REMARKS ON THE SIGNAL TO NOISE RATIO IN THE VIBROSEIS SYSTEM*

The paper presents a discussion of some of the noise features of the VIBROSEIS SYSTEM *** ** Trademark of Continental Oil Company.
and their bearing on the determination of the optimally weighted stack.     

THE PERFORMANCE OF OPTIMUM STACKING FILTERS IN SUPPRESSING UNCORRELATED NOISE*

Optimum stacking filters based on estimates of trace signal-to-uncorrelated noise ratios are assessed and compared in performance with conventional straight stacking. It is shown that for the trace durations and signal bandwidths normally encountered in seismic reflection data the errors in estimating signal/noise ratios largely counteract the theoretical advantages of the optimum filter. The more specific the filter (e.g. the more frequency components included in its design) the more this is true. Even for a simple weighted stack independent of frequency, the performance is likely to be better than a straight (equal weights) stack only for relatively high signal/noise ratios, when the performance is not critical anyway.     

OPTIMUM HYPERBOLIC MOVEOUT FILTERS WITH APPLICATIONS TO SEISMIC DATA*

Optimum multichannel filters can be designed to process seismic events falling on hyperbolic moveout curves using the conventional least-squares method. Contrary to the linear moveout filters, autocorrelation and crosscorrelation functions inherent in the normal equations have to be computed numerically. However, computation times of filter coefficients are comparable to linear moveout operators. For a given source-receiver geometry and assuming straight ray-path, relative moveout of a seismic reflection event is dependent on the two way arrival time and rms velocity. Consequently, to avoid overlapping of pass and reject moveout windows, hyperbolic moveout filters have to be designed over time gates rather than for the whole record lengths. Hyperbolic and hyperbolic-linear moveout filters applied to synthetic and field seismic reflection traces show good signal-to-noise (S/N) ratio improvements. Results of some combined synthetic and field data examples are presented.     

ZD-1型信号增强浅层勘探地震仪

本仪器用于探测地表以下几十米至数百米范围内的介质构造。通过对信号波形的迭加处理,达到改善信噪比的目的。 该仪器采用8位大规模集成单片A/D转换器,取样速度为5000,2000,1000和500样值/秒。內存尺寸为1024字相似文献   

OPTIMIZATION OF SHORT DIGITAL LINEAR FILTERS FOR INCREASED ACCURACY*

The accuracy of short length digital linear filter operators can be substantially increased if the sampling interval as well as the abscissa shift are properly adjusted. This may be done by a trial and error process of adjustment of these parameters until the error made by the filter operator, applied to a suitably chosen test function, is smallest. As an illustration of the application of this method, 7-, 11- and 19-point filters for the calculation of Schlumberger apparent resistivity from a known resistivity transform are designed. Errors with the new 7-point filter are seen to be less than those with a 19-point filter of conventional design. The errors with the new 19-point filter are two to three orders of magnitude smaller than those made by the conventional 19-point filter. The new method should provide digital linear operators that allow significant improvements in accuracy for comparable computation efforts, or substantial reduction in computation for comparable accuracy of results, or something of both.     

THREE-DIMENSIONAL OPTIMUM MULTICHANNEL VELOCITY FILTERS*

Design procedures and characteristics of three stacking filters are discussed which may find application in various three-dimensional velocity filtering problems. These filters are derived in the time-domain as optimum multichannel Wiener filters. Random stationary functions are assumed as stochastic models for the seismic traces. All power and crosspower spectra which are the basic elements of the multichannel normal equations are statistically averaged according to specific three-dimensional considerations. Various properties of the input traces may be incorporated in the design of the optimum filters. With fairly general assumptions about the input these filters are deterministic in the sense that they are applicable to a broad class of input traces with similar statistics in amplitudes and arrival times of signals.     

TRANSFORMATION OF DIPOLE TO SCHLUMBERGER SOUNDING CURVES BY MEANS OF DIGITAL LINEAR FILTERS*

Linear relationship between dipole and Schlumberger sounding resistivities leads to the use of digital filters to transform the former to the latter. This transformation is of importance from the viewpoint that Schlumberger interpretational techniques and know-how could then be applied to the pseudo-Schlumberger field curve. Filters for this transformation are presented for the radial, perpendicular, and parallel (30°) dipole method. The characteristics of these filters are similar to the ones for transforming dipole data to the kernel and are favourable in that they do not amplify noise. A sampling interval of (In 10) /6 has been used in determining the filter yielding good accuracy. Like previous filters the present one is handy and fast in operation.     

PREDICTION ERROR FILTERS,WHITE NOISE AND ORTHOGONAL COORDINATES*

Optimum filters can be computed using orthogonal coordinates obtained from the eigenvalues and eigenvectors of the autocorrelation matrix. The method is used to obtain unit distance prediction error filters. The output of a unit distance prediction error filter when applied to the input wavelet is an impulse at zero time. The effect on the output of added white noise is easily obtained using the approach through the orthogonal coordinates. The added white noise results in output wavelets which are no longer impulses at zero time. The decrease in time resolution gives a filter that does not increase undesirable high frequency noise as much as filters computed without white noise. Orthogonal coordinates with little signal energy can be omitted from the filter computation resulting in output wavelets resembling those computed using added white noise.     

USE OF EXPECTED ERROR IN THE DESIGN OF LEAST-SQUARES OPTIMUM FILTERS*

The design of least-squares optimum filters is based upon minimizing a suitably defined error criterion. The expected value of this error is easily computable after the coefficients of the filter have been determined. When a particular filtering problem is specified, there are several parameters which are specifically not included in the optimization procedure. However, the magnitude of the expected error may be quite sensitive to these parameters. The examination of the relative values of the expected error for variations of these unspecified parameters may lead to a better definition of the filter problem. The parameters which are left unspecified by the general least-square filter definition include: 1. The addition of white noise to the signal autocorrelation to stabilize the filter behavior. 2. The specification of the shape of the desired output of the filter. 3. The specification of the lag between the desired output and the input. Examples are given showing the relationship between these parameters and the value of the expected error.     

SIGNAL-TO-NOISE RATIO ENHANCEMENT IN SEISMIC MULTIFOLD DATA USING BAYESIAN STATISTICS*

Bayesian statistics are applied to the problem of signal-to-noise ratio enhancement from a common-midpoint gather. By maximizing the a posteriori probability distribution of the gather with respect to the minimum-offset trace and suppressing multiples via a semblance criterion, a statistically biased stack is formed with signal-to-noise ratio comparable to that of the usual stack while preserving the resolution and registration of the original noisy trace. Application of the algorithm to real data reveals geologically significant features which are indistinct in the standard stacked section.     

SIGNAL ENHANCEMENT OF VIBRATORY SOURCE DATA IN THE PRESENCE OF ATTENUATION*

Amplitude spectra of input FM signals used in the vibratory source method of seismic exploration often show undesirable oscillations near the initial and terminal frequencies. These oscillations have an effect on the correlation background and distort the output signal. Considerable improvement in reducing the amplitude of these oscillations is obtained using a proper taper fuction. Attention is given to the relation between the tapering time and bandwidth of the spectrum. Analyses of the spectra of the received data from vibratory sources show considerable attenuation in comparison with the original field sweep. Since the matched filtering process will result in a series of waveforms which have the shape of the autocorrelation of the input signal, consideration is given to the autocorrelation function and its zero-lag coefficient of the FM signal in the presence of attenuation. A method has been developed which compensates for the attenuation and recovers the distortion of waveforms when the received data is correlated. The design of a waveform shaping filter for vibratory source data is given to reduce the influence of phase distortion on the received waveforms as well as to increase S/N ratio resolution. Parameters used for this filter are based on the properties of the FM signal and its autocorrelation function. Several examples from field data are presented to illustrate the methods. The results indicate that the use of the above techniques yields sections with good frequency resolution and improved S/N ratio.     

OPTIMUM DIGITAL FILTERING AND INVERSE FILTERING IN THE FREQUENCY DOMAIN*

Two distinct filters are developed in the frequency domain which represent an attempt to increase the resolution of fine structure contained in the signal whilst keeping the expected filtered noise energy within reasonable bounds. A parameter termed the White Noise Amplification is defined and used together with a measure of the deconvolved pulse width in order to provide a more complete characterisation of the filters. Each of the two main types of frequency domain filters discussed varies in properties with respect to a single adjustable parameter. This may be contrasted with a time domain Wiener filter which in general has three variables: length, delay and an adjustable noise parameter or weight. The direct frequency domain analogue of the Wiener filter is termed a gamma-Fourier filter, and is shown to have properties which span the range from those of a spiking filter with zero least square error at one extreme, to those of a matched filter at the other extreme of its variable parameter's range. The second type of filter considered—termed the modulated Gaussian filter—is similarly shown to be a perfect spiking filter at one extreme of its parameter range, but adopts the properties of an output energy filter at the other extreme.     

TRANSFORMATION OF SCHLUMBERGER APPARENT RESISTIVITY TO DIPOLE APPARENT RESISTIVITY OVER LAYERED EARTH BY THE APPLICATION OF DIGITAL LINEAR FILTERS *

A simple extension of our previous work in which digital filters were developed to transform dipole resistivity measurements over layered earth to Schlumberger ones leads us to the development of filters for transforming the latter to the former. As in the previous work we use a sampling interval of 1/6 In 10 in designing the filters that are both accurate and fast in operation.     

小波变换的过零点特性与地震勘探信号的信噪比和分辨率

利用小波变换研究地震勘探信号小波变换的过零点特性,本文提出了用小波变换的过零点特性和地震勘探信号相邻道的横向相关性提高信号分辨率和信噪比的新方法．该方法包括两个主要步骤：①利用相邻地震道信号具有很好相关性,而噪音相关性差的特点以及小波变换的过零点特性得到有效反射波同相轴随空间坐标的变化信息．②利用奇异值分解和最小二乘（SVD-TLS）方法沿同相轴对振幅进行多项式拟合去噪并增加信号高频提高信号分辨率．     

小波变换的过零点特性与地震勘探信号的信噪比和分辨率

利用小波变换研究地震勘探信号小波变换的过零点特性，本文提出了用小波变换的过零点特性和地震勘探信号相邻道的横向相关性提高信号分辨率和信噪比的新方法．该方法包括两个主要步骤：①利用相邻地震道信号具有很好相关性，而噪音相关性差的特点以及小波变换的过零点特性得到有效反射波同相轴随空间坐标的变化信息．②利用奇异值分解和最小二乘（SVD-TLS）方法沿同相轴对振幅进行多项式拟合去噪并增加信号高频提高信号分辨率．     

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.     

COMBINED SWEEP SIGNALS FOR CORRELATION NOISE SUPPRESSION*

Comparison of both synthetic and field data shows that considerable suppression of correlation noise can be achieved with the Combisweep technique and with the Encoded Sweep Technique. In the first technique, the spectrum is shaped by superposition of linear sweeps with different frequency range; in the second technique, short sweeps of different polarity are combined to form the “alphabet” of a code.     

ZERO—PHASE FORWARD FILTERS FOR RESISTIVITY SOUNDING*

Forward filters to transform the apparent resistivity function over a layered half-space into the resistivity transform have been derived for a number of sample intervals. The filters have no apparent Gibbs' oscillations and hence require no phase shift. In addition, the end points of the filter were modified to compensate for truncation. The filters were tested on simulated ascending and descending two-layer cases. As expected, “dense” filters with sample spacing of In (10)/6 or smaller performed very well. However, even “sparse” filters with spacing of In (10)/2 and a total of nine coefficients have peak errors of less than 5% for p₁:p₂ ratios of 10^–6 to 10⁶. If a peak error of 5.5% is acceptable, then an even sparser filter with only seven coefficients at a spacing of 3 In (10)/5 may be used.     

调制解调器(MODEM)在数字化地震信号传输中的作用分析

数字信号的传输是数据通信的关键,用调制解调器（ＭＯＤＥＭ）既能把数字信号变换成模拟信号,又能把收到的模拟信号恢复成数字信号,研究分析了Ｖ．２４接口的工作原理,同时还介质了ＭＯＤＥＭ的基本原理。