国土遥感调查的空间抽样优化决策

利用遥感信息进行国土资源调查, 调查费用与调查精度是一对矛盾, 而空间抽样提供了解决这对矛盾的方法. 针对空间抽样问题先验数据缺乏及受多因素影响的复杂情况, 在前人方法单一且缺乏比较的应用模型基础上, 提出空间抽样优化决策模型, 该模型是经探索分析后采用多种可能组合方法获取精度变化图, 多次实验回归模拟, 归一化到同一坐标系中, 采用离散化的决策函数计算比较得到抽样优化决策方案. 通过遥感耕地调查的实验, 结果表明用航片进行细小地物及耕地面积调查, Sandwich方法能较好实现投入与精度的平衡组合. 空间抽样优化决策用于国土遥感调查中, 将会提高调查精度, 同时有效地节省投入, 是比较好的工具. 为空间抽样优化决策在资源调查中推广应用, 提出组件开发原型, 通过组件内嵌到GIS与遥感的软件环境中去, 提高分析效率.     

基于jitter采样和曲波变换的三维地震数据重建

传统的地震勘探数据采样必须遵循奈奎斯特采样定理,而野外数据采样可能由于地震道缺失或者勘探成本限制,不一定满足采样定理要求,因此存在数据重建问题.本文基于压缩感知理论,利用随机欠采样方法将传统规则欠采样所带来的互相干假频转化成较低幅度的不相干噪声,从而将数据重建问题转为更简单的去噪问题.在数据重建过程中引入凸集投影算法(POCS),提出采用e^-√x(0≤x≤1)衰减规律的阈值参数,构建基于曲波变换三维地震数据重建技术.同时针对随机采样的不足,引入jitter采样方式,在保持随机采样优点的同时控制采样间隔.数值试验表明,基于曲波变换的重建效果优于傅里叶变换,jitter欠采样的重建效果优于随机欠采样,最后将该技术应用于实际地震勘探资料,获得较好的应用效果.     

基于插值原理的检查点技术波场重构与叠前逆时偏移

叠前逆时偏移等基于波场互相关原理的地球物理方法存在极大的计算与存储需求,因此采用合适的波场重构方法显得尤为重要.常规的随机边界法容易产生成像噪声,而有效边界法在三维情况仍难以实现,检查点技术具有内存要求小的特点,但存在较高的重算率,因此本文提出了插值原理的检查点技术波场重构方法.在满足Nyquist采样定理的前提下对相邻检查点间的波场进行规则抽样,将抽样波场作为插值节点,运用多项式插值算法重构任意时刻的波场,从而避免优化检查点技术反复递推造成的计算效率问题.数值实验表明：插值检查点重构算法能有效的恢复波场,其中三次样条插值重构精度最高,而牛顿法插值法计算代价较小适合于快速重构.经Sigsbee模型的叠前逆时偏移证明了插值算法的可行性,并且极大的提高了波场重构的计算效率.三维模型分析得出在增加少量存储的情况下插值重构法的重算率大幅度降低,存储量减少为有效边界法的7.1%,对于三维尺度的叠前逆时偏移有实际意义.     

有限频率线性理论的波恩近似佯谬

对有限频率层析成像线性理论的波恩近似问题进行梳理, 用数值方法统计分析其适用范围, 结果表明波恩近似要求最大速度扰动不超过1%; 然后对相关走时一阶近似进行统计分析, 结果表明它也只适用于最大速度扰动在1%以内的情形. 然而, 结合波恩近似和相关走时一阶近似而得到的有限频率线性理论, 其适用的速度扰动范围最大可达10%. 这个表面上的逻辑悖论, 称为“波恩近似佯谬”. 此佯谬是由于不恰当地使用波恩近似造成的. 本文摒弃波恩近似, 使用泛函的Fréchet微分和隐函数定理推导得到有限频率线性理论, 圆满解释了波恩近似佯谬. 由于有限频率非线性理论早已摒弃了波恩近似, 因此波恩近似概念在有限频率层析成像理论中完全没有必要.      

生态环境曲面建模基本定理及其应用

在高精度曲面建模方法和地球表层系统建模基本定理研究结果基础上,演绎提出了生态环境曲面建模基本定理.以京津冀地区为案例,对基于生态环境曲面建模基本定理的空间升尺度、空间降尺度、空间插值、数据融合和模型-数据同化等算法进行了实证研究,与传统算法精度进行了比较分析.结果表明,由于基于生态环境曲面建模基本定理的各种算法综合了外蕴量信息和内蕴量信息,同时运用了理论上完善的信息综合方法,使海拔高度曲面的升尺度均方根误差至少降低了9m,年平均气温未来情景的降尺度精度至少提高16%,年平均气温过去变化趋势的数据融合精度至少提高70%,年平均降雨量过去变化趋势的空间插值精度至少提高0.2%,碳储量的模型-数据同化精度提高了40%.文章最后讨论了生态曲面建模基本定理亟待解决的五大理论问题和四大应用基础问题.     

固体潮磁带记录的重取样及强地震干扰的消除

本文讨论取样间距为5s的固体潮磁带数据的重取样及消除强地震干扰的方法.所提出的多项式拟合平滑取样方法(PFSS)使读带、平滑、取样同步进行.读带一结束,计算机内存就有了按给定间距的取样结果.由于只对有关点作格式变换和预处理,故可以节省计算时间;由于只存取样结果,故可以节省计算机空间.因此,这种方法适用于小间距而延续时间长的固体潮磁带数据.采用功率谱分析,并对PFSS方法的结果作了检验,证明这种方法具有良好的滤波功能.为了消除强地震干扰所引起的畸变,采用Nakai方法并给出迭代程序,也用谱分析作了检验.校正后的观测数据,其谱分析结果与理论潮结果相似.      

湍流强度定理和湍流发展的宏观机制

湍流是普遍存在而至今仍未被充分理解的自然现象. 简单回顾了湍流理论的发展历史和现状, 指出以不同层次利用和不同方法探讨湍流特征和机制的必要性. 为此利用非平衡态热力学理论将Reynolds湍流和Bénard湍流统一地表述在动量湍流输送定理和湍流强度定理中. 证明了流体湍流发展的宏观原因是速度剪切效应和温度剪切效应共同作用的结果, 速度剪切效应和温度剪切效应也是湍流场相空间轨线不断拉伸和折叠的宏观原因. 并以大气实验资料证明, 湍流强度唯象系数不仅是速度剪切的函数, 还是温度剪切, 即大气热力层结稳定度的函数. 从而以实验事实证明了湍流强度定理的真实性.     

地面γ能谱测量中连续测量的理论基础和实验结果

在物化探方法中,地面γ能谱测量过去主要用于大比例尺异常检查,采用的是定点测量方式。理论分析表明,如果将其应用于1:5万地质填图,这种测量方式取样代表性差,工效较低,不能满足地质工作的要求。为了解决这一问题,充分发挥地面γ能谱测量的作用,本文提出了步行连续测量方式。 步行连续测量就是将探测器提在手上或背在身上,沿测线以一定速度边走边测的工作方式。     

基于景观形状指数的地表覆盖检验样本自适应抽样方法

大范围地表覆盖常常具有极强的空间异质性,直接影响着检验样本的数量计算与空间布设.致使传统抽样方法在区域样本量确定、地类间样本量分配和样本空间分布方面存在着较大局限性.本文提出了一种顾及地表覆盖空间异质性的样本抽样方法,计算验证区域、区内地类和抽样格网三个层级的景观形状指数,推导出基于区域级景观形状指数及面积的区域样本量解析计算公式,建立了顾及地类级景观形状指数的样本量内曼分配公式,提出了基于格网级景观形状指数曲线的样点抽取方法,为大范围地表覆盖验证提供了定量化的自适应抽样方法.以毛里塔尼亚、西班牙和孟加拉三个国家为验证区域进行的实验表明:(1)基于区域级景观形状指数的样本量解析计算,较好地顾及了地表覆盖空间异质性强弱的影响,有效实现了区域样本量的自动调整;(2)引入地类级景观形状指数的内曼分配计算,有效提高了稀少类的抽样比例,解决了现有抽样方法难以顾及稀少类的问题;(3)在格网级景观形状指数曲线所构成的异质性强度空间中抽取样点,可使样本分布兼顾破碎与均质地域.此外,在西班牙区域进行了精度对比,发现本文提出的自适应抽样方法的精度评价结果更接近真实精度,尤其是稀少类的精度评价准确度平均提高了10%以上.     

小波变换及其应用

小波变换是近年来发展起来的一门新的数学分支.它适宜于分析研究信号的局部性质,对于图象数据压缩、奇性检测、非卷积型算子的化简及取样插值定理等方面都有着重要的应用,在地震勘探、大气湍流、语声合成、图象处理等许多领域中都有着广泛应用的前景.本文介绍了小波变换及其正交基的基本概念,并对它的一些重要应用作了概括的介绍.     

Seismic data reconstruction based on CS and Fourier theory

Traditional seismic data sampling follows the Nyquist sampling theorem. In this paper, we introduce the theory of compressive sensing (CS), breaking through the limitations of the traditional Nyquist sampling theorem, rendering the coherent aliases of regular undersampling into harmless incoherent random noise using random undersampling, and effectively turning the reconstruction problem into a much simpler denoising problem. We introduce the projections onto convex sets (POCS) algorithm in the data reconstruction process, apply the exponential decay threshold parameter in the iterations, and modify the traditional reconstruction process that performs forward and reverse transforms in the time and space domain. We propose a new method that uses forward and reverse transforms in the space domain. The proposed method uses less computer memory and improves computational speed. We also analyze the antinoise and anti-aliasing ability of the proposed method, and compare the 2D and 3D data reconstruction. Theoretical models and real data show that the proposed method is effective and of practical importance, as it can reconstruct missing traces and reduce the exploration cost of complex data acquisition.     

Sensitivity studies of a high accuracy surface modeling method

The sensitivities of the initial value and the sampling information to the accuracy of a high accuracy surface modeling(HASM) are investigated and the implementations of this new modeling method are modified and enhanced. Based on the fundamental theorem of surface theory, HASM is developed to correct the error produced in geographical information system and ecological modeling process. However, the earlier version of HASM is theoretically incomplete and its initial value must be produced by other surface modeling methods, such as spline, which limit its promotion. In other words, we must use other interpolators to drive HASM. According to the fundamental theorem of surface theory, we modify HASM, namely HASM.MOD, by adding another important nonlinear equation to make it independent of other methods and, at the same time, have a complete and solid theory foundation. Two mathematic surfaces and monthly mean temperature of 1951–2010 are used to validate the effectiveness of the new method. Experiments show that the modified version of HASM is insensitive to the selection of initial value which is particular important for HASM. We analyze the sensitivities of sampling error and sampling ratio to the simulation accuracy of HASM.MOD. It is found that sampling information plays an important role in the simulation accuracy of HASM.MOD. Another feature of the modified version of HASM is that it is theoretically perfect as it considers the third equation of the surface theory which reflects the local warping of the surface. The modified HASM may be useful with a wide range of spatial interpolation as it would no longer rely on other interpolation methods.     

数字强震记录“精确”插值、积分和微分的权函数算法——I.时域离散序列数值分析方法与应用研究

现有强震记录常规处理程度中采用的插值、积分、微分运算方法计算简单、省时,但在某些情况下,不能确保所要求的计算精度,针对这一问题,本文假定强震记录是理想的有限长记录并满足采定理,在此基础上提出了对强震记录进行“精确”插值,积分和微分运算以及权函数的概念,并推导建立了相应的计算公式,理论和算例分析表明：（１）本文算法中使用的插值,积分和微分运算权函数均具有不变和快速收敛的性质;（２）只需要少量的权系数,本文算法就能获得足够的计算精度;（３）选取足够多的权系数,本文算法能以任意精度副近真实的精确解序列,（４）本文算法可以成为强震数据处理和相关结构动力分析的基础。     

Frequency-domain double-plane-wave least-squares reverse time migration

Least-squares reverse time migration is often formulated as an iterative updating process, where estimating the gradient of the misfit function is necessary. Traditional time domain shot-profile least-squares reverse time migration is computationally expensive because computing the gradient involves solving the two-way wave equation several times in every iteration. To reduce the computational cost of least-squares reverse time migration, we propose a double-plane-wave least-squares reverse time migration method based on a misfit function for frequency-domain double-plane-wave data. In double-plane-wave least-squares reverse time migration, the gradient is computed by multiplying frequency-domain plane-wave Green's functions with the corresponding double-plane-wave data residual. Because the number of plane-wave Green's functions used for migration is relatively small, they can be pre-computed and stored in a computer's discs or memory. We can use the pre-computed plane-wave Green's functions to obtain the gradient without solving the two-way wave equation in each iteration. Therefore, the migration efficiency is significantly improved. In addition, we study the effects of using sparse frequency sampling and sparse plane-wave sampling on the proposed method. We can achieve images with correct reflector amplitudes and reasonable resolution using relatively sparse frequency sampling and plane-wave sampling, which are larger than that determined by the Nyquist theorem. The well-known wrap-around artefacts and linear artefacts generated due to under-sampling frequency and plane wave can be suppressed during iterations in cases where the sampling rates are not excessively large. Moreover, implementing the proposed method with sparse frequency sampling and sparse plane-wave sampling further improves the computational efficiency. We test the proposed double-plane-wave least-squares reverse time migration on synthetic models to show the practicality of the method.     

怀4井气体取样对水位观测干扰的解决措施

怀4井水位观测一直存在取气样所造成的干扰,其表现为水位分钟值曲线每天出现有规律的向上脉冲式突跳且持续时间较长,这使得数据连续率及完整率降低。为改变怀4井长期存在的取气样影响水位观测的现状,减少水位观测数据突跳次数,提高观测质量精度,针对取气样方式进行改进,采用球胆排水真空脱气法进行溶解气样品的采集与脱气,避开直接在泄流口采样时的压力效应,从而解决了水位观测中遇到的实际问题。     

THE QUANTITATIVE INTERPRETATION OF DIPOLE SOUNDINGS BY MEANS OF THE RESISTIVITY TRANSFORM FUNCTION*

In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression. As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.     

Alternative theory for signal contribution sections and depth of investigation characteristics in electrical prospecting

We present an alternative to Roy's theorem for direct current regimes with the aim of validating the theoretical basis of signal contribution sections in electrical prospecting. Roy's theorem establishes that the electrical potential at a point can be expressed as an integral over all space of the electric field weighted by the gradient of inverse distance. The integrand is interpreted to represent elementary contributions to the potential that can be analyzed to compare different electrode arrays. Signal contribution sections and depth of investigation characteristics can be beautifully illustrated with important practical applications. However, the electric potential, being the solution of a boundary value problem, cannot be uniquely decomposed into elementary contributions. There is no guarantee for the integrand of a given integral to be meaningful in all situations. In the case of Roy's theorem, the concept has been severely criticized by respected scholars who challenged the scientific legitimacy of his approach. If we are going to keep the concept of elementary contributions alive, we need to go beyond Roy's theorem. In this paper, we develop an alternative theorem and show that it merges with the concept of sensitivity, which is unique and mathematically sound, and is also open to physical validation. This prevents any possible contradictions in the future and, equally important, eliminates the dichotomy between sensitivity and elementary contributions.