反插值法实现地球物理数据快速网格化

本文借鉴反演理论，采用反插值法实现地球物理数据的快速网格化.首先由已知点与未知网格点的反距离拓扑关系建立反演方程，用已知点值直接计算出其所在网格的未知网格点值，再利用Laplacian算子滤波，使得模型光滑，且能量最小化.利用预条件共轭梯度法求解网格化方程组，并结合螺旋坐标系思想和Wilson\|Burg谱分解法，将二维数据的滤波处理转换到一维空间进行处理，实现二维数据快速滤波.另外，引入了阻尼约束，保证求解稳定、迭代收敛.最后，应用该方法对合成数据和实际资料进行了试验.     

岩石圈磁场数据网格化方法研究

选取最小曲率、克里格、改进Shepard、反距离加权和径向基函数等5种网格化数学模型,对小江断裂地磁总强度加密区岩石圈磁场数据进行数据网格化,采用均方根预测误差和插值数据残差均方根等评价指标对网格化结果进行评价,结果表明,克里格插值与反距离加权插值法的精度最高。进一步比较克里格插值与反距离加权插值法的网格化图形质量,结果显示克里格插值网格化过程中兼顾了数据的平滑性和各实测点与待估点之间的空间位置关系,避免了系统误差,得出克里格插值更适用于岩石圈磁场数据网格化的结论。     

考虑航磁水平梯度变化的ΔT网格化方法研究

实测航磁横向水平梯度反映垂直于测线的磁场梯度,比传统航磁ΔT数据包含测线之间更多的磁场信息.针对航磁数据网格化问题,采用Hardwick提出的方法,利用航磁水平梯度与ΔT数据构建拟测线,并结合Akima插值法,开展了双方向测线型ΔT网格化方法研究,最终实现了考虑航磁水平梯度变化的ΔT网格化;针对网格化结果中的虚假异常采取了有效滤波方法.通过理论模型数据和实际数据网格化处理,表明该方法可以突出航磁测线之间的异常细节、更清晰地反映线性构造或磁性体走向,提高了网格化的精度和分辨率.     

一种稳定的位场数据最小曲率网格化方法研究

在进行位场数据处理和转换之前均要对离散数据进行网格化,网格化的精度直接影响位场处理和转换结果的精度、网格化方法的计算量大小直接影响位场处理和转换结果的效率.本文在已有最小曲率网格化算法的基础上提出了一种稳定的最小曲率网格化算法,该算法不但提高了网格化结果的精度,而且网格化结果受点(线)距大小的影响较小,通过实际资料验证...     

平面网格位场数据的空间域非线性曲率滤波方法

剖面测线位场数据的空间域非线性曲率涯波方法能够较好地分离提取剖面到线位场的趋势和剩余异常，本文首次将该方法推广应用到平面网格位场数据情况，为平面网格位场的趋势和剩余异常的分离提取提供了一种新的实用方法。在新疆某地区的实例计算表明，本文提出的平面网格位场数据的空间域非线性曲率滤波方法的应用效果好、计算速度快。     

从瞬变电磁扩散场到拟地震波场的全时域反变换算法

将瞬变电磁满足的扩散方程转变为波动方程,然后利用地震类成像方法实现瞬变电磁虚拟波场成像,是实现瞬变电磁三维反演的有效手段之一.为了实现由扩散场到虚拟波场的转换,文中采用预条件正则化共轭梯度法求解波场反变换问题.首先,对几种离散方式进行比较,采用条件数最小的离散方式进行离散;然后选择最优的正则化参数,并利用超松弛预条件技术对系数矩阵进行预条件处理;最后,利用共轭梯度法进行迭代求解.超松弛预条件有效降低了系数矩阵的条件数,正则化方法使得反变换得到的波场稳定、可靠,共轭梯度法能够保证计算快速收敛.将反变换结果与已知虚拟波场函数对比,证明算法稳定、可信.将文中算法结果与前人研究结果进行对比,说明方法效果.通过实测数据的波场变换处理给出了文中方法的实际应用效果.结合反变换算法,对不同参数模型进行分析,总结了虚拟波场在色散介质中的传播规律.     

基于源波场重构的子波自适应频移算子

地震信号中的多尺度信息对于分辨率、成像精度和反演结果有非常重要的意义,本文提出一种基于直达波模拟波场重建震源子波的地震数据频移算子,以期能应用于基于波动的地震信号多尺度分频.频移过程主要分为两步,第一步利用直达波反传构建震源子波,第二步借助震源子波和频移算子进行多尺度分频.与常规数字滤波器相比,频移算子突破了滤波造成信...     

基于构造导向滤波的多震源最小二乘逆时偏移方法研究（英文）

多震源同时采集技术能够有效提高采集效率,得到来自多个震源的混合地震数据,该技术能缩短采集周期,降低采集成本,但对混合地震数据直接成像会在成像结果中引入串扰噪音,影响成像质量。因此,本文在实现多震源最小二乘逆时偏移的基础上,引入构造导向滤波算子作为多震源最小二乘逆时偏移的预条件算子,沿着构造走向应用非平稳滤波在有效保护构造信息的前提下压制串扰噪音,通过共轭梯度法使得反偏移数据与观测数据之间的误差达到最小,最终得到信噪比更高的成像结果。合成数据的数值实验表明,本文所提出的方法能够有效压制串扰噪音,提高成像精度。     

局部倾角约束最小二乘偏移方法研究

随着石油勘探难度的进一步加大,地震数据往往存在采样不规则、地震道缺失等现象,如果不对其进行处理,会对后续的地震成像产生影响,引入成像噪音.针对这一问题,一般是通过地震道插值或数据规则化对叠前数据进行处理,然后采用常规的偏移方法进行成像,本文则是将地震成像看作最小二乘反演问题,在共成像点道集引入平滑算子,在共偏移距/角度道集引入平面波构造算子(PWC)进行约束,通过预条件共轭梯度法使得反偏移后数据与输入数据之间的误差达到最小,最终得到信噪比更高、振幅属性更为可靠的成像结果.理论模型和实际资料处理表明,本文方法不仅可以有效压制数据不规则对成像产生的噪音,而且具有更高的成像精度.     

基于误差准则和循环迭代的时移地震匹配滤波方法

分析了用于时移地震互均衡处理中的传统匹配滤波算法适用范围，结果表明该方法在滤波算子的反算子为最小相位时效果最好.对该方法难以解决的混合相位问题，推导出通用公式，并提出基于最小平方误差准则和循环迭代的求解方法.理论和实际数据都验证了该方法较已有方法的优越性.     

The Wilson–Burg method of spectral factorization with application to helical filtering

Spectral factorization is a computational procedure for constructing minimum-phase (stable inverse) filters required for recursive inverse filtering. We present a novel method of spectral factorization. The method iteratively constructs an approximation of the minimum-phase filter with the given autocorrelation by repeated forward and inverse filtering and rearranging of the terms. This procedure is especially efficient in the multidimensional case, where the inverse recursive filtering is enabled by the helix transform. To exemplify a practical application of the proposed method, we consider the problem of smooth two-dimensional data regularization. Splines in tension are smooth interpolation surfaces whose behaviour in unconstrained regions is controlled by the tension parameter. We show that such surfaces can be efficiently constructed with recursive filter preconditioning and we introduce a family of corresponding two-dimensional minimum-phase filters. The filters are created by spectral factorization on a helix.     

波场延拓短算子构造方法

在频率-空间域显式叠前深度偏移中，波场深度延拓是通过显 式差分短算子与波场的空间褶积完成的. 基于对显式差分短算子的设计方法的研究，提出了 一种基于相移算子约束的离散光滑插值的构造一维显式短算子的方法. 通过离散光滑插值法 ，在频率-波数域中，以传播区内的相移算子为约束，在传播区外的算子两端处以零点为约 束，进行离散光滑插值，使得所得算子具有二阶光滑可导性，则其对应的频率-空间域中的 算子就可以取得很短. 该方法设计简单，精度高，能够满足波场深度延拓的需要.     

Reduction of distortion and improvement of efficiency for gridding of scattered gravity and magnetic data

This paper presents a reasonable gridding-parameters extraction method for setting the optimal interpolation nodes in the gridding of scattered observed data. The method can extract optimized gridding parameters based on the distribution of features in raw data. Modeling analysis proves that distortion caused by gridding can be greatly reduced when using such parameters. We also present some improved technical measures that use human-machine interaction and multi-thread parallel technology to solve inadequacies in traditional gridding software. On the basis of these methods, we have developed software that can be used to grid scattered data using a graphic interface. Finally, a comparison of different gridding parameters on field magnetic data from Ji Lin Province, North China demonstrates the superiority of the proposed method in eliminating the distortions and enhancing gridding efficiency.     

基于Bregman迭代的复杂地震波场稀疏域插值方法

在地震勘探中,野外施工条件等因素使观测系统很难记录到完整的地震波场,因此,资料处理中的地震数据插值是一个重要的问题。尤其在复杂构造条件下,缺失的叠前地震数据给后续高精度处理带来严重的影响。压缩感知理论源于解决图像采集问题,主要包含信号的稀疏表征以及数学组合优化问题的求解,它为地震数据插值问题的求解提供了有效的解决方案。在应用压缩感知求解复杂地震波场的插值问题中,如何最佳化表征复杂地震波场以及快速准确的迭代算法是该理论应用的关键问题。Seislet变换是一个特殊针对地震波场表征的稀疏多尺度变换,该方法能有效地压缩地震波同相轴。同时,Bregman迭代算法在以稀疏表征为核心的压缩感知理论中,是一种有效的求解算法,通过选取适当的阈值参数,能够开发地震波动力学预测理论、图像处理变换方法和压缩感知反演算法相结合的地震数据插值方法。本文将地震数据插值问题纳入约束最优化问题,选取能够有效压缩复杂地震波场的OC-seislet稀疏变换,应用Bregman迭代方法求解压缩感知理论框架下的混合范数反问题,提出了Bregman迭代方法中固定阈值选取的H曲线方法,实现地震波场的快速、准确重建。理论模型和实际数据的处理结果验证了基于H曲线准则的Bregman迭代稀疏域插值方法可以有效地恢复复杂波场的缺失信息。     

Delineation of layer boundaries from smooth models obtained from the geoelectrical sounding data inversion

Two techniques have been presented for the delineation of boundaries from smooth models obtained by smooth inversion techniques of geoelectrical sounding data, such as straightforward inversion scheme, Occam’s and Zohdy’s methods. The smooth model consists of a large number of equally spaced layers, wherein the real geological boundaries are missing. The techniques proposed here suppress the geologically irrelevant boundaries and support the real structural boundaries present in the geoelectrical data. In the first technique, solution of linear inverse problem is improved iteratively through weighted minimum norm inverse, the weight being taken from the current solution. The technique is referred as Iterative Straightforward Inversion Scheme. The second method is analytical, based on the application of smoothing filter, referred in the literature as edge-preserving smoothing. A few examples of theoretical magnetotelluric, dc resistivity and field sounding data have been presented to demonstrate the capabilities of the techniques. The methodologies also reduce the conspicuous oscillations in the smooth solutions caused by the conversion of sharp boundaries to the smooth ones.     

RADON TRANSFORM APPLICATION TO THE IMPROVED GRIDDING OF AIRBORNE GEOPHYSICAL SURVEY DATA1

The Radon transform is applied to airborne geophysical data, which consist of parallel profiles, analogous to a seismic record. The plane-wave decomposition (PWD) thus becomes the strike-direction decomposition (SDD) since the observed spatially distributed information is represented by its strike directions in a domain achieved by the transformation. It is important that, after the SDD, we can identify anomalies and work on them according to their strikes. In particular, for gridding purposes, we may guide the second interpolation of the bi-directional gridding approach along the strike directions. In principle, the proposed Radon transform gridding method (RTGM) transforms the observed parallel profiles into a domain where information is mapped as its strike-direction ‘traces’ against its wavelengths. The number of strike directions into which the data are decomposed is equal to the number of lines to be interpolated. The Fourier spectrum of the grid is reconstructed from the strike-wavenumber domain by using the projection-slice theorem and the final square grid is obtained by performing an inverse Fourier transformation on the spectrum. The SDD is restricted to the Nyquist wavenumber bandwidth imposed by the survey line-spacing, so that there is no addition of ambiguous short wavelengths in the gridded data. A tapering window is employed to prevent any Gibb's oscillation in the final grid because of the sharp Nyquist cut-off in the reconstructed spectrum due to the survey line-spacing. The RTGM is first tested on a set of synthetic line-based data. It is also applied to aeromagnetic profile data from northern Botswana as a practical example.