地震采集观测系统的共聚焦分析

Focal beam analysis is a method for assessment of acquisition geometries that is directly linked to pre-stack migration. About dealing with the complex subsurface structures, the conventional survey design methods which do not take into account the subsurface are no longer valid. Based on the Fourier finite-difference (FFD) large-step wave field extrapolation and Born-Kirchhoff (BK) small-step wavefield interpolation, the thesis presents a rapid resolution analysis of 3D seismic survey design by focal beams in complicated media. Subsequently, The SEG/EAEG salt model is used to illustrate the method. Based on the focal beam resolution definition, each kind of influence factor is discussed. The focal beam analysis usually is carried out in a single frequency, but the actual seismic waves always contain a frequency bandwidth. In this thesis, theoretical relationship between focal beam analysis and frequency is derived. Since the effects of focal beam analysis are linear with frequency simply, the multi-frequency focal beam analysis using interpolation is developed. At the same time, the resolution of different frequency bandwidth is interconvertible in accordance with Signal uncertainty principle. The resolution of all frequency bands can be calculated by using only a few focal beam analysis for a seismic survey. In the last section of this thesis, I propose a new approach to predicting acquisition footprint, based on the assumption of Common-Middle-Point stack without constructing a special velocity model. The approach is a simplistic analytical method in which the acquisition footprint pattern is a weighted, linear summation of limited-offset fold-of-stack plots. Because the value of acquisition can be got by quantificational and rapidly calculating, we can exactly do a comparative analysis among different plans of seismic survey by this method.

地震P-S波时差耦合作用的斜坡崩滑效应研究

China locates between the circum-Pacific and the Mediterranean-Himalayan seismic belt. The seismic activities in our country are very frequent and so are the collapses and slides of slope triggered by earthquakes. Many collapses and slides of slope take place mainly in the west of China with many earthquakes and mountains, especially in Sichuan and Yunnan Provinces. When a strong earthquake happening, the damage especially in mountains area caused by geological hazards it triggered such as rock collapses, landslides and debris flows is heavier than that it caused directly. A conclusion which the number of lives lost caused by geological hazards triggered by a strong earthquake in mountains area often accounts for a half even more of the total one induced by the strong earthquake can be made by consulting the statistical loss of several representative earthquakes. As a result, geological hazards such as collapses and slides of slope triggered by strong earthquakes attract wide attention for their great costs. Based on field geological investigation, engineering geological exploration and material data analysis, chief conclusions have been drawn after systematic research on formation mechanism, key inducing factors, dynamic characteristics of geological hazards such as collapses and slides of slope triggered by strong earthquakes by means of engineering geomechanics comprehensive analysis, finite difference numerical simulation test, in-lab dynamic triaxial shear test of rock, discrete element numerical simulation. Based on research on a great number of collapses and landslides triggered by Wenchuan and Xiaonanhai Earthquake, two-set methods, i.e. the method for original topography recovering based on factors such as lithology and elevation comparing and the method for reconstructing collapsing and sliding process of slope based on characteristics of seism tectonic zone, structural fissure, diameter spatial distribution of slope debris mass, propagation direction and mechanical property of seismic wave, have been gotten. What is more, types, formation mechanism and dynamic characteristics of collapses and slides of slope induced by strong earthquakes are discussed comprehensively. Firstly, collapsed and slided accumulative mass is in a state of heavily even more broken. Secondly, dynamic process of slope collapsing and sliding consists of almost four stages, i.e. broken, thrown, crushed and river blocked. Thirdly, classified according to failure forms, there are usually four types which are made up of collapsing, land sliding, land sliding-debris flowing and vibrating liquefaction. Finally, as for key inducing factors in slope collapsing and sliding, they often include characteristics of seism tectonic belts, structure and construction of rock mass, terrain and physiognomy, weathering degree of rock mass and mechanical functions of seismic waves. Based on microscopic study on initial fracturing of slope caused by seismic effect, combined with two change trends which include ratio of vertical vs. horizontal peak ground acceleration corresponding to epicentral distance and enlarging effect of peak ground acceleration along slope, key inducing factor of initial slope fracturing in various area with different epicentral distance is obtained. In near-field area, i.e. epicentral distance being less than 30 km, tensile strength of rock mass is a key intrinsic factor inducing initial fracturing of slope undergoing seismic effect whereas shear strength of rock mass is the one when epicentral distance is more than 30 km. In the latter circumstance, research by means of finite difference numerical simulation test and in-lab dynamic triaxial shear test of rock shows that initial fracture begins always in the place of slope shoulder. The fact that fracture strain and shear strength which are proportional to buried depth of rock mass in the place of slope shoulder are less than other place and peak ground acceleration is enlarged in the place causes prior failure at slope shoulder. Key extrinsic factors inducing dynamic fracture of slope at different distances to epicenter have been obtained through discrete element numerical simulation on the total process of collapsing and sliding of slope triggered by Wenchuan Earthquake. Research shows that combined action of P and S seismic waves is the key factor inducing collapsing and sliding of slope at a distance less than 64 km to initial epicenter along earthquake-triggering structure. What is more, vertical tensile action of P seismic wave plays a leading role near epicenter, whereas vertical shear action of S seismic wave plays a leading role gradually with epicentral distance increasing in this range. On the other hand, single action of P seismic wave becomes the key factor inducing collapsing and sliding of slope at a distance between 64 km and 216 km to initial epicenter. Horizontal tensile action of P seismic wave becomes the key factor gradually from combined action between vertical and horizontal tensile action of P seismic wave with epicentral distance increasing in this distance range. In addition, initial failure triggered by strong earthquakes begins almost in the place of slope shoulder. However, initial failure beginning from toe of slope relates probably with gradient and rock occurrence. Finally, starting time of initial failure in slope increases usually with epicentral distance. It is perhaps that the starting time increasing is a result of attenuating of seismic wave from epicenter along earthquake-triggering structure. It is of great theoretical and practical significance for us to construct towns and infrastructure in fragile geological environment along seism tectonic belts and conduct risk management on earthquake-triggered geological hazards by referring to above conclusions.

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.

三维油藏数值模拟正反演算法研究

The dynamic prediction of complex reservoir development is one of the important research contents of dynamic analysis of oil and gas development. With the increase development of time, the permeabilities and porosities of reservoirs and the permeability of block reservoir at its boundaries are dynamically changing. How to track the dynamic change of permeability and porosity and make certain the permeability of block reservoir at its boundary is an important practical problem. To study developing dynamic prediction of complex reservoir, the key problem of research of dynamic prediction of complex reservoir development is realizing inversion of permeability and porosity. To realize the inversion, first of all, the fast forward and inverse method of 3-dimension reservoir simulation must be studied. Although the inversion has been widely applied to exploration and logging, it has not been applied to3-dimension reservoir simulation. Therefore, the study of fast forward and inverse method of 3-dimension reservoir simulation is a cutting-edge problem, takes on important realistic signification and application value. In this dissertation, 2-dimension and 3-dimension fluid equations in porous media are discretized by finite difference, obtaining finite difference equations to meet the inner boundary conditions by Peaceman's equations, giving successive over relaxation iteration of 3-dimension fluid equations in porous media and the dimensional analysis. Several equation-solving methods are compared in common use, analyzing its convergence and convergence rate. The alternating direction implicit procedure of 2-dimension has been turned into successive over relaxation iteration of alternating direction implicit procedure of 3-dimension fluid equations in porous media, which possesses the virtues of fast computing speed, needing small memory of computer, good adaptability for heterogeneous media and fast convergence rate. The geological model of channel-sandy reservoir has been generated with the help of stochastic simulation technique, whose cross sections of channel-sandy reservoir are parabolic shapes. This method makes the hard data commendably meet, very suit for geological modeling of containing complex boundary surface reservoir. To verify reliability of the method, theoretical solution and numerical solution are compared by simplifying model of 3-dimension fluid equations in porous media, whose results show that the only difference of the two pressure curves is that the numerical solution is lower than theoretical at the wellbore in the same space. It proves that using finite difference to solve fluid equations in porous media is reliable. As numerical examples of 3-dimension heterogeneous reservoir of the single-well and multi-well, the pressure distributions have been computed respectively, which show the pressure distributions there are clearly difference as difference of the permeabilities is greater than one order of magnitude, otherwise there are no clearly difference. As application, the pressure distribution of the channel-sandy reservoir have been computed, which indicates that the space distribution of pressure strongly relies on the direction of permeability, and is sensitive for space distributions of permeability. In this dissertation, the Peaceman's equations have been modified into solving vertical well problem and horizontal well problem simultaneously. In porous media, a 3D layer reservoir in which contain vertical wells and horizontal wells has been calculated with iteration. For channel-sandy reservoir in which there are also vertical wells and horizontal wells, a 3D transient heterogeneous fluid equation has been discretized. As an example, the space distribution of pressure has been calculated with iteration. The results of examples are accord with the fact, which shows the modification of Peaceman's equation is correct. The problem has been solved in the space where there are vertical and horizontal wells. In the dissertation, the nonuniform grid permeability integration equation upscaling method, the nonuniform grid 2D flow rate upscaling method and the nonuniform grid 3D flow rate upscaling method have been studied respectively. In those methods, they enhance computing speed greatly, but the computing speed of 3D flow rate upscaling method is faster than that of 2D flow rate upscaling method, and the precision of 3D flow rate upscaling method is better than that of 2D flow rate upscaling method. The results also show that the solutions of upscaling method are very approximating to that of fine grid blocks. In this paper, 4 methods of fast adaptive nonuniform grid upscaling method of 3D fluid equations in porous media have been put forward, and applied to calculate 3D heterogeneous reservoir and channel-sandy reservoir, whose computing results show that the solutions of nonuniform adaptive upscaling method of 3D heterogeneous fluid equations in porous media are very approximating to that of fine grid blocks in the regions the permeability or porosity being abnormity and very approximating to that of coarsen grid blocks in the other region, however, the computing speed of adaptive upscaling method is 100 times faster than that of fine grid block method. The formula of sensitivity coefficients are derived from initial boundary value problems of fluid equations in porous media by Green's reciprocity principle. The sensitivity coefficients of wellbore pressure to permeability parameters are given by Peaceman's equation and calculated by means of numerical calculation method of 3D transient anisotropic fluid equation in porous media and verified by direct method. The computing results are in excellent agreement with those obtained by the direct method, which shows feasibility of the method. In the dissertation, the calculating examples are also given for 3D reservoir, channel-sandy reservoir and 3D multi-well reservoir, whose numerical results indicate: around the well hole, the value of the sensitivity coefficients of permeability is very large, the value of the sensitivity coefficients of porosity is very large too, but the sensitivity coefficients of porosity is much less than the sensitivity coefficients of permeability, so that the effect of the sensitivity coefficients of permeability for inversion of reservoir parameters is much greater than that of the sensitivity coefficients of porosity. Because computing the sensitivity coefficients needs to call twice the program of reservoir simulation in one iteration, realizing inversion of reservoir parameters must be sustained by the fast forward method. Using the sensitivity coefficients of permeability and porosity, conditioned on observed valley erosion thickness in wells (hard data), the inversion of the permeabilities and porosities in the homogeneous reservoir, homogeneous reservoir only along the certain direction and block reservoir are implemented by Gauss-Newton method or conjugate gradient method respectively. The results of our examples are very approximating to the real data of permeability and porosity, but the convergence rate of conjugate gradient method is much faster than that of Gauss-Newton method.

各向异性与非线性介质中弹性波场传播特征研究

The topic of this study is about the propagation features of elastic waves in the anisotropic and nonlinear media by numerical methods with high accuracy and stability. The main achievements of this paper are as followings: Firstly, basing on the third order elastic energy formula, principle of energy conservation and circumvolved matrix method, we firstly reported the equations of non-linear elastic waves with two dimensions and three components in VTI media. Secondly, several conclusions about some numerical methods have been obtained in this paper. Namely, the minimum suitable sample stepth in space is about 1/8-1/12 of the main wavelength in order to distinctly reduce the numerical dispersion resulted from the numerical mehtod, at the same time, the higher order conventional finite difference (CFD) schemes will give little contribution to avoid the numerical solutions error accumulating with time. To get the similar accuracy with the fourth order center finite difference method, the half truncation length of SFFT should be no less than 7. The FDFCT method can present with the numerical solutions without obvious dispersion when the paprameters of FCT is suitable (we think they should be in the scope from 0.0001 to 0.07). Fortunately, the NADM method not only can reported us with the higher order accuracy solutions (higher than that of the fourth order finite difference method and lower than that of the sixth order finite difference method), but also can distinctly reduce the numerical dispersion. Thirdly, basing on the numerial and theoretical analysis, we reported such nonlinear response accumulating with time as waveform aberration, harmonic generation and resonant peak shift shown by the propagation of one- and two-dimensional non-linear elasticwaves in this paper. And then, we drew the conclusion that these nonlinear responses are controlled by the product between nonlinear strength (SN) and the amplitude of the source. At last, the modified FDFCT numerical method presented by this paper is used to model the two-dimensional non-linear elastic waves propagating in VTI media. Subsequently, the wavelet analysis and polarization are adopted to investigate and understand the numerical results. And then, we found the following principles (attention: the nonlinear strength presented by this paper is weak, the thickness of the -nonlinear media is thin (200m), the initial energy of the source is weak and the anisotropy of the media is weak too): The non-linear response shown by the elastic waves in VTI media is anisotropic too; The instantaneous main frequency sections of seismic records resulted from the media with a non-linear layer have about 1/4 to 1/2 changes of the initial main frequency of source with that resulted from the media without non-linear layer; The responses shown by the elasic waves about the anisotropy and nonlinearity have obvious mutual reformation, namely, the non-linear response will be stronger in some directions because of the anisotropy and the anisotropic strength shown by the elastic waves will be stronger when the media is nonlinear.

Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel

Numerical analysis of fully developed laminar slip flow and heat transfer in trapezoidal micro-channels has been studied with uniform wall heat flux boundary conditions. Through coordinate transformation, the governing equations are transformed from physical plane to computational domain, and the resulting equations are solved by a finite-difference scheme. The influences of velocity slip and temperature jump on friction coefficient and Nusselt number are investigated in detail. The calculation also shows that the aspect ratio and base angle have significant effect on flow and heat transfer in trapezoidal micro-channel. (c) 2005 Elsevier Ltd. All rights reserved.