling of wave equation. ③ The description of subtle trap structural feature is launched. According to the different reflection of frequency wave field structural attribute, the fluid property of subtle trap can be identified by wave field attenuation attribute and absorption analysis. ④ It’s the first time to identify subtle trap by geophysical technique and provide exploration drilling well location. ⑤ The technique system of subtle reservoir geophysical identification is formed to provide available workflow and research ideas for other region of interest.

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.

地震数据波动方程反演方法研究

Geophysical inversion is a theory that transforms the observation data into corresponding geophysical models. The goal of seismic inversion is not only wave velocity models, but also the fine structures and dynamic process of interior of the earth, expanding to more parameters such as density, aeolotropism, viscosity and so on. As is known to all, Inversion theory is divided to linear and non-linear inversion theories. In rencent 40 years linear inversion theory has formed into a complete and systematic theory and found extensive applications in practice. While there are still many urgent problems to be solved in non-linear inversion theory and practice. Based on wave equation, this dissertation has been mainly involved in the theoretical research of several non-linear inversion methods: waveform inversion, traveltime inversion and the joint inversion about two methods. The objective of gradient waveform inversion is to find a geologic model, thus synthetic seismograms generated by this geologic model are best fitted to observed seismograms. Contrasting with other inverse methods, waveform inversion uses all characteristics of waveform and has high resolution capacity. But waveform inversion is an interface by interface method. An artificial parameter limit should be provided in each inversion iteration. In addition, waveform information will tend to get stuck in local minima if the starting model is too far from the actual model. Based on velocity scanning in traditional seismic data processing, a layer-by-layer waveform inversion method is developed in this dissertation to deal with weaknesses of waveform inversion. Wave equation is used to calculate the traveltime and derivative (perturbation of traveltime with respect to velocity) in wave-equation traveltime inversion (WT). Unlike traditional ray-based travetime inversion, WT has many advantages. No ray tracing or traveltime picking and no high frequency assumption is necessary and good result can be got while starting model is far from real model. But, comparing with waveform inversion, WT has low resolution. Waveform inversion and WT have complementary advantages and similar algorithm, which proves that the joint inversion is a better inversion method. And another key point which this dissertation emphasizes is how to give fullest play to their complementary advantages on the premise of no increase of storage spaces and amount of calculation. Numerical tests are implemented to prove the feasibility of inversion methods mentioned above in this dissertation. Especially for gradient waveform inversion, field data are inversed. This field data are acquired by our group in Wali park and Shunyi district. Real data processing shows there are many problems for waveform inversion to deal with real data. The matching of synthetic seismograms with observed seismograms and noise cancellation are two primary problems. In conclusion, on the foundation of the former experiences, this dissertation has implemented waveform inversions on the basis of acoustic wave equation and elastic wave equation, traveltime inversion on the basis of acoustic wave equation and traditional combined waveform traveltime inversion. Besides the traditional analysis of inversion theory, there are two innovations: layer by layer inversion of seimic reflection data inversion and rapid method for acoustic wave-equation joint inversion.

改进叠前深度偏移的计算效率＆叠前高分辨率成像

An high-resolution prestack imaging technique of seismic data is developed in this thesis. By using this technique, the reflected coefficients of sheet sands can be gained in order to understand and identify thin oil reservoirs. One-way wave equation based migration methods can more accurately model seismic wave propagation effect such as multi-arrivals and obtain almost correct reflected energy in the presence of complex inhomogeneous media, and therefore, achieve more superiorities in imaging complex structure. So it is a good choice to apply the proposed high-resolution imaging to the presatck depth migration gathers. But one of the main shorting of one-way wave equation based migration methods is the low computational efficiency, thus the improvement on computational efficiency is first carried out. The method to improve the computational efficiency of prestack depth migration is first presented in this thesis, that is frequency-dependent varying-step depth exploration scheme plus a table-driven, one-point wavefield interpolation technology for wave equation based migration methods; The frequency-dependent varying-step depth exploration scheme reduces the computational cost of wavefield depth extrapolation, and the a table-driven, one-point wavefield interpolation technology reconstructs the extrapolated wavefield with an equal, desired vertical step with high computational efficiency. The proposed varying-step depth extrapolation plus one-point interpolation scheme results in 2/3 reduction in computational cost when compared to the equal-step depth extrapolation of wavefield, but gives the almost same imaging. The frequency-dependent varying-step depth exploration scheme is presented in theory by using the optimum split-step Fourier. But the proposed scheme can also be used by other wave equation based migration methods of the frequency domain. The proposed method is demonstrated by using impulse response, 2-D Marmousi dataset, 3-D salt dataset and the 3-D field dataset. A method of high-resolution prestack imaging is presented in the 2nd part of this thesis. The seismic interference method to solve the relative reflected coefficients is presented. The high-resolution imaging is obtained by introducing a sparseness- constrained least-square inversion into the reflected coefficient imaging. Gaussian regularization is first imposed and a smoothed solution is obtained by solving equation derived from the least-square inversion. Then the Cauchy regularization is introducing to the least-square inversion , the sparse solution of relative reflected coefficients can be obtained, that is high-resolution solution. The proposed scheme can be used together with other prestack imaging if the higher resolution is needed in a target zone. The seismic interference method in theory and the solution to sparseness-constrained least-square inversion are presented. The proposed method is demonstrated by synthetic examples and filed data.