Filtration and prediction of inhomogeneous anomalous geophysical potential fields

Summary A mathematical model for optimum prediction, filtration and simultaneous prediction and filtration of the fields considered has been constructed using Hilbert spaces with a reproduction kernel, formed by the covariance function of the observed anomalous geophysical potential field under the assumption that the field is an inhomogeneous random function.     

分离重磁区域场与局部场的维纳滤波器

本文从最佳线性滤波理论出发,对目前重磁资料数据处理中分离区域场与局部场的两种滤波器--匹配滤波和维纳滤波的频率响应特性作了分析比较,指出了匹配滤波只是一般维纳滤波的一个特例。将该两种滤波器与一般情况的维纳滤波器的误差作了对比,并通过简单的理论试例,说明它们的局限性和应用范围。     

PRINCIPLES OF DIGITAL WIENER FILTERING*

The theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so-called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.     

位场向下延拓的改进迭代维纳滤波法

根据维纳滤波理论导出的位场向下延拓滤波器为最佳下延滤波器,但因其实现需要已知待求位场和噪声的功率谱而在实际应用中受到限制.针对该问题,本文首先提出一种基于位场径向平均功率谱的位场噪声水平估计方法,进而利用偏差准则求取正则化参数,实现位场正则化向下延拓;然后将位场正则化下延结果的功率谱作为待求位场功率谱的估计初值,采用带修正项的迭代维纳滤波方法来更新对待求位场功率谱的估计,最后提出本文的位场向下延拓改进迭代维纳滤波方法.基于理论重力模型数据及航磁实测数据进行了向下延拓对比试验,结果表明,改进迭代法具有较好的收敛性,且下延精度优于Tikhonov正则化法和递增型维纳滤波法.     

最佳数字滤波器及其应用

最佳数字滤波器是分离有给定周期的波或消除时间序列中短周期波动的有效数学工具。它可分成三种类型:低通滤波器、带通滤波器和高通滤波器。 本文提出一个计算正弦积分的新公式。在不同的地质领域内使用了最佳数字滤波器     

二维Wiener滤波器及在物探中应用的一些问题

本文结合二维随机场函数z（x,y）及其统计特征、平稳性和各态遍历性的概念,导出了二维Wiener滤波器的两个波数响应H_opt（u,v）和 _opt（u,v）,并详细地讨论了导出它们的条件。为了正确地应用Wiener滤波技术,我们提供了检验物探观测数据的平稳性和各态遍历性的简单而适用的方法。最后还指出,当应用Wiener滤波的不相关技术时,将在区域异常的谱函数中引入一个非线性畸变因子,这个区域异常是从具有局部干扰的观测数据中提取的。于是,所提取的区域异常必然会产生某种程度的失真。     

APPLICATION OF WIENER FILTERS TO TRANSFORMATIONS OF GRAVITY AND MAGNETIC FIELDS*

Consideration of the spectral representation of gravity and magnetic fields shows the field to be the result of the convolution of factors depending on the parameters of the field. Wiener filters, calculated using model transformations, provide an optimum method for altering these factors and hence effecting field transformations.     

An experimental study of potential distribution in different geological structures

Summary This paper deals with the problem of finding a Wiener filter when the length of the filter output in not larger than the length of the filter input. Measure for the efficiency of a filter is defined in terms of the relation between the desired filter output and the actual filter output. This measure, called the filter efficiency, is used to find the optimum length of the filter memory function. The relation between the signal-to-noise-ratio (SNR) of the filter input and the SNR of the filter output is discussed. It is shown that there is always some improvement in the SNR through the use of a Wiener filter.     

Parametrization of spectra of plasma bubble induced VHF satellite scintillations and its geophysical significance

An important component of ionospheric plasma irregularity studies in the Indian low latitudes involves the study of the plasma bubbles which produce intense scintillations of the transionospheric satellite signals. Many such plasma bubble induced (FBI) scintillation events were identified while recording 244 MHz signal from the geostationary satellite Fleetsat (73°E) at Delhi (28.6°N, 77.2°E) during March-April 1991. This type of scintillations represents changes in plasma processes. These scintillations are spectrally analyzed using an autoregressive (AR) scheme, which is equivalent to maximum entropy method of spectrum analysis, amenable to extracting optimum spectral content from short data lengths (20–40 s). Each spectrum is assigned a level of detectability using the final prediction error (FPE) derived from the optimum filter order required to resolve the spectrum. Lower detectability together with a higher order filter indicate a higher level of coherence for the plasma irregularities (discrete structures). Consistent patterns for these scintillations emerge from the present analysis as follows: (1) the initial and final phases of a scintillation patch display quasiperiodic oscillations. Their corresponding spectra show dominant (Gaussian shaped) spectral features with detectability levels of –6 dB to –12 dB and requiring a higher order (>6) AR filter for their spectral resolution. These are most likely associated with discrete filament-like or sheet-like plasma structures that exist near the bubble walls. (2) Two main features of the scintillation spectra could be positively associated with the well-developed plasma bubble stage: (a) spectra displaying a power-law process with a single component spectral slope between 1.6 to 3.0. Generally such spectra are resolved with a 2nd order filter and have a 1 dB to 6 dB of detectability. (b) Spectra displaying a double slope, indicating an inner and an outer scale regime for the power-law irregularities. These spectra are resolved with higher order filters (>3 but <7) and possess detectability levels of –1 dB to 3 dB. These spectra display finer spectral changes, perhaps indicative of the nature of continuously evolving plasma irregularities. As an example, an analysis of a single scintillation patch is presented to highlight the geophysical significance of the present approach. Some important parameters used in the AR scheme of spectral analysis are given in the Appendix.     

Sparsity‐enhanced wavelet deconvolution

We propose a three‐step bandwidth enhancing wavelet deconvolution process, combining linear inverse filtering and non‐linear reflectivity construction based on a sparseness assumption. The first step is conventional Wiener deconvolution. The second step consists of further spectral whitening outside the spectral bandwidth of the residual wavelet after Wiener deconvolution, i.e., the wavelet resulting from application of the Wiener deconvolution filter to the original wavelet, which usually is not a perfect spike due to band limitations of the original wavelet. We specifically propose a zero‐phase filtered sparse‐spike deconvolution as the second step to recover the reflectivity dominantly outside of the bandwidth of the residual wavelet after Wiener deconvolution. The filter applied to the sparse‐spike deconvolution result is proportional to the deviation of the amplitude spectrum of the residual wavelet from unity, i.e., it is of higher amplitude; the closer the amplitude spectrum of the residual wavelet is to zero, but of very low amplitude, the closer it is to unity. The third step consists of summation of the data from the two first steps, basically adding gradually the contribution from the sparse‐spike deconvolution result at those frequencies at which the residual wavelet after Wiener deconvolution has small amplitudes. We propose to call this technique “sparsity‐enhanced wavelet deconvolution”. We demonstrate the technique on real data with the deconvolution of the (normal‐incidence) source side sea‐surface ghost of marine towed streamer data. We also present the extension of the proposed technique to time‐varying wavelet deconvolution.     

THE DETERMINATION OF DIGITAL WIENER FILTERS FROM AN ILL-CONDITIONED SYSTEM OF NORMAL EQUATIONS*

The system of normal equations associated with the discrete Wiener filter is sometimes ill-conditioned. The purpose of this paper is to show that in such cases the solutions obtained vary drastically with the particular choice of an algorithm and of the computer used for its implementation. A review of the basic mathematical theory behind an ill-conditioned matrix is first presented. Numerical examples are then given to illustrate that the solutions of the normal equations are sensitive to the word length of a given computer. Finally, two possible remedies are described: (1) The well-known method of prewhitening and (2) the use of the conjugate-gradient algorithm for solving the normal equations.     

Directional and correlation analysis from the geomagnetic monitoring and seismic data on the Boso Peninsula in 2000

The mathematical technique is developed for cluster analysis of the orientation structure of the vector geophysical fields. In order to solve the problem of revealing correlations between quasi-linear processes, the notion of the correlation with the nonrigid metric of distance is introduced for the vectors generated by the flows of discrete events with a high degree of sparseness in time. The method is tested on the data from monitoring the magnetic field in a seismically active region of Japan. It is found that the cluster portrait of the orientation structure of the magnetic field is substantially different during quiet and disturbed days. The influence of seismic vibrations of the ground on the results of magnetic measurements is established.     

叠前三维地震近地表吸收补偿技术在大庆油田的应用研究(英文)

与深层致密岩石相比,相对疏松的近地表地层严重吸收了地震波的高频成分,降低了地震数据的分辨率和高频成分的信噪比。本文利用井中雷管激发、地面检波器接收的微测井直达波资料,通过分析近地表地层不同传播距离的地震直达波频谱信息差异,采用维纳滤波方法,进行近地表吸收补偿反滤波器的求取,将不同微测井测量点对应的近地表吸收补偿反滤波器应用于相应的叠前共检波点道集地震数据,完成了叠前地震数据的空变吸收衰减补偿,克服了叠后地震数据无法实现空变补偿的难题。叠前三维地震近地表吸收补偿后的数据,较补偿前地震数据的优势信噪比频带宽度明显拓宽,低频成分基本保持,反射信息量有较大程度增加,而且与合成记录吻合更好,能更好的满足地质解释的需要,提高解释精度。     

重力异常分层分离方法改进及应用:以安徽五河地区为例

本文在原有位场分层分离技术的基础上,提出了动态改进型插值切割算子.通过理想模型实验和谱分析,证明了改进算子对异常源产生的重力场有更好的分离效果.使用新方法对安徽省五河地区布格重力异常进行了分离和分析,分离后的浅部地球物理特征与地表地质调查结果的吻合度高,从而验证了改进算子的有效性和准确性.在结合基础地质资料和分离后的地球物理特征的基础上,进一步分析了五河地区构造格架、区域岩浆岩及红层盆地的空间分布和形态特征,并获取了对研究区内郯庐断裂系各条断裂的延伸、形态和相互关系的新认识.     

Hankel transform filters for dipole antenna radiation in a conductive medium

We discuss the Hankel transforms related to a particular application, i.e. the dipole antenna radiation in conductive media, such as the antenna radiation in sea-bed electromagnetic applications. In this application, the electromagnetic wavefields decay very rapidly with distance. A good filter means that it can be used to evaluate weak fields. Exponential sampling transforms a Hankel transform into a convolution equation, which must be solved to obtain the filter coefficients. Here, we use a direct matrix inversion method to solve the convolution equation in the sample domain, instead of the Fourier transform method and the Wiener–Hopf method, previously used to solve the convolution equation. This direct method is conceptually simple and is suitable for our optimization process: by using the Sommerfeld identity, we search for the optimum sampling interval, which corresponds to the minimum wavefield, evaluated for a given length filter. The performances of the new filters obtained are compared with some well-known filters. We find that our filters perform better for our application; that is, for the same length filters, our filters are able to calculate weaker fields. For users working in similar applications, three sets of filters with lengths 61, 121, 241 are available from the author.     

用于塔里木地壳构造成像的重力场谱矩方法研究

现代地壳探测取得的各种地球物理场中包含有大量地壳构造信息,如果提取这些信息,可以在数学物理普适规律指导下计算出关于地壳构造的图件.由于区域重力场的高阶谱矩包含了场轮廓面的几何信息,可用于地质构造要素的分析计算,为地质构造要素选取和定位的计算机自动制图提供理论依据.由地面布格重力场的二阶谱矩的统计不变量计算,可导出表征地壳变形带的脊形化系数,用于计算机自动制作区域地壳变形带分布图.脊形化系数强弱区的边界代表了活动的和稳定的构造单元的边界.在计算脊形化系数的基础上,还可进一步计算其二阶谱矩的统计不变量并作进一步增强处理,计算构造单元的边界系数,对地壳构造单元边界作连续和精细的追踪.文中介绍了脊形化系数和边界系数的计算方法,以及用在塔里木盆地进行地壳构造分析的结果.圈定了塔里木盆地深层满中高密度扰动带和满南、满北低密度扰动带,为深层油气勘探提供重要基础资料.     

ADAPTIVE SIGNAL PROCESSING THROUGH STOCHASTIC APPROXIMATION*

One of the problems in signal processing is estimating the impulse response function of an unknown system. The well-known Wiener filter theory has been a powerful method in attacking this problem. In comparison, the use of stochastic approximation method as an adaptive signal processor is relatively new. This adaptive scheme can often be described by a recursive equation in which the estimated impulse response parameters are adjusted according to the gradient of a predetermined error function. This paper illustrates by means of simple examples the application of stochastic approximation method as a single-channel adaptive processor. Under some conditions the expected value of its weight sequence converges to the corresponding Wiener optimum filter when the least-mean-square error criterion is used.     

Application of singularity index mapping technique to gravity/magnetic data analysis in southeastern Yunnan mineral district,China

The fractal/multifractal based singularity index mapping technique efficient in characterizing singular physical or chemical properties is applied for the analysis of gravity and aeromagnetic data in southeastern Yunnan mineral district, China. As follow-up after the introduction of singularity theory to geochemical and geological mapping scenarios, this study extends its application to delineate geophysical potential fields. Based on low gravity and low magnetic properties of granitic intrusions in the study area, singularity mapping technique is used as a high-pass filter to emphasize the geophysical anomalies caused by granitic intrusions in support of future mineral exploration. Comparing with the traditionally used band-pass filtering method, it is shown that the new technique provides an improved and simplified approach in geophysical data analysis with the advantage of scale independence.     

A COMPARISON BETWEEN WIENER FILTERING,KALMAN FILTERING,AND DETERMINISTIC LEAST SQUARES ESTIMATION*

The least squares estimation procedures used in different disciplines can be classified in four categories:

• a. Wiener filtering,
• b. b. Autoregressive estimation,
• c. c. Kalman filtering,
• d. d. Recursive least squares estimation.

The recursive least squares estimator is the time average form of the Kalman filter. Likewise, the autoregressive estimator is the time average form of the Wiener filter. Both the Kalman and the Wiener filters use ensemble averages and can basically be constructed without having a particular measurement realisation available. It follows that seismic deconvolution should be based either on autoregression theory or on recursive least squares estimation theory rather than on the normally used Wiener or Kalman theory. A consequence of this change is the need to apply significance tests on the filter coefficients. The recursive least squares estimation theory is particularly suitable for solving the time variant deconvolution problem.