3-D Geological Modeling-Concept,Methods and Key Techniques

3-D geological modeling plays an increasingly important role in Petroleum Geology, Mining Geology and Engineering Geology. The complexity of geological conditions requires different modeling methods in different situations. This paper summarizes the general concept of geological modeling; compares the characteristics of borehole-based modeling, cross-section based modeling and multi- source interactive modeling; analyses key techniques in 3-D geological modeling; and highlights the main difficulties and directions of future studies.

ANALYSIS OF SLAB EDGING BY A 3-D RIGID VISCO-PLASTIC FINITE ELEMENT METHOD

3-D rigid visco-plastic finite element method (FEM) is used in the analysisof metal forming processes, including strip and plate rolling, shape rolling, slab edging, specialstrip rolling. The shifted incomplete Cholesky decomposition of the stiffness matrix with thesolution of the equations for velocity increment by the conjugate gradient method is combined. Thistechnique, termed the shifted ICCG method, is then employed to solve the slab edging problem. Theperformance of this algorithm in terms of the number of iterations, friction variation, shiftedparameter psi and the results of simulation for processing parameters are analysed. Numerical testsand application of this technique verify the efficiency and stability of the shifted ICCG method inthe analysis of slab edging.

A, ■-Ω METHOD FOR 3-D EDDY CURRENT ANALYSIS

After the field equations and the snonumuoo conditions between the interfaces for 3D eddy current problems Under various gauges were discussed, it was pointed cut in this paper that using the magnetic vector potential A. the electric scalar potential and Coulomb gauge △ .A = 0 in eddy current regions and using the magntetic scalar potential Ω in the non-conducting regions are more suitable. All field equations, the boundary conditions, the interface continuity conditions and the corresponding variational principle of this method are also given

A TENSOR ANALYSIS METHOD FOR ESTIMATING 3-D MOTION PARAMETERS

By using the center projection image sequence to estimate 3-D motion parameters,one needs to know the corresponding relationship between the feature of motion object in spaceand the projection coordinate on image plane.In order to avoid using the relationship of featurecorrespondence,the tensor analysis method in the affine transformation system is presented,andthe simulation data of experimental results are given.

A study on 3-D velocity structure of crust and upper mantle in Sichuan -Yunnan region, China

Based on the first arrival P and S data of 4 625 regional earthquakes recorded at 174 stations dispersed in the Yunnan and Sichuan Provinces, the 3-D velocity structure of crust and upper mantle in the region is determined, incorporating with previous deep geophysical data. In the upper crust, a positive anomaly velocity zone exists in the Sichuan basin, whereas a negative anomaly velocity zone exists in the western Sichuan plateau. The boundary between the positive and negative anomaly zones is the Longmenshan fault zone. The images of lower crust and upper mantle in the Longmenshan fault, Xianshuihe fault, Honghe fault and others show the characteristic of tectonic boundary, indicating that the faults likely penetrate the Moho discontinuity. The negative velocity anomalies at the depth of 50 km in the Tengchong volcanic area and the Panxi tectonic zone appear to be associated with the temperature and composition variations in the upper mantle. The overall features of the crustal and the upper mantle structures in the SichuanYunnan region are the lower average velocity in both crust and uppermost mantle, the large crustal thickness variations, and the existence of high conductivity layer in the crust or/and upper mantle, and higher geothermal value. All these features are closely related to the collision between the India and the Asia plates. The crustal velocity in the SichuanYunnan rhombic block generally shows normal value or positive anomaly, while the negative anomaly exists in the area along the large strike-slip faults as the block boundary. It is conducive to the crustal block side-pressing out along the faults. In the major seismic zones, the seismicity is relative to the negative anomaly velocity. Most strong earthquakes occurred in the upper-mid crust with positive anomaly or normal velocity, where the negative anomaly zone generally exists below.

Thre-dimensional topographic responses in MT using finite diference method

In this paper, the magnetotelluric response to 3-D earth topography was studied using the finite difference method for rectangular cells. Three numerical modeling calculations were carried out; the results indicate that the finite difference method is applicable to the magnetotelluric problem in estimating the 3-D topographic responses.

A SELF-SIMILAR CRACK EXPANSION METHOD FOR THREE-DIMENSIONAL CRACKS IN AN INFINITE OR SEMI-INFINITE MEDIUM

The Self-Similar Crack Expansion (SSCE) method is used to calculate stress intensity factors for three-dimensional cracks in an infinite medium or semi-infinite medium by the boundary integral element technique, whereby, the stress intensity factors at crack tips are determined by calculating the crack-opening displacements over the crack surface. For elements on the crack surface, regular integrals and singular integrals are precisely evaluated based on closed form expressions, which improves the accuracy. Examples shaw that this method yields very accurate results for stress intensity factors of penny-shaped cracks and elliptical cracks in the full space, with errors of less than 1% as compared with analytical solutions. The stress intensity factors of subsurface cracks ate in good agreement with other analytical solutions.

Improved treatments for evaluating horizontal magnetic components through the 3-D FDM in E-polarization induction problems

To improve the accuracy of the numerical evaluation through the 3-D finite difference method, the surface boundary conditions are added to modify the old program. The author has tested the new program by making calculations for the model constructed by Wanamaker, et al (1984). The comparison between the numerical results obtained from this paper and those by Wannamaker, et al (1984) indicates that a pronounced improvement is realized in the evaluation of the horizontal magnetic components. Moreover, better calculations for the vertical magnetic components are also obtainable by using the new program.

Scattering of seismic waves by three-dimensional large-scale hill topography simulated by a fast parallel IBEM

To solve seismic wave scattering by a large-scale three-dimensional(3-D) hill topography, a fast parallel indirect boundary element method(IBEM) is developed by proposing a new construction method for the wave field, modifying the generalized minimum residual(GMRES) algorithm and constructing an Open MP plus MPI parallel model. The validations of accuracy and efficiency show that this method can solve 3-D seismic response of a large-scale hill topography for broadband waves, and overcome the weakness of large storage and low efficiency of the traditional IBEM. Based on this new algorithm architecture, taking the broadband scattering of plane SV waves by a large-scale Gaussian-shaped hill of thousands-meters height as an example, the influence of several important parameters is investigated, including the incident frequency, the incident angle and the height-width and length-width ratio of the hill. The numerical results illustrate that the amplification effect on the ground motion by a near-hemispherical hill is more significant than the narrow hill. For low-frequency waves, the scattering effect of the higher hill is more pronounced, and there is only a single peak near the top of the hill. However, for high-frequency waves, rapid spatial variation of displacement amplitude appears on the hill surface.

Propagation of traveling wave solutions for nonlinear evolution equation through the implementation of the extended modi ed direct algebraic method

In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.

Numerical simulation of 3-D water collapse with an obstacle by FEM-level set method

An interface capturing approach based on a level set function for simulating transient two-phase viscous incompressible flows is applied in this paper. A narrow-band signed distance function is adopted to indicate the phase fields and the interface. The multiphase flow is numerically solved by three stages with finite element method （FEM）： （1） solving a two-fluid Navier-Stokes （N-S） equations over the whole domain, （2） transporting the level set function with the obtained velocity field, （3） the level set function correction through a renormalization with continuous penalization which preserves the thickness of the interface. In this paper, the 3-D water colunm collapse with an obstacle is simulated, which yielded good agreement with the experimental data.

Exponential Convergence Theory of the Multipole and Local Expansions for the 3-D Laplace Equation in Layered Media

In this paper,we establish the exponential convergence theory for the multipole and local expansions,shifting and translation operators for the Green's function of 3-dimensional Laplace equation in layered media.An immediate application of the theory is to ensure the exponential convergence of the FMM which has been shown by the numerical results reported in[27].As the Green's function in layered media consists of free space and reaction field components and the theory for the free space components is well known,this paper will focus on the analysis for the reaction components.We first prove that the density functions in the integral representations of the reaction components are analytic and bounded in the right half complex wave number plane.Then,by using the Cagniard-de Hoop transform and contour deformations,estimates for the remainder terms of the truncated expansions are given,and,as a result,the exponential convergence for the expansions and translation operators is proven.

Analysis of 3-D Frictional Contact Mechanics Problems by a Boundary Element Method

The development of two boundary element algorithms for solving 3-D, frictional, and linear elastostatic contact problems is reported in this paper. The algorithms employ nonconforming discreti- zations for solving 3-D boundary element models, which provide much needed flexibility in the bound- ary element modeling for 3-D contact problems. These algorithms are implemented in a new 3-D boundary element code and verified using several examples. For the numerical examples studied, the results using the new boundary element algorithms match very well with the results using a commercial finite element code, and clearly demonstrate the feasibility of the new boundary element approach for 3-D contact analysis.

Stability Conditions for Wave Simulation in 3-D Anisotropic Media with the Pseudospectral Method

Simulation of elastic wave propagation has important applications in many areas such as inverse problemand geophysical exploration.In this paper,stability conditions for wave simulation in 3-D anisotropic media with the pseudospectral method are investigated.They can be expressed explicitly by elasticity constants which are easy to be applied in computations.The 3-Dwave simulation for two typical anisotropic media,transversely isotropic media and orthorhombic media,are carried out.The results demonstrate some satisfactory behaviors of the pseudospectral method.

Compute extremely low-frequency electromagnetic field exposure by 3-D impendance method

A 3-D impedance method has been introduced to compute the electric currents induced in a human body exposed to extremely low-frequency electromagnetic field. The 3-D impedance method has been deduced from Maxwell equations and is put into the computation and simulation effectively to the visible human body model, which has 196×114×626 cells and more than 40 types of tissues. As the result, two representative cases are investigated. One is exposure of the human body to 100 μT （1 000 mG）, the limit recommended by the International Commission on Non-Ionizing Radiation Protection for the public and the other one is the exposure of human body to 0.4 laT （4 mG）, the level at which a statistical link appears with a doubled risk of development of childhood leukaemia. The distribution of induced current density can be obtained and the maximum of induced current are found to be 16 mA/m^2 and 0.07 mA/m^2.

New Multipole Method for 3-D Capacitance Extraction

This paper describes an efficient improvement of the multipole accelerated boundary element method for 3-D capacitance extraction. The overall relations between the positions of 2-D boundary elements are considered instead of only the relations between the center-points of the elements, and a new method of cube partitioning is introduced. Numerical results are presented to demonstrate that the method is accurate and has nearly linear computational growth as O(n), where n is the number of panels/boundary elements. The proposed method is more accurate and much faster than Fastcap.

陀螺系统特征值问题的一些探讨

陀螺系统特征值问题是在转子动力学中提出的一个典型的数学问题。它的研究一直受到力学界的重视。研究它具有较大的理论意义和工程应用价值。作为本专题的第一部分，本文探讨三维旋转法本身存在的问题。指出三维旋转法不是对任何反对称矩阵都是合适的，而应有条件地应用它。

SIMULATION OF HYDRAULIC TRANSIENTS IN HYDROPOWER SYSTEMS USING THE 1-D-3-D COUPLING APPROACH

Although the hydraulic transients in pipe systems are usually simulated by using a one-dimensional （l-D） approach, local three-dimensional （3-D） simulations are necessary because of obvious 3-D flow features in some local regions of the hydropower systems. This paper combines the 1-D method with a 3-D fluid flow model to simulate the Multi-Dimensional （MD） hydraulic transients in hydropower systems and proposes two methods for modeling the compressible water with the correct wave speed, and two strategies for efficiently coupling the 1-D and 3-D computational domains. The methods are validated by simulating the water hammer waves and the oscillations of the water level in a surge tank, and comparing the results ~with the 1-D solution data. An MD study is conducted for the transient flows in a realistic water conveying system that consists of a draft tube, a tailrace surge tank and a tailrace tunnel. It is shown that the 1-D-3-D coupling approach is an efficient and promising way to simulate the hydraulic transients in the hydropower systems in which the interactions between 1-D hydraulic fluctuations of the pipeline systems and the local 3-D flow patterns should be considered.

GIS tools for correlation of tectonics and seismicity in the Altay-Sayan area,Russia

Fault-block structures of the Altay-Sayan folded area （ASFA） southeastern Siberia of Russia were used as the basis for creating a 3-D model. The surface structures were projected to depths by previous correlations between long and deep faults, with all layers and deformation factors defined. The mean deformation factor （Ds） is 0.12 unit/km^3 in the upper layer, 0.012 unit/km^3 in the intermediate layer, and 0.007 unit/km^3 in the lower layer of the 3-D ASFA neotectonic model. Ds allows correlation of the three distinguished layers with theological bodies that differ in their potential for accumulating elastic energy. 3-D modeling can be used as a methodological approach to projections in seismic prone areas such as the Krasnoyarsk region, for earthquake-hazard monitoring.

Numerical modeling of 3-D terrain effect on MT field

Using the boundary element method, the numerical modeling problem of three-dimensional terrain effect on magnetotelluric (MT) field is solved. This modeling technique can be run on PC in the case of adopting special net division. The result of modeling test for 2-D terrain by this modeling technique is basically coincident with that by 2-D modeling technique, but there is a great difference between the results of 3-D and 2-D modeling for 3-D terrain.