Iteratively re‐weighted and refined least squares algorithm for robust inversion of geophysical data

A robust metric of data misfit such as the ?₁‐norm is required for geophysical parameter estimation when the data are contaminated by erratic noise. Recently, the iteratively re‐weighted and refined least‐squares algorithm was introduced for efficient solution of geophysical inverse problems in the presence of additive Gaussian noise in the data. We extend the algorithm in two practically important directions to make it applicable to data with non‐Gaussian noise and to make its regularisation parameter tuning more efficient and automatic. The regularisation parameter in iteratively reweighted and refined least‐squares algorithm varies with iteration, allowing the efficient solution of constrained problems. A technique is proposed based on the secant method for root finding to concentrate on finding a solution that satisfies the constraint, either fitting to a target misfit (if a bound on the noise is available) or having a target size (if a bound on the solution is available). This technique leads to an automatic update of the regularisation parameter at each and every iteration. We further propose a simple and efficient scheme that tunes the regularisation parameter without requiring target bounds. This is of great importance for the field data inversion where there is no information about the size of the noise and the solution. Numerical examples from non‐stationary seismic deconvolution and velocity‐stack inversion show that the proposed algorithm is efficient, stable, and robust and outperforms the conventional and state‐of‐the‐art methods.     

广义Stein无偏风险估计与地球物理反问题正则化参数求取

地球物理反演是获取地球信息的重要手段,其求解具有严重的不适定性.为获得稳定的反问题结果,通常需要在目标泛函中加入正则化约束项.正确地估计正则化参数一直是地球物理反问题中的难点.目前存在的选取方法需要根据大量的试验来确定正则化参数,工作量十分巨大,并且存在很大的经验性,很难得到最优的正则化参数.针对这个问题,本文提出了一种基于广义Stein无偏风险估计的正则化参数求取方法.该方法的具体思路是通过求解模型参数均方误差的广义Stein无偏风险估计函数,在反问题求解过程中自动求取正则化参数.本文模型测试结果表明,相比于目前常用的方法,通过该方法得到的正则化参数是最优的.     

自适应Kalman滤波反褶积的快速实现方法

提出了以二进小波变换为基础的自适应Kalman滤波反褶积(AKFD)新方法，针对该方法的计算复杂程度，提出了一种快速实现方法.二进小波变换的AKFD抛弃了传统预测反褶积对信号平稳性的假设，克服了提高分辨率而信噪比明显降低的问题，具有很好的抗噪性能.在小波域进行的AKFD在压制假反射以及提高分辨率方面比时间域的AKFD好，克服了在时域内进行AKFD抬升低频成分的缺陷.利用二维地震数据的局部平稳性的假设提出了快速实现方法，通过分段求取自适应预测算子，分别于横向及纵向采用样条插值的方法进行插值，来减少求取自适应预测算子的计算量，达到快速实现的目的.经过大量实验表明计算速度提高数百倍，仍能保持原来的计算效果.     

地震资料自适应时变卡尔曼反褶积

应用卡尔曼滤波的一步预测方法,并根据卡尔曼滤波方程适用于时变系统的特点,给出了利用卡尔曼滤波进行地震资料自适应时变反褶积的方法,文中给出了理论和实际资料处理的例子.     

地震资料自适应时变卡尔曼反褶积

应用卡尔曼滤波的一步预测方法,并根据卡尔曼滤波方程适用于时变系统的特点,给出了利用卡尔曼滤波进行地震资料自适应时变反褶积的方法,文中给出了理论和实际资料处理的例子.     

Limitations Of The Tangent Plane Approximation For Wide-field Imaging Using The Mauritius Radio Telescope

The Mauritius Radio Telescope (MRT) is a Fourier synthesis, non-coplanar T array. The primary objective of the telescope is to survey the southern sky at 151.5 MHz in the declination range -70^° to -10^°. Due to non-coplanarity, wide-field imaging and deconvolution of wide field images made using MRT are challenging problems in applications of radio interferometric techniques. This paper discusses the usefulness and limitations of the tangent plane approximation in transforming the measured visibilities to wide field images and in estimating the point spread function (PSF) required for the deconvolution. This revised version was published online in July 2006 with corrections to the Cover Date.     

Ground penetrating radar signal processing improves mapping accuracy of underground voids and seawater table: an application in deteriorating coastal structure, Nanfangao Port, Taiwan

Efficient restoration of deteriorating coastal structures requires an accurate picture of both above ground and underground features. Although ground penetrating radar (GPR) can map underground features, it creates reflection artifacts. Here, a model for deconvolution calibration was developed in an outdoor small-scale experiment. GPR parameters were established, then applied at a deteriorating fishing port in northeast Taiwan. The deconvolution filter removed repetitive reflection patterns under the lowest part of the void creating a more accurate map. A 3D-map was created from interpolated sketched void boundaries. Due to its high lossy nature at radar frequencies and large contrasting relative dielectric permittivity (RDP) to the upper medium, the seawater table (SWT) is easily identified. The upper boundary of reflection-free area in the deconvoluted radargram, therefore, indicates the SWT. The methods developed here are easily modified to fit a wide range of situations.     

提高碳氧比能谱测井分辨率的反褶积法

在地层孔隙度比较低的情况下,由于受放射性统计涨落以及地层中其它核反应所产生的伽马射线的影响,传统的碳氧比能谱测井解释的分辨率不高。这些伽马射线形成了碳氧比能谱测井的本底,本底越高,碳氧比值精度越差。因此,必须设法降低本底值来提高谱线的分辨率。本文通过反褶积技术来提高谱线的分辨率,应用修正的高斯函数作为系统响应函数对测井曲线进行反褶积;采用修正的 Blackman 窗函数来消除放射性统计涨落的高频噪声,通过实际资料验证,利用"反褶积-开窗"法对碳氧比能谱测井的谱线进行处理以及用变系数法求取非弹性散射伽马谱,提高了测井资料对油、水储集层的分辨率,对油田的合理开发及油藏管理具有重要的现实意义。     

一种反演雷达波束内不均匀反射率场的方法

本文从原始雷达方程出发,提出了一种雷达加密观测方案和退卷积的数据反演方法,以实现雷达天线波束内的反射率不均匀结构信息的提取。反演方法的数值试验表明,此反演方法比常规测量方法在角分辨率方面提高约３倍,对波束内尺度为０．５８－２．０ＨＷ（ＨＷ是天线３ｄＢ波束宽度）的反射率变化有明显的反演能力。观测数据的测量误差对反演质量的影响也进行了计算和分析。本文还讨论了反演方法对雷达观测中的一些技术参数的要求。这些结果对于提高雷达尤其是星载微波主被动遥感器在测量降水量和云中含水量等参数中的精度有重要作用和现实意义。     

基于逆虚折射干涉法有效提取近地表弱地震信号

在地震勘探中,地形起伏和近地表速度的剧烈变化会导致地震波旅行时的扰动,通常会通过折射波信息来估算和消除这些扰动.本文在虚折射的基础上提出了逆虚折射干涉法,通过虚折射波场和原始折射波场的互相关,并对所有位于固定相位点上的检波点进行叠加,重构出逆虚折射波场.通过逆虚折射与超级虚折射的叠加,保证了不同偏移距下折射波振幅恢复的一致性,显著提高折射波的信噪比,有效提取弱信号.同时,本文采用反褶积干涉法来压制由于互相关和褶积产生的子波旁瓣的影响,弥补低频和高频能量的损失,改善恢复的折射波场的稳定性和分辨率.该新方法不需要知道近地表复杂速度模型的信息,可以将虚折射的勘探孔径恢复到原始地震记录的最大孔径.合成资料和实际资料的计算结果表明,基于反褶积的逆虚折射干涉法能够从低信噪比的资料中,有效恢复出折射波信息.