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.

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.

复杂介质边界元法数值模拟研究

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

表面相关多次波衰减方法与应用研究

The function of seismic data in prospecting and exploring oil and gas has exceeded ascertaining structural configuration early. In order to determine the advantageous target area more exactly, we need exactly image the subsurface media. So prestack migration imaging especially prestack depth migration has been used increasingly widely. Currently, seismic migration imaging methods are mainly based on primary energy and most of migration methods use one-way wave equation. Multiple will mask primary and sometimes will be regarded as primary and interferes with the imaging of primary, so multiple elimination is still a very important research subject. At present there are three different wavefield prediction and subtraction methods: wavefield extrapolation; feedback loop; and inverse-scattering series. I mainly do research on feedback loop method in this paper. Feedback loop method includs prediction and subtraction.Currently this method has some problems as follows. Firstly, feedback loop method requires the seismic data used to predict multiple is full wavefield data, but usually the original seismic data don’t meet this assumption, so seismic data must be regularized. Secondly, Multiple predicted through feedback loop method usually can’t match the real multiple in seismic data and they are different in amplitude, phase and arrrival time. So we need match the predicted multiple and that in seismic data through estimating filtering factors and subtract multiple from seismic data. It is the key for multiple elimination how to select a correct matching filtering method. There are many matching filtering methods and I put emphasis on Least-square adaptive matching filtering and L1-norm minimizing adaptive matching filtering methods. Least-square adaptive matching filtering method is computationally very fast, but it has two assumptions: the signal has minimum energy and is orthogonal to the noise. When seismic data don’t meet the two assumptions, this method can’t get good matching results and then can’t attenuate multiple correctly. L1-norm adaptive matching filtering methods can avoid these two assumptions and then get good matching results, but this method is computationally a little slow. The results of my research are as follows: 1. Proposed a method that interpolates seismic traces based on F-K migration and demigration. The main advantage of this method is that it can interpolate seismic traces in any offsets. It shows this method is valid through a simple model. 2. Comparing different Least-square adaptive matching filtering methods. The results show that equipose multi-channel adaptive matching filtering methods can get better results of multiple elimination than other matcing methods through three model data and two field data. 3. Proposed equipose multi-channel L1-norm adaptive matching filtering method. Because L1-norm is robust to large amplitude differences, there are no assumption on the signal has minimum energy and orthogonality, this method can get better results of multiple elimination. 4. Research on multiple elimination in inverse data space. The method is a new multiple elimination method and it is different from those methods mentioned above.The advantages of this method is that it is simple in theory and no need for the adaptive subtraction and computationally very fast. The disadvantage of this method is that it is not stabilized in its solution. The results show that equipose multi-channel and equipose pesudo-multi-channel least-square matching filtering and equipose multi-channel and equipose pesudo-multi-channel L1-norm matching filtering methods can get better results of multiple elimination than other matcing methods through three model data and many field data.

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.

叠前时间偏移：各向异性、多次波衰减及应用

At present, in order to image complex structures more accurately, the seismic migration methods has been developed from isotropic media to the anisotropic media. This dissertation develops a prestack time migration algorithm and application aspects for complex structures systematically. In transversely isotropic media with a vertical symmetry axis (VTI media), the dissertation starts from the theory that the prestack time migration is an approximation of the prestack depth migration, based on the one way wave equation and VTI time migration dispersion relation, by combining the stationary-phase theory gives a wave equation based VTI prestack time migration algorithm. Based on this algorithm, we can analytically obtain the travel time and amplitude expression in VTI media, as while conclude how the anisotropic parameter influence the time migration, and by analyzing the normal moveout of the far offset seismic data and lateral inhomogeneity of velocity, we can update the velocity model and estimate the anisotropic parameter model through the time migration. When anisotropic parameter is zero, this algorithm degenerates to the isotropic time migration algorithm naturally, so we can propose an isotopic processing procedure for imaging. This procedure may keep the main character of time migration such as high computational efficiency and velocity estimation through the migration, and, additionally, partially compensate the geometric divergence by adopting the deconvolution imaging condition of wave equation migration. Application of this algorithm to the complicated synthetic dataset and field data demonstrates the effectiveness of the approach. In the dissertation we also present an approach for estimating the velocity model and anisotropic parameter model. After analyzing the velocity and anisotropic parameter impaction on the time migration, and based on the normal moveout of the far offset seismic data and lateral inhomogeneity of velocity, through migration we can update the velocity model and estimate the anisotropic parameter model by combining the advantages of velocity analysis in isotropic media and anisotropic parameter estimation in VTI media. Testing on the synthetic and field data, demonstrates the method is effective and very steady. Massive synthetic dataset、2D sea dataset and 3D field datasets are used for VTI prestack time migration and compared to the stacked section after NMO and prestack isotropic time migration stacked section to demonstrate that VTI prestack time migration method in this paper can obtain better focusing and less positioning errors of complicated dip reflectors. When subsurface is more complex, primaries and multiples could not be separated in the Radon domain because they can no longer be described with simple functions (parabolic). We propose an attenuating multiple method in the image domain to resolve this problem. For a given velocity model，since time migration takes the complex structures wavefield propagation in to account, primaries and multiples have different offset-domain moveout discrepancies, then can be separated using techniques similar to the prior migration with Radon transform. Since every individual offset-domain common-reflection point gather incorporates complex 3D propagation effects, our method has the advantage of working with 3D data and complicated geology. Testing on synthetic and real data, we demonstrate the power of the method in discriminating between primaries and multiples after prestack time migration, and multiples can be attenuated in the image space considerably.

波动方程基准面校正方法研究

Datuming which has not been well solved in complex areas is a long-existing problem in seismic processing and imaging. Theoretically, Wave-equation datuming(WED) works well in the areas with substantial surface topography and areas of complex velocity structure. However, many difficulties still exist in practice. There are three main reasons: (1) It’s difficult to obtain the velocity model. (2) The computational cost is high and the efficiency is low. (3) Reflection waveform distortions are introduced by low S/N ratio in seismic data. The second and third problems are involved in the paper. To improve computational efficiency, DP1 proposed by Fu Li-Yun is applied in WED. Some quantitative and semi-quantitative conclusions of assessing the computational accuracy and efficiency have been obtained by comparing the adaptation of three operators( PS, SSF, DP1) to the surface topography and the lateral velocity variation. Moreover, the impacts of near surface scattering associated with complex surface topography on WED is analyzed theoretically. According to the analysis results, the following conclusions have been obtained. WED is stable and effective when the field data has high S/N ratio and velocity model is accurate. However ,it doesn’t work well when S/N ratio of field data is low. So denoising techniques in process of WED is important for low S/N data. The paper presents the theoretical analysis for the issues facing WED, which is expected to provide a useful reference to the further development of this technology.

波动方程偏移速度分析

On the subject of oil and gas exploration, migration is an efficacious technique for imagining structures underground. Wave-equation migration (WEM) dominates over other migration methods in accuracy, despite of higher computational cost. However, the advantages of WEM will emerge as the progress of computer technology. WEM is sensitive to velocity model more than others. Small velocity perturbations result in grate divergence in the image pad. Currently, Kirrchhoff method is still very popular in the exploration industry for the reason of difficult to provide precise velocity model. It is very urgent to figure out a way to migration velocity modeling. This dissertation is mainly devoted to migration velocity analysis method for WEM: 1. In this dissertation, we cataloged wave equation prestack depth migration. The concept of migration is introduced. Then, the analysis is applied to different kinds of extrapolate operator to demonstrate their accuracy and applicability. We derived the DSR and SSR migration method and apply both to 2D model. 2. The output of prestack WEM is in form of common image gathers (CIGs). Angle domain common image gathers (ADCIGs) gained by wave equation are proved to be free of artifacts. They are also the most potential candidates for migration velocity analysis. We discussed how to get ADCIGs by DSR and SSR, and obtained ADCIGs before and after imaging separately. The quality of post stack image is affected by CIGs, only the focused or flattened CIGs generate the correct image. Based on wave equation migration, image could be enhanced by special measures. In this dissertation we use both prestack depth residual migration and time shift imaging condition to improve the image quality. 3. Inaccurate velocities lead to errors of imaging depth and curvature of coherent events in CIGs. The ultimate goal of migration velocity analysis (MVA) is to focus scattered event to correct depth and flatten curving event by updating velocities. The kinematic figures are implicitly presented by focus depth aberration and kinetic figure by amplitude. The initial model of Wave-equation migration velocity analysis (WEMVA) is the output of RMO velocity analysis. For integrity of MVA, we review RMO method in this dissertation. The dissertation discusses the general ideal of RMO velocity analysis for flat and dipping events and the corresponding velocity update formula. Migration velocity analysis is a very time consuming work. Respect to computational convenience, we discus how RMO works for synthetic source record migration. In some extremely situation, RMO method fails. Especially in the areas of poorly illuminated or steep structure, it is very difficult to obtain enough angle information for RMO. WEMVA based on wave extrapolate theory, which successfully overcome the drawback of ray based methods. WEMVA inverses residual velocities with residual images. Based on migration regression, we studied the linearized scattering operator and linearized residual image. The key to WEMVA is the linearized residual image. Residual image obtained by Prestack residual migration, which based on DSR is very inefficient. In this dissertation, we proposed obtaining residual migration by time shift image condition, so that, WEMVA could be implemented by SSR. It evidently reduce the computational cost for this method.

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.

波动方程叠前深度偏移辛算法及速度建模

On 70~(th) SEG Annual meeting, many author have announced their result on the wave equation prestack depth migration. The methods of the wave-field imaging base on wave equation becomes mature and the main direction of seismic imaging. The direction of imaging the complex media has been the main one of the projects that the national "85" and "95" reservoir geophysics key projects and "Knowledge innovation key project of Chinese Academy of Science" have been supported. Furthermore, we began the study for special oil field situation of our nation with the international research groups. Under the background, the author combined the thoughts of symplectic with wave equation pre-stack depth migration, and develops and efficient wave equation pre-stack depth migration method. The purpose of this work is to find out a way to imaging the complex geological goals of Chinese oilfields and form a procedure of seismic data processing. The paper gives the approximation of one way wave equation operator, and shows the numerical results. The comparisons have been made between split-step phase method, Kirchhoff and Ray+FD methods on the pulse response, simple model and Marmousi model. The results shows that the method in this paper has an higher accuracy. Four field data examples have also be given in this paper. The results of field data demonstrate that the method can be usable. The velocity estimation is an important part of the wave equation pre-stack depth migration. A parallel velocity estimation program has been written and tested on the Beowulf clusters. The program can establish a velocity profile automatically. An example on Marmousi model has shown in the third part of the paper to demonstrate the method. Another field data was also given in the paper. Beowulf cluster is the converge of the high performance computer architecture. Today, Beowulf Cluster is a good choice for institutes and small companies to finish their task. The paper gives some comparison results the computation of the wave equation pre-stack migration on Beowulf cluster, IBM-SP2 (24 nodes) in Daqing and Shuguang 3000, and the comparison of their prize. The results show that the Beowulf cluster is an efficient way to finish the large amount computation of the wave equation pre-stack depth migration, especially for 3D.

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.

辛格式波动方程叠前深度偏移及速度建模

On 70~(th) SEG Annual meeting, many author have announced their result on the wave equation pre-stack depth migration. The methods of the wave-field imaging base on wave equation becomes mature and the main direction of seismic imaging. The direction of imaging the complex media has been the main one of the projects that the national "85" and "95" reservoir geophysics key projects and "Knowledge innovation key project of Chinese Academy of Science" have been supported. Furthermore, we began the study for special oil field situation of our nation with the international research groups. Under the background, the author combined the thoughts of symplectic with wave equation pre-stack depth migration, and develops and efficient wave equation pre-stack depth migration method. The purpose of this work is to find out a way to imaging the complex geological goals of Chinese oilfields and form a procedure of seismic data processing. The paper gives the approximation of one way wave equation operator, and shows the numerical results. The comparisons have been made between split-step phase method, Kirchhoff and Ray+FD methods on the pulse response, simple model and Marmousi model. The result shows that the method in this paper has an higher accuracy. Four field data examples have also be given in this paper. The results of field data demonstrate that the method can be usable. The velocity estimation is an important part of the wave equation pre-stack depth migration. A. parallel velocity estimation program has been written and tested on the Beowulf clusters. The program can establish a velocity profile automatically. An example on Marmousi model has shown in the third part of the paper to demonstrate the method. Another field data was also given in the paper. Beowulf cluster is the converge of the high performance computer architecture. Today, Beowulf Cluster is a good choice for institutes and small companies to finish their task. The paper gives some comparison results the computation of the wave equation pre-stack migration on Beowulf cluster, IBM-SP2 (24 nodes) in Daqing and Shuguang3000, and the comparison of their prize. The results show that the Beowulf cluster is an efficient way to finish the large amount computation of the wave equation pre-stack depth migration, especially for 3D.

泥岩裂缝储层地震识别的理论和方法

During the exploration of fractured reservoirs, worldwide difficult problems will be encountered: how to locate the fractured zones, how to quantitatively determine the azimuth, density, and distribution of the fractures, and how to compute the permeability and porosity of the fractures. In an endeavor to solve these problems, the fractured shale reservoir in SiKou area of ShengLi oil field was chosen as a study area. A study of seismic predictive theory and methods for solving problems encountered in fractured reservoir exploration are examined herein. Building on widely used current fractured reservoir exploration techniques, new seismic theories and methods focusing on wave propagation principles in anisotropic medium are proposed. Additionally, integrated new seismic data acquisition and processing methods are proposed. Based on research and application of RVA and WA methods from earlier research, a new method of acoustic impedance varying with azimuth (IPVA) creatively is put forth. Lastly combining drilling data, well log data, and geologic data, an integrated seismic predictive method for cracked reservoir bed was formed. A summary of the six parts of research work of this paper is outlined below. In part one, conventional geologic and geophysical prediction methods etc. for cracked reservoir exploration are examined, and the weaknesses of these approaches discussed. In part two, seismic wave propagation principles in cracked reservoirs are studied. The wave equation of seismic velocity and attenuation factor in three kinds of fracture mediums is induced, and the azimuth anisotropy of velocity and attenuation in fracture mediums is determined. In part three, building on the research and application of AVA and WA methods by a former researcher, a new method of acoustic impedance creatively varying with azimuth (IPVA) is introduced. A practical software package utilizing this technique is also introduced. In part four, Base on previously discussed theory, first a large full azimuth 3d seismic data (70km~2) was designed and acquired. Next, the volume was processed with conventional processing sequence. Then AVA, WA, and IPVA processing was applied, and finally the azimuth and density of the fractures were quantitatively determined by an integrated method. Predictions were supported by well data that indicate the approach is highly reliable. in part five, geological conditions contributing to cracked reservoir bed formation are analyzed in the LuoJia area resulting in the discovery that the main fractured zones are related to fault distribution in the basin, that also control the accumulation of the oil and gas, the generation mechanisms and types of fractured shale reservoirs are studied. Lastly, by using full 3D seismic attributes, azimuth and density of cracked reservoir zones are successfully quantitative predicted. Using an integrated approach that incorporates seismic, geologic and well log data, the best two fractured oil prospects in LouJia area are proposed. These results herein represent a break through in seismic technology, integrated seismic predictive theory, and production technology for fractured reservoirs. The approach fills a void that can be applied both inside China, and internationally. Importantly, this technique opens a new exploration play in the ShengLi oil field that while difficult has substantial potential. Properly applied, this approach could play an important role toward stabilizing the oil field' production. In addition, this technique could be extended fracture exploration in other oil fields producing substantial economic reward.

改善三维波动方程叠前深度偏移处理效果的方法研究

3D wave equation prestack depth migration is the effective tool for obtaining the exact imaging result of complex geology structures. It's a part of the 3D seismic data processing. 3D seismic data processing belongs to high dimension signal processing, and there are some difficult problems to do with. They are: How to process high dimension operators? How to improve the focusing? and how to construct the deconvolution operator? The realization of 3D wave equation prestack depth migration, not only realized the leap from poststack to prestack, but also provided the important means to solve the difficult problems in high dimension signal processing. In this thesis, I do a series research especially for the solve of the difficult problems around the 3D wave equation prestack depth migration and using it as a mean. So this thesis service for the realization of 3D wave equation prestack depth migration for one side and improve the migration effect for another side. This thesis expatiates in five departs. Summarizes the main contents as the follows: In the first part, I have completed the projection from 3D data point area to low dimension are using de big matrix transfer and trace rearrangement, and realized the liner processing of high dimension signal. Firstly, I present the mathematics expression of 3D seismic data and the mean according to physics, present the basic ideal of big matrix transfer and describe the realization of five transfer models for example. Secondly, I present the basic ideal and rules for the rearrange and parallel calculate of 3D traces, and give a example. In the conventional DMO focusing method, I recall the history of DM0 process firstly, give the fundamental of DMO process and derive the equation of DMO process and it's impulse response. I also prove the equivalence between DMO and prestack time migration, from the kinematic character of DMO. And derive the relationship between DMO base on wave equation and prestack time migration. Finally, I give the example of DMO process flow and synthetic data of theoretical models. In the wave equation prestak depth migration, I firstly recall the history of migration from time to depth, from poststack to prestack and from 2D to 3D. And conclude the main migration methods, point out their merit and shortcoming. Finally, I obtain the common image point sets using the decomposed migration program code.In the residual moveout, I firstly describe the Viterbi algorithm based on Markov process and compound decision theory and how to solve the shortest path problem using Viterbi algorithm. And based on this ideal, I realized the residual moveout of post 3D wave equation prestack depth migration. Finally, I give the example of residual moveout of real 3D seismic data. In the migration Green function, I firstly give the concept of migration Green function and the 2D Green function migration equation for the approximate of far field. Secondly, I prove the equivalence of wave equation depth extrapolation algorithms. And then I derive the equation of Green function migration. Finally, I present the response and migration result of Green function for point resource, analyze the effect of migration aperture to prestack migration result. This research is benefit for people to realize clearly the effect of migration aperture to migration result, and study on the Green function deconvolution to improve the focusing effect of migration.

地震波场延拓+菲涅尔体叠加方法及成像效果

In the increasingly enlarged exploration target, deep target layer(especially for the reservoir of lava) is a potential exploration area. As well known, the reflective energy becomes weak because the seismic signals of reflection in deep layer are absorbed and attenuate by upper layer. Caustics and multi-values traveltime in wavefield are aroused by the complexity of stratum. The ratio of signal to noise is not high and the fold numbers are finite(no more than 30). All the factors above affect the validity of conventional processing methods. So the high S/N section of stack can't always be got with the conventional stack methods even if the prestack depth migration is used. So it is inevitable to develop another kind of stack method instead. In the last a few years, the differential solution of wave equation was hold up by the condition of computation. Kirchhoff integral method rose in the initial stages of the ninetieth decade of last century. But there exist severe problems in it, which is are too difficult to resolve, so new method of stack is required for the oil and gas exploration. It is natural to think about upgrading the traditionally physic base of seismic exploration methods and improving those widely used techniques of stack. On the other hand, great progress is depended on the improvement in the wave differential equation prestack depth migration. The algorithm of wavefield continuation in it is utilized. In combination with the wavefield extrapolation and the Fresnel zone stack, new stack method is carried out It is well known that the seismic wavefield observed on surface comes from Fresnel zone physically, and doesn't comes from the same reflection points only. As to the more complex reflection in deep layer, it is difficult to describe the relationship between the reflective interface and the travel time. Extrapolation is used to eliminate caustic and simplify the expression of travel time. So the image quality is enhanced by Fresnel zone stack in target. Based on wave equation, high-frequency ray solution and its character are given to clarify theoretical foundation of the method. The hyperbolic and parabolic travel time of the reflection in layer media are presented in expression of matrix with paraxial ray theory. Because the reflective wave field mainly comes from the Fresnel Zone, thereby the conception of Fresnel Zone is explained. The matrix expression of Fresnel zone and projected Fresnel zone are given in sequence. With geometrical optics, the relationship between object point in model and image point in image space is built for the complex subsurface. The travel time formula of reflective point in the nonuniform media is deduced. Also the formula of reflective segment of zero-offset and nonzero offset section is provided. For convenient application, the interface model of subsurface and curve surface derived from conventional stacks DMO stack and prestack depth migration are analyzed, and the problem of these methods was pointed out in aspects of using data. Arc was put forward to describe the subsurface, thereby the amount of data to stack enlarged in Fresnel Zone. Based on the formula of hyperbolic travel time, the steps of implementation and the flow of Fresnel Zone stack were provided. The computation of three model data shows that the method of Fresnel Zone stack can enhance the signal energy and the ratio of signal to noise effectively. Practical data in Xui Jia Wei Zhi, a area in Daqing oilfield, was processed with this method. The processing results showed that the ability in increasing S/N ratio and enhancing the continuity of weak events as well as confirming the deep configuration of volcanic reservoir is better than others. In deeper target layer, there exists caustic caused by the complex media overburden and the great variation of velocity. Travel time of reflection can't be exactly described by the formula of travel time. Extrapolation is bring forward to resolve the questions above. With the combination of the phase operator and differential operator, extrapolating operator adaptable to the variation of lateral velocity is provided. With this method, seismic records were extrapolated from surface to any different deptlis below. Wave aberration and caustic caused by the inhomogenous layer overburden were eliminated and multi-value curve was transformed into the curve.of single value. The computation of Marmousi shows that it is feasible. Wave field continuation extends the Fresnel Zone stack's application.