三维F－K域DMO方法及应用效果

在常速情况下，从三维时距方程出发，通过倾角代换，将三维倾角时差分裂为两个正交方向上的二维倾角时差，然后在这两个正交方向上分别做一次二维倾角时差校正，便可达到三维倾角时差校正的目的．应用实例表明这种三维ＤＭＯ分裂方法是切实有效的．     

三维F－K域DMO方法及应用效果

在常速情况下，从三维时距方程出发，通过倾角代换，将三维倾角时差分裂为两个正交方向上的二维倾角时差，然后在这两个正交方向上分别做一次二维倾角时差校正，便可达到三维倾角时差校正的目的．应用实例表明这种三维ＤＭＯ分裂方法是切实有效的．     

三维VTI介质中波动方程深度偏移的最优分裂Fourier方法

从含Thomsen各向异性参数的qP波相速度表示式出发,建立并求解三维VTI介质中的频散方程,得到三维VTI介质中的相移算子,进而将以相移算子为基础的最优分裂Fourier方法推广到三维VTI介质,发展了一个三维VTI介质的深度偏移方法.文中使用的各向异性介质的速度模型与现行的各向异性构造的速度估计方法一致,将各向同性、弱各向异性及强各向异性统一在一个模型中.文中提出的偏移算法对相移法引入了高阶校正项来补偿介质横向变化的影响,使该方法可应用于横向非均匀VTI介质的陡角度成像,文中给出的偏移脉冲响应很好地证明了这一点.     

Global SH-wavefield calculation for a two-dimensional whole-Earth model with the parallel hybrid PSM/FDM algorithm

We present a parallel hybrid algorithm based on pseudospectral method (PSM) and finite difference method (FDM) for two-dimensional (2-D) global SH-wavefield simulation. The whole-Earth model is taken as a cross section of spherical Earth, and corresponding wave equations are defined in 2-D cylindrical coordinates. Spatial derivatives in the wave equations are approximated with efficient and high accuracy PSM in the lateral and high-order FDM in the radial direction on staggered grids. This algorithm allows us to divide the whole-Earth into sub-domains in radial direction and implement efficient parallel computing on PC cluster, while retains high accuracy and efficiency of PSM in lateral direction. A transformation of moment tensor between 3-D spherical Earth and our 2-D model was proposed to give corresponding moment tensor components used in 2-D modeling. Comparison of modeling results with those obtained by direct solution method shows very good accuracy of our algorithm. We also demonstrate its feasibility with a lateral heterogeneous whole-Earth model with localized velocity perturbation.     

2.5-D modeling in electromagnetic methods of geophysics

Understanding, using, or eliminating three-dimensional (3-D) effects in electromagnetic methods of geophysics are critical requirements. Numerous achievements in 3-D modeling sometimes give the impression that they are widely available today in geophysical practice. This is not necessarily true. Existing 3-D modeling packages prove that we know how to perform 3-D modeling. However, the computer resources and costs involved make the practical application of 3-D EM modeling in geophysical applications very limited.A practical compromise, or even alternative, is represented by 2.5-D modeling characterized by the use of a 3-D source in a 2-D medium. This combination allows one to mathematically describe the related boundary value problem as a sequence of independent two-dimensional problems. The typical technique leading to such a split formulation is Fourier analysis. That is why the individual terms of a split solution are often referred to as harmonics.Although each independent problem is two-dimensional, the algorithmic implementation of finite differences or integral equations for the higher harmonics has some specific features not present in the classical 2-D cases. In this paper, a hybrid scheme consisting of a combination of the finite difference technique with the integral equation approach for transient fields is described. Evaluation of algorithm accuracy is presented and a transient logging technique application is considered. The algorithm is fast and easily implemented on a personal computer     

用改进的光滑约束最小二乘正交分解法实现电阻率三维反演

对三维电阻率反演问题进行了深入研究,提供了一种利用地表观测数据实现三维反演的实用算法.该方法应用有限差分求正演解,并通过对粗糙度矩阵元素进行适当改进,使之适用于各种情况下粗糙度矩阵的求取,进而建立在模型的总粗糙度极小条件下的反演方程.对反演方程采用收敛速度快且稳定的最小二乘正交分解（LSQR）法进行迭代求解,在迭代求解过程中只需利用偏导数矩阵和其转置矩阵乘以一个向量的结果,回避了直接求偏导数矩阵的繁琐计算,节省了内存,加快了反演的计算速度.不同的计算实例表明上述方法是求解大规模三维电阻率反演问题的有效方法.     

三维地震数据可视化原理及方法

可视化是实现三维地震数据真三维解释的有效方法,本文介绍了三维地震数据可视化的基本原理,论述了用光线投射算法实现可视化的主要步骤,详细推导了合成可视化图像的计算公式,分析了阻光度曲线的物理意义及对可视化图像的调节作用,并用两个实际三维地震数据进行了试验.结果表明该方法能够由原始三维地震数据直接对地质体进行成像,能将分散的、孤立的信息互相联系起来,揭示隐藏在数据中的地质现象和规律.     

三维地形直流电阻率有限元法模拟

基于稳定电流场的基本方程、三维区域满足的边值问题以及相应的变分问题,研究了三维起伏地形条件下电阻率的有限单元数值模拟算法. 离散积分区域时,以三棱柱为最小研究单元,推导了含有地形特征信息的三线性插值型函数以及单元刚度矩阵. 采用变带宽、一维数组方式只存储稀疏刚度矩阵中非零元素,能够节约内存. 利用Cholesky分解法只分解一次大型稀疏矩阵,通过回代可以求出方程组的全部解,当求解有多个供电点的测深问题时可以缩短计算时间. 模型计算表明,在水平层状介质模型上,三维计算结果与解析解或二维数值解十分吻合,计算精度满足误差要求. 在二维山脊上的二极剖面或三维山谷上的中间梯度剖面上,其三维计算结果与相应模型的土槽实验结果或边界元法计算结果也非常接近.     

三维各向异性介质中的波动方程叠前深度偏移方法

基于三维VTI各向异性介质的频散关系,构建波数项和空间项分离的单程波算子表达式,以优化算法,确定算子的待定系数,实现广角逼近三维VTI介质的广义相移算子,发展了可灵活处理强或弱各向异性介质的波动方程叠前深度偏移方法.文中同时也针对其工业应用建议了三维VTI各向异性介质中可提高计算效率的频率相关变步长波场深度延拓算法及稀...     

水平层状介质中基于DTA的三维电磁波逆散射快速模拟算法

为提高水平层状介质中三维电磁波散射和逆散射数值模拟的效率,在对角张量近似(DTA)的基础上根据不同回代方式得到了求解积分方程的DTA1和DTA2两种近似. 这两种近似可以作为计算积分方程稳定型双共轭梯度快速Fourier变换(BCGS-FFT)算法的初始猜测值和预条件因子,从而形成效率更高的混合DTA-BCGS算法. 散射实例说明了DTA2的高精度和混合DTA-BCGS算法尤其是混合DTA2-BCGS算法的高效率. 由于DTA2近似程度更高,将DTA2与变型Born迭代反演方法(DBIM)相结合形成了一种对三维异常体进行重构的快速电磁波逆散射技术. 文中的逆散射实例说明所开发的逆散射技术对重构水平层状介质中的任意三维异常体是非常有效的.     

THREE-DIMENSIONAL KINEMATIC MIGRATION IN VARIABLE VELOCITY MEDIA*

A three-dimensional (3-D) kinematic migration algorithm for media in which migration velocity varies linearly with depth is developed, implemented and tested. The algorithm is based on the concept that a single reflection or diffraction in a (zero- or finite-offset) trace may have originated at any point on a constant traveltime surface within the Earth defined by the observed two-way traveltime. The envelope of all such constant time surfaces, for all observed reflections and diffractions produced by one reflector, is the desired migrated 3-D image. The optimal envelope position in depth is determined, beneath each point on a regular grid, by a statistical imaging condition; an incremental function of depth containing the number of constant time surfaces passing through that depth increment is cross-correlated with a Gaussian function whose width is chosen to correspond to the vertical scale of the features of interest. The numerical procedures are based on the observation that, in a medium in which velocity varies linearly with depth, ray segments are circular so traveltimes can be computed analytically. Also, traveltimes are independent of azimuth so the 3-D problem can be collapsed into an equivalent 2-D problem. The algorithm is illustrated and tested by application to synthetic data and to scale-model data from the Seismic Acoustics Laboratory at the University of Houston.     

三维重磁交互解释及区域与局部异常的分离

探讨了三维重磁交互解释的方法技术，提出构制任意形状三维物体模型的用于计算机的橡皮膜技术．针对通常分离区域与局部异常所存在的问题，提出在异常交互解释过程中同时进行异常分离的方法，并提出相应的算法．最后介绍一个应用实例．     

三维复杂介质中转换波走时快速计算

复杂介质中转换波走时计算是多波勘探地震学中重要内容之一.本项研究利用惠更斯原理和费玛原理,获得了三维复杂介质中转换波快速计算的改进型最小走时树方法.其中,在保证精度的条件下,为了提高三维转换波走时计算效率,首先对初至波最小走时树基本算法进行了改进.本方法通过将转换波分为上、下行波分别进行射线追踪以实现三维转换波走时的快速计算.模型计算表明,方法的计算速度快,而且稳定性强,对多波地震勘探具有较大的应用价值.     

大地电磁非线性共轭梯度拟三维反演

提出了非线性共轭梯度法大地电磁拟三维反演.该方法选取共轭梯度反演算法为拟三维反演的核心.在计算灵敏度（Jacobian）矩阵时,吸取近似灵敏度矩阵思想,采用一维灵敏度矩阵来代替三维灵敏度矩阵,并对非测点的灵敏度元素提出一种近似方法.在第一次反演之后,采用拟牛顿法更新灵敏度矩阵.拟三维反演法在很大程度上节省了计算时间,并且理论模型和实际资料的反演试算结果表明大地电磁拟三维反演法具有一定的实用价值.     

地壳三维构造反演和速度层析成像

本文给出利用空间深地震测深反射资料重建地壳三维构造和速度分布的方法，适用于任意分层并且每层可由若干断块组成的地壳模型。通过采用适当的反演方法获得地壳界面的三维构造，并在此结果基础之上，进一步将剩余走时残差归因于地壳速度的不均匀性，采用东分块的反演方法，重建地壳三维速度分布，数值模拟的结果表明算法是有效的。     

三维粘弹介质地震波场有限差分并行模拟

有限差分法在三维粘弹性复杂介质正演模拟地震波的传播中对计算机内存和计算速度要求比较高,单个PC机或工作站只能计算较少网格内短时间的波场。本文介绍一种基于MPI的并行有限差分法,可在PCCluster上模拟较大规模三维粘弹性复杂介质中地震波传播时的波场;可预测地震波在此类条件下传播时的运动学和动力学性质。对于更好地理解波动传播现象,解释实际地震资料及反问题的解决等均具有重要的理论与实际意义。     

Multidimensional GPR array processing using Kirchhoff migration

We compare the ability of several practical ground-penetrating radar (GPR) array processing methods to improve signal-to-noise ratio (SNR), increase depth of signal penetration, and suppress out-of-plane arrivals for data with SNR of roughly 1. The methods include two-dimensional (2-D) monostatic, three-dimensional (3-D) monostatic, and 3-D bistatic Kirchhoff migration. The migration algorithm is modified to include the radiation pattern for interfacial dipoles. Results are discussed for synthetic and field data. The synthetic data model includes spatially coherent noise sources that yield nonstationary signal statistics like those observed in high noise GPR settings. Array results from the model data clearly indicate that resolution and noise suppression performance increases as array dimensionality increases. Using 50-MHz array data collected on a temperate glacier (Gulkana Glacier, AK), we compare 2-D and 3-D monostatic migration results. The data have low SNR and contain reflections from a complex, steeply dipping bed. We demonstrate that the glacier bed can only be accurately localized with the 3-D array. In addition, we show that the 3-D array increases SNR (relative to a 2-D array) by a factor of three.     

3-D acoustic modelling of edge diffractions — revisited

An accurate, fast, and simple algorithm for 3-D acoustic modelling of seismic edge diffractions, originally developed in the 1980s, is revisited in this paper. The main objective is to reintroduce this simple approach to edge-diffraction modelling and for the first time give the details of the theory in the open literature. The method is based on a combination of Kirchhoff theory and uniform asymptotic techniques developed within a high-frequency assumption. The diffraction contributions are then computed at stationary edge points only, by analogy with the geometrical ray contributions associated with internal stationary points or specular points. To be able to handle sampling inaccuracies of the critical edge points, a modified algorithm is proposed. Its robustness is verified in case of scattering from a circular edge. Also the extension from rigid or free boundary conditions to the case of edges defined by two penetrable surfaces is discussed in this paper. Both experimental and synthetic 3-D data are presented to demonstrate the potential of this edge-diffraction modelling technique. Since all parameters needed in the computations are obtained from dynamic ray tracing, the algorithm can readily be incorporated in existing software packages for 3-D seismic ray modelling.     

用可视化技术分析虚拟现实环境下三维地震数据场的研究

目的 用可视化方法分析三维地震数据，直接观察数据中隐藏的地质现象。方法：将第每个反射子波用一个粒子模型表示，来自同一反射面的子波粒子相互叠合成一个同相面。为加快显示速度，将一个三维地震数据体转换为三维二值图像，用有序扩展算法追踪同相面所在的三维连通域，细化后得到反射面的坐标数据。再在虚拟现实系统下的对反射面进行立体显示，直观地分析地下地层的结构。结果 实际数据试验得到了反射面的三维形态及断层的分布规律，立体显示更深刻地揭示了复杂地质现象及其规律。结论 只有在虚拟现实系统中进行三维地震数据的可视化，才能直观地看到地下地层的真实场景，真正实现三维数据的全三维解释，所提出的方法是有效。     

井间电磁场的一维、二维联合反演方法

提出了针对轴对称二维井间模型的一维、二维联合反演方法.该方法基于纵向成层背景地层的Green函数,以一维反演结果作为联合反演的迭代初始值,同时反演一维背景地层和二维异常剖面的电导率.采用递推技术计算Green函数的系数,可以很方便地同时得到Green函数对空间坐标的积分和对背景层电导率的微分,大大加快了计算雅可比矩阵〖WTHX〗M〖WTBZ〗的速度并使计算方便、准确.反演实例说明了该方法的有效性.反演实例还显示,背景层电导率较二维成像剖面的电导率收敛速度要快,测量数据的精度对二维剖面电导率成像质量的影响大于对背景层电导率分布的影响.