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.

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.

Fourier有限差分法深度偏移与正演模拟

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 3D exploration. Fourier finite-difference (FFD) method is one of the most valuable methods in complex structure exploration, which keeps the ability of finite-differenc method in dealing with laterally varing media and inherits the predominance of the phase-screen method in stablility and efficiency. In this thesis, the accuracy of the FFD operator is highly improved by using simulated annealing algorithm. This method takes the extrapolation step and band width into account, which is more suitable to various band width and discrete scale than the commonely-used optimized method based on velocity contrast alone. In this thesis, the FFD method is extended to viscoacoustic modeling. Based on one-way wave equation, the presented method is implemented in frequency domain; thus, it is more efficient than two-way methods, and is more convenient than time domain methods in handling attenuation and dispersion effects. The proposed method can handle large velocity contrast and has a high efficiency, which is helpful to further research on earth absorption and seismic resolution. Starting from the frequency dispersion of the acoustic VTI wave equation, this thesis extends the FFD migration method to the acoustic VTI media. Compared with the convetional FFD method, the presented method has a similar computational efficiency, and keeps the abilities of dealing with large velocity contrasts and steep dips. The numerical experiments based on the SEG salt model show that the presented method is a practical migration method for complex acoustical VTI media, because it can handle both large velocity contrasts and large anisotropy variations, and its accuracy is relatively high even in strong anisotropic media. In 3D case, the two-way splitting technique of FFD operator causes artificial azimuthal anisotropy. These artifacts become apparent with increasing dip angles and velocity contrasts, which prevent the application of the FFD method in 3D complex media. The current methods proposed to reduce the azimuthal anisotropy significantly increase the computational cost. In this thesis, the alternating-direction-implicit plus interpolation scheme is incorporated into the 3D FFD method to reduce the azimuthal anisotropy. By subtly utilizing the Fourier based scheme of the FFD method, the improved fast algorithm takes approximately no extra computation time. The resulting operator keeps both the accuracy and the efficiency of the FFD method, which is helpful to the inhancements of both the accuracy and the efficiency for prestack depth migration. The general comparison is presented between the FFD operator and the generalized-screen operator, which is valuable to choose the suitable method in practice. The percentage relative error curves and migration impulse responses show that the generalized-screen operator is much sensiutive to the velocity contrasts than the FFD operator. The FFD operator can handle various velocity contrasts, while the generalized-screen operator can only handle some range of the velocity contrasts. Both in large and weak velocity contrasts, the higher order term of the generalized-screen operator has little effect on improving accuracy. The FFD operator is more suitable to large velocity contrasts, while the generalized-screen operator is more suitable to middle velocity contrasts. Both the one-way implicit finite-difference migration and the two-way explicit finite-differenc modeling have been implemented, and then they are compared with the corresponding FFD methods respectively. This work gives a reference to the choosen of proper method. The FFD migration is illustrated to be more attractive in accuracy, efficiency and frequency dispertion than the widely-used implicit finite-difference migration. The FFD modeling can handle relatively coarse grids than the commonly-used explicit finite-differenc modeling, thus it is much faster in 3D modeling, especially for large-scale complex media.

地震波模拟：非规则网格离散的数值解法、吸收边界及其实际应用

This dissertation presents a series of irregular-grid based numerical technique for modeling seismic wave propagation in heterogeneous media. The study involves the generation of the irregular numerical mesh corresponding to the irregular grid scheme, the discretized version of motion equations under the unstructured mesh, and irregular-grid absorbing boundary conditions. The resulting numerical technique has been used in generating the synthetic data sets on the realistic complex geologic models that can examine the migration schemes. The motion equation discretization and modeling are based on Grid Method. The key idea is to use the integral equilibrium principle to replace the operator at each grid in Finite Difference scheme and variational formulation in Finite Element Method. The irregular grids of complex geologic model is generated by the Paving Method, which allow varying grid spacing according to meshing constraints. The grids have great quality at domain boundaries and contain equal quantities of nodes at interfaces, which avoids the interpolation of parameters and variables. The irregular grid absorbing boundary conditions is developed by extending the Perfectly Matched Layer method to the rotated local coordinates. The splitted PML equations of the first-order system is derived by using integral equilibrium principle. The proposed scheme can build PML boundary of arbitrary geometry in the computational domain, avoiding the special treatment at corners in a standard PML method and saving considerable memory and computation cost. The numerical implementation demonstrates the desired qualities of irregular grid based modeling technique. In particular, (1) smaller memory requirements and computational time are needed by changing the grid spacing according to local velocity; (2) Arbitrary surfaces and interface topographies are described accurately, thus removing the artificial reflection resulting from the stair approximation of the curved or dipping interfaces; (3) computational domain is significantly reduced by flexibly building the curved artificial boundaries using the irregular-grid absorbing boundary conditions. The proposed irregular grid approach is apply to reverse time migration as the extrapolation algorithm. It can discretize the smoothed velocity model by irregular grid of variable scale, which contributes to reduce the computation cost. The topography. It can also handle data set of arbitrary topography and no field correction is needed.

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.

基于广义Lippmann-Schwinger方程的地震波场模拟算法与应用

In the last several decades, due to the fast development of computer, numerical simulation has been an indispensable tool in scientific research. Numerical simulation methods which based on partial difference operators such as Finite Difference Method (FDM) and Finite Element Method (FEM) have been widely used. However, in the realm of seismology and seismic prospecting, one usually meets with geological models which have piece-wise heterogeneous structures as well as volume heterogeneities between layers, the continuity of displacement and stress across the irregular layers and seismic wave scattering induced by the perturbation of the volume usually bring in error when using conventional methods based on difference operators. The method discussed in this paper is based on elastic theory and integral theory. Seismic wave equation in the frequency domain is transformed into a generalized Lippmann-Schwinger equation, in which the seismic wavefield contributed by the background is expressed by the boundary integral equation and the scattering by the volume heterogeneities is considered. Boundary element-volume integral method based on this equation has advantages of Boundary Element Method (BEM), such as reducing one dimension of the model, explicit use the displacement and stress continuity across irregular interfaces, high precision, satisfying the boundary at infinite, etc. Also, this method could accurately simulate the seismic scattering by the volume heterogeneities. In this paper, the concrete Lippmann-Schwinger equation is specifically given according to the real geological models. Also, the complete coefficients of the non-smooth point for the integral equation are introduced. Because Boundary Element-Volume integral equation method uses fundamental solutions which are singular when the source point and the field are very close，both in the two dimensional and the three dimensional case, the treatment of the singular kernel affects the precision of this method. The method based on integral transform and integration by parts could treat the points on the boundary and inside the domain. It could transform the singular integral into an analytical one both in two dimensional and in three dimensional cases and thus it could eliminate the singularity. In order to analyze the elastic seismic wave scattering due to regional irregular topographies, the analytical solution for problems of this type is discussed and the analytical solution of P waves by multiple canyons is given. For the boundary reflection, the method used here is infinite boundary element absorbing boundary developed by a pervious researcher. The comparison between the analytical solutions and concrete numerical examples validate the efficiency of this method. We thoroughly discussed the sampling frequency in elastic wave simulation and find that, for a general case, three elements per wavelength is sufficient, however, when the problem is too complex, more elements per wavelength are necessary. Also, the seismic response in the frequency domain of the canyons with different types of random heterogeneities is illustrated. We analyzed the model of the random media, the horizontal and vertical correlation length, the standard deviation, and the dimensionless frequency how to affect the seismic wave amplification on the ground, and thus provide a basis for the choice of the parameter of random media during numerical simulation.

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.

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.

旋转轴对称介质中的qP波一阶射线追踪

Elastic anisotropy is a very common phenomenon in the Earth’s interior, especial for sedimentary rock as important gas and oil reservoirs. But in the processing and interpretation of seismic data, it is assumption that the media in the Earth’s interior is completely elastic and isotropic, and then the methods based on isotropy are used to deal with anisotropic seismic data, so it makes the seismic resolution lower and the error on images is caused. The research on seismic wave simulation technology can improve our understanding on the rules of seismic wave propagation in anisotropic media, and it can help us to resolve problems caused by anisotropy of media in the processing and interpretation of seismic data. So researching on weakly anisotropic media with rotated axis of symmetry, we study systematically the rules of seismic wave propagation in this kind of media, simulate the process with numerical calculation, and get the better research results. The first-order ray tracing (FORT) formulas of qP wave derived can adapt to every anisotropic media with arbitrary symmetry. The equations are considerably simpler than the exact ray tracing equations. The equations allow qP waves to be treated independently from qS waves, just as in isotropic media. They simplify considerably in media with higher symmetry anisotropy. In isotropic media, they reduce to the exact ray tracing equations. In contrast to other perturbation techniques used to trace rays in weakly anisotropic media, our approach does not require calculation of reference rays in a reference isotropic medium. The FORT-method rays are obtained directly. They are computationally more effective than standard ray tracing equations. Moreover the second-order travel time corrections formula derived can be used to reduce effectively the travel time error, and improve the accuracy of travel time calculation. The tensor transformation equations of weak-anisotropy parameters in media with rotated axis of symmetry derived from the Bond transformation equations resolve effectively the problems of coordinate transformation caused by the difference between global system of coordinate and local system of coordinate. The calculated weak-anisotropy parameters are completely suitable to the first-order ray tracing used in this paper, and their forms are simpler than those from the Bond transformation. In the numerical simulation on ray tracing, we use the travel time table calculation method that the locations of the grids in the ray beam are determined, then the travel times of the grids are obtained by the reversed distance interpolation. We get better calculation efficiency and accuracy by this method. Finally we verify the validity and adaptability of this method used in this paper with numerical simulations for the rotated TI model with anisotropy of about 8% and the rotated ORTHO model with anisotropy of about 20%. The results indicate that this method has better accuracy for both media with different types and different anisotropic strength. Keywords: weak-anisotropy, numerical simulation, ray tracing equation, travel time, inhomogeneity

叠前地震多角度三参数同步反演方法

Pre-stack seismic inversion has become the emphasis and hotspot owing to the exploration & exploitation of oil field and the development of seismic technology. Pre-stack seismic inversion has the strongpoint of making the most of amplitude versus offset compared with the post-stack method. In this dissertation, the three parameters were discussed from multi-angle reflectance of P-wave data based on Zoeppritz’s and Aki & Richard’s equation, include P-wave velocity, S-wave velocity, and density. The three parameters are inversed synchronously from the pre-stack multi-angle P-wave data, based on rockphysics model and aimed at the least remnant difference between model simulation and practical data. In order to improve the stability of inversion and resolution to thin bed, several techniques were employed, such as the wavelet transform with multi-scale function, adding the Bayesian soft constraint and hard constraints (the horizon, structure and so on) to the inversion process. Being the result, the uncertainty of the resolution is reduced, the reliability and precision are improved, the significance of parameters becomes clearer. Meeting to the fundamental requirement of pre-stack inversion, some research in rockphysics are carried out which covered the simulation and inversion of S-wave velocity, the influence of pore fluids to geophysical parameters, and the slecting and analyzing of sensitive parameters. The difference between elastic wave equation modeling and Zoeppritz equation method is also compared. A series of key techniques of pre-stack seismic inversion and description were developed, such as attributes optimization, fluid factors, etc. All the techniques mentioned above are assembled to form a technique sets and process of synchronous pre-stack seismic inversion method of the three parameters based on rock physics and model simulation. The new method and technology were applied in many areas with various reservoirs, obtained both geological and economic significance, which proved to be valid and rational. This study will promote the pre-stack inversion technology and it’s application in hidden reservoirs exploration, face good prospects for development and application.

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.

温度、压力耦合背景下多相流体运移的数学模型研究

The Mathematical modeling of multiphase fluid flow is an important aspect of basin simulation, and also is a topic of geological frontier. Based on coupling relation of temperature, pressure and fluid flow, this dissertation discusses the modeling which conform to geological regularities of fluid migration. The modeling that is multi-field and multiphase includes heat transport equation, pressure evolvement equation, solution transport equation and fluid transport equation. The finite element method is effective numerical calculation methods. Author applies it to solve modeling and implements the finite element program, and the modeling is applied to Ying-Qiong Basin. The channels of fluid vertical migration are fault, fracture and other high penetrability area. In this thesis, parallel fracture model and columnar channel model have been discussed, and a characteristic time content and a characteristic space content been obtained to illustrate the influences of stratigraphic and hydrodynamic factors on the process. The elliptoid fracture model is established and its approximately solution in theory is gotten. Three kinds of modeling are applied to analyze the transient variation process of fluid pressure in the connected permeable formations. The elliptoid fracture model is the most similar geology model comparing with the other fracture models so the research on this fracture model can enhance the understanding to fluid pressure. In the non-hydrodynamic condition, because of the difference between water density and nature gas density, nature gas can migrate upon by float force. A one-dimension mathematical model of nature gas migration by float force is established and also applied to analyze the change in the saturation of gas. In the process of gas migration its saturation is non-continuous. Fluid flow is an important factor which influences the distribution of the temperature-field, the change of temperature can influence fluid property (including density, viscidity, and solubility),a nd the temperature field has coupling relations to the fluid pressure field. In this dissertation one-dimension and two-dimension thermal convection modeling is developed and also applied to analyze convective and conductive heat transfer. Author has established one-dimension and two-dimension mathematical modeling in which fluid is a mixture of water and nature gas based on the coupling relation between temperature and pressure, discussed mixture fluid convection heat transfer in different gas saturation, and analyzed overpressure form mechanism. Based on geothermal abnormity and pore pressure distribution in Dongfong 1-1, Yinggehai Basin, South China Sea, one-dimension mathematical modeling of coupling temperature and pressure is established. The modeling simulates the process that fluid migrates from deep to shallow and overpressure forms in shallow. When overpressure is so large that fractures appear and overpressure is released. As deep fluid flow to shallow, the high geothermal then forms in shallow. Based on the geological characteristics in Ya13-1, two-dimension mathematical modeling of coupling temperature and pressure is established. Fluid vertically flows in fault and then laterally migrates in reservoir. The modeling simulates the geothermal abnormity and pore pressure distribution in reservoir.

各向同性与各向异性介质中地震波旅行时正演模拟与反演成像

By seismic tomography, interesting results have been achieved not only in the research of the geosphere with a large scale but also in the exploration of resources and projects with a small scale since 80'. Compared with traditional inversion methods, seismic tomography can offer more and detailed information about subsurface and has been being paid attention by more and more geophysicists. Since inversion based on forward modeling, we have studied and improved the methods to calculate seismic traveltimes and raypaths in isotropic and anisotropic media, and applied the improved forward methods to traveltime tomography. There are three main kinds of methods to calculate seismic traveltime field and its ray path distribution, which are ray-tracing theory, eikonal equation by the finite-difference and minimum traveltime tree algorithm. In ray tracing, five methods are introduced in the paper, including analytic ray tracing, ray shooting, ray bending, grid ray tracing and rectangle grid ray perturbation with three points. Finite-difference solution of eikonal equation is very efficient in calculation of seismic first-break, but is awkward in calculation of reflection traveltimes. We have put forward a idea to calculate traveltimes of reflected waves using a combining way of eikonal equation method and other one in order to improve its capability of dealing with reflection waves. The minimum traveltime tree algorithm has been studied with emphases. Three improved algorithms are put forward on the basis of basic algorithm of the minimum traveltime tree. The first improved algorithm is called raypath tracing backward minimum traveltime algorithm, in which not only wavelets from the current source but also wavelets from upper source points are all calculated. The algorithm can obviously improve the speed of calculating traveltimes and raypaths in layered or blocked homogeneous media and keep good accuracy. The second improved algorithm is raypath key point minimum traveltime algorithm in which traveltimes and raypaths are calculated with a view of key points of raypaths (key points of raypths mean the pivotal points which determine raypaths). The raypath key point method is developed on the basis of the first improved algorithm, and has better applicability. For example, it is very efficient even for inhomogeneous media. Another improved algorithm, double grid minimum traveltime tree algorithm, bases upon raypath key point scheme, in which a model is divided with two kinds of grids so that the unnecessary calculation can be left out. Violent undulation of curved interface often results in the phenomenon that there are no reflection points on some parts of interfaces where there should be. One efficacious scheme that curved interfaces are divided into segments, and these segments are treated respectively is presented to solve the problem. In addition, the approximation to interfaces with discrete grids leads to large errors in calculation of traveltimes and raypaths. Noting the point, we have thought a new method to remove the negative effect of mesh and to improve calculation accuracy by correcting the traveltimes with a little of additional calculation, and obtained better results.

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.