THE ESTIMATION OF SIGNAL SPECTRA AND RELATED QUANTITIES BY MEANS OF THE MULTIPLE COHERENCE FUNCTION *

A seismic trace recorded with suitable gain control can be treated as a stationary time series. Each trace, χ_j(t), from a set of traces, can be broken down into two stationary components: a signal sequence, α_j(t) *s(t—τ_j), which correlates from trace to trace, and an incoherent noise sequence, n_j(t), which does not correlate from trace to trace. The model for a seismic trace used in this paper is thus χ_j(t) =α_j(t) * s(t—τ_j) +n_j(t) where the signal wavelet α_j(t), the lag (moveout) of the signal τ_j, and the noise sequence n_j(t) can vary in any manner from trace to trace. Given this model, a method for estimating the power spectra of the signal and incoherent noise components on each trace is presented. The method requires the calculation of the multiple coherence function γ_j(f) of each trace. γ_j(f) is the fraction of the power on traced at frequency f that can be predicted in a least-square error sense from all other traces. It is related to the signal-to-noise power ratio ρ_j(f) by where K_j(f) can be computed and is in general close to 1.0. The theory leading to this relation is given in an Appendix. Particular attention is paid to the statistical distributions of all estimated quantities. The statistical behaviour of cross-spectral and coherence estimates is complicated by the presence of bias as well as random deviations. Straightforward methods for removing this bias and setting up confidence limits, based on the principle of maximum likelihood and the Goodman distribution for the sample multiple coherence, are described. Actual field records differ from the assumed model mainly in having more than one correctable component, components other than the required sequence of reflections being lumped together as correlated noise. When more than one correlatable component is present, the estimate for the signal power spectrum obtained by the multiple coherence method is approximately the sum of the power spectra of the correlatable components. A further practical drawback to estimating spectra from seismic data is the limited number of degrees of freedom available. Usually at least one second of stationary data on each trace is needed to estimate the signal spectrum with an accuracy of about 10%. Examples using synthetic data are presented to illustrate the method.     

INTERPRETATION OF GRAVITV ANOMALIES BY MEANS OF LOCAL POWER SPECTRA*

A statistical model of the medium is introduced as source of a gravimetric anomaly. On the basis of this model the estimation of the parameters of the medium is proposed based on the statistically transformed power spectrum of the gravity anomaly. The method permits to associate the estimated depths to the disturbing limit with the profile points. Practical examples illustrate usefulness of this method to interpretation.     

ESTIMATION OF DEPTH TO CONDUCTORS BY THE USE OF ELECTROMAGNETIC TRANSIENTS*

The transient response of a layered structure to plane wave excitation can be considered to be composed of a series of waves and a ground wave. For the case of a half-space of conductivity σ and permeability μ the maximum in the electric field is found at a depth z and time t when t=z²σμ/2. This formula can be used to estimate the depth to a buried horizontal conductor with an accuracy that depends upon the resistive contrast at the conductor's surface. The above ray type of solution can be converted to a solution composed of a number of modes by the use of a Poisson transform and the transformed solutions yield decay constants that are consistent with the previously reported results. In the case of a finite source, the maximum in the electric field is strongly directed. The direction depends upon the geometry of the source and the air-earth interface. Although the maximum varies with direction it can be shown that in some directions similar laws to that above are valid. The depth to a conductor can be estimated from the early part of the transients when the ground wave is removed. The removal of the ground wave from the transient is facilitated by the use of an apparent conductivity formula. Although these results were obtained under restrictive conditions they do provide some insight into the electrical transients that are encountered by studying more complex models.     

最大似然法速度谱估计的改进

本文分析了现行的最大似然法速度谱估计的基本运算过程。结果表明,各记录道间的幅度差异将严重降低方法的分辨率,对此,文中提出两种改进方法,并用人工合成记录方式进行了方法的可行性试验。     

最大似然法速度谱估计的改进

本文分析了现行的最大似然法速度谱估计的基本运算过程。结果表明,各记录道间的幅度差异将严重降低方法的分辨率,对此,文中提出两种改进方法,并用人工合成记录方式进行了方法的可行性试验。     

INTERPRETATION OF MAGNETIC ANOMALIES USING SPECTRAL ESTIMATION TECHNIQUES*

The depth of causative bodies may be derived from the power spectrum of their magnetic anomalies. After a short review of the theoretical basis of the method, several examples of its application to synthetic cases are shown. Disturbing effects due to improper choice of the sampling interval and to anomalies only partially contained in the examined segment of the profile are studied. The spectral method is then applied to real cases; the tapering of the anomalies, the application of non-linear filters and the effects of anomaly superpositions are investigated. In conclusion, an appraisal of the method and of its possible practical impact has been given.     

TIME-VARYING PREDICTION FILTERING BY MEANS OF UPDATING*

In contrast to the conventional deconvolution technique (Wiener-Levinson), the spike-, predictive-, and gap-deconvolution is realized with the help of an adaptive updating technique of the prediction operator. As the prediction operator will be updated from sample to sample, this procedure can be used for time variant deconvolution. Updating formulae discussed are the adaptive updating formula and the sequential algorithm for the sequential estimation technique. This updating technique is illustrated using both synthetic and real seismic data.     

武昌同步卫星信号振幅闪烁功率谱

本文利用自制的微机数据采集与分析系统,处理了1985年12月至1986年6月在武昌接收日本ETS-Ⅱ卫星信标136MHz信号所观测到的振幅闪烁。共分析了133例闪烁功率谱得出,谱指数随闪烁指数S_4的增加有增大的趋势,平均谱指数值为3.1;大多数的对数功率谱曲线都在低频部分平坦或以略小于1的斜率上升,而在高频部分以-2.5～-4.0的斜率迅速下降;有1 3例功率谱在高频部分发生“折断”现象,即负幂律谱有两个谱指数,发生折断的频率f_b约为0.07Hz,相应的电离层不规则结构的空间尺度约为280m。     

武昌同步卫星信号振幅闪烁功率谱

本文利用自制的微机数据采集与分析系统,处理了1985年12月至1986年6月在武昌接收日本ETS-Ⅱ卫星信标136MHz信号所观测到的振幅闪烁。共分析了133例闪烁功率谱得出,谱指数随闪烁指数S_4的增加有增大的趋势,平均谱指数值为3.1;大多数的对数功率谱曲线都在低频部分平坦或以略小于1的斜率上升,而在高频部分以-2.5～-4.0的斜率迅速下降;有1 3例功率谱在高频部分发生“折断”现象,即负幂律谱有两个谱指数,发生折断的频率fb约为0.07Hz,相应的电离层不规则结构的空间尺度约为280m。     

利用视振幅比方差判别地震序列类型的方法

本文分析了我国东部地区九个省及其沿海发生的16个不同类型的地震序列,提出用纵、横波的视振幅比方差来判別地震序列类型,特别是判别前震序列的方法。 结果表明,对于视振幅比方差而言,前震序列小于0.25,震群序列在0.26—0.50之间,余震及完整的前—主—余震序列大于0.55,正常的地震活动与震群序列差不多。如果把所有的方差两两组合,相互之间进行F检验,则不同类型的地震序列之间,大部份都存在显著差异,相同类型的地震序列之间,大部份均不存在显著差异。利用得分法进行统计,其准确率在置信水平相似文献   

COMPUTATION OF TYPE CURVES FOR ELECTROMAGNETIC DEPTH SOUNDING WITH A HORIZONTAL TRANSMITTING COIL BY MEANS OF A DIGITAL LINEAR FILTER*

The computation method described in this paper is based on the existence of a linear relationship between the mutual coupling ratio and the kernel function in the integral expression for it. Accordingly, the mutual coupling ratio can be determined by first computing sample values of the kernel function and then subjecting these to a digital linear filter. In the present paper the appropriate sampling distance is determined and the values of the digital filter coefficients are computed, both for electromagnetic sounding with horizontal coils and for electromagnetic sounding with perpendicular coils.     

CALCULATION OF GALVANIC EFFECTS BY MEANS OF THE METHOD OF SUB-AREAS*

A numerical method is proposed for solving the problem of steady current flow. The electrodynamic model is replaced by the equivalent stationary charge distribution obtained by Poisson's analysis, in which the surface integral equation for field intensity is reduced to a set of simultaneous linear algebraic equations by means of the method of sub-areas. The solution of the set allows the calculation of an approximation for the charge density distribution on the discontinuity surfaces of conductivity. The method is valid for complex conductivities, whereby the apparent phase shift of IP can be calculated from the complex potential or field intensity. The phase shift anomaly calculated as an application is very similar to the corresponding frequency effect anomaly. The method allows the calculation of the mise-à-la-masse effect as a solution to a potential problem, in which the primary current electrode is located within the body to be surveyed.     

EXPLORATION OF HIGH RESISTIVITY BASEMENT USING ELECTRICAL AND MAGNETIC FIELDS OF QUASI-STATIC POINT SOURCES*

Determination of thickness of sediments (usually of high conductivity) overlying a high-resistivity basement is one of the basic problems of electrical exploration methods. This paper proposes to determine horizontal electrical conductance on the basis of impedance calculated from electrical and magnetic fields of distant quasi-static (low-frequency) point sources. Using the proposed method, horizontal conductance of the sediments can be determined also from artificial quasi-static noise-impulses coming from sources of unknown position and intensity. The results of analogue modeling and field examples prove the potential of the proposed technique.     

ESTIMATION OF REFLECTOR PARAMETERS BY THE VIRTUAL IMAGE TECHNIQUE*

The seismic interpretation process generally exploits three of the following independent basic assumptions:

• 1 Input quantities are obtained by simplification of measured data (travel time curves).
• 2 2. The geological model contains only a few parameters (for example, plane interfaces and constant interval velocities).
• 3 3. Approximate transformations may be applied.

The first two are related to the simplification of the phenomena and enhance their essential features. The transformation which establishes relations between simplified data and model is required to be unique, stable, and sufficiently accurate. Practically, the travel time curves are almost exclusively regarded as hyperbolas. We also accept this approximation. The paper presents a simple recursive algorithm for the evaluation of the depth and dip of plane reflectors and the interval velocities. It is a simple fact, that there exists a unique relationship between three hyperbolic parameters and a homogeneous dipping layer. Accordingly, two layers can be replaced by a single layer and the parameters of the lower boundary can be estimated when the upper one is known, initiating virtual shotpoints and geophone points (virtual surface). So, the case of multilayered media can be reduced in sequential steps to the case of a single homogeneous layer using a stripping type procedure. Some synthetic model examples are provided to demonstrate the abilities of the algorithm.     

ESTIMATION OF SPECTRUM AND CROSS-SPECTRUM OF AEROMAGNETIC FIELD USING FAST DIGITAL FOURIER TRANSFORM (FDFT) TECHNIQUES*

An efficient method of computing spectrum and cross-spectrum of large scale aero-magnetic field (or of any other two-dimensional field) has been developed and programmed for a digital computer. The method uses fast Fourier transform techniques. Briefly, the method is as follows: a digitized aeromagnetic map is divided into a number of rectangular blocks. Fourier transforms of these blocks are computed using a two-dimensional fast Fourier transform method. Finally, the amplitude of the Fourier transforms is averaged to give the desired spectrum. Computation of cross-spectrum follows the same lines. In fact, the same programme may be used to a compute the spectrum as well as cross-spectrum. The method has a number of computational advantages, in particular it reduces greatly computational time and storage requirements. The programme has been tested on synthetic data as well as on real aeromagnetic data. It took less than 30 seconds on an IBM 360/50 computer to compute the spectrum of an aeromagnetic map covering an area of approximately 4500 square miles.     

DETECTION OF CAVES IN A KARST FORMATION BY MEANS OF ELECTROMAGNETIC WAVES*

The application of classical geophysical methods in locating karst caves did not yield always unambiguous results. It was our task to verify a new method that has not yet been tested. In investigating caves in a karst formation, electromagnetic waves in the band 2–10 MHz were applied. The physical analysis of the problem is carried out, the measuring device used for the perradiation of the rocks between the boreholes is described, and the results of the measurements made in the karst area of East Slovakia (?SSR) are shown. The verification from mines is included. The results mentioned are demonstrated in a space model. The work performed in the mines verified unambiguously the interpretation of the indications measured. The results show the suitability of putting the electromagnetic method in question into the set of geophysical methods within the hydrogeological survey of karst areas.     

PARAMETER OPTIMIZATION OF VELOCITY DEPTH FUNCTIONS OF GIVEN FORM BY USE OF ROOT-MEAN-SQUARE VELOCITIES*

From seismic surveys zero offset reflection times and root-mean-square velocities are obtained. By use of Dix-Krey's formula, the interval velocities can be calculated. If no well velocity survey exists, the interval velocities and T(o) times are the only available information. The suggested way to get a regionally valid velocity distribution is to select N“leading horizons”, where a major change in the velocity parameters occurs and to compute the parameters of the selected velocity depth function (in most cases linear increase with depth) by a special approximation for the interval between two adjacent “leading horizons”. Herewith all reflection horizons within the interval are taken into account.     

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.     

强地震动幅值谱随机涨落特征的研究

本文从工程应用的观点，将强地面运动幅值谱?Ａ（ｆ）│表示为强度受到调制的随机过程即│Ａ（ｆ）│＝│Ａ（ｆ）│〔１＋ｎ（ｆ）〕其中，│Ａ（ｆ）│为随频率变化的确定性函数亦是│Ａ（ｆ）│的均值，ｎ（ｆ）为均值为零的随机过程。在随机过程ｎ（ｆ）为各态历经的假定下，研究了ｎ（ｆ）的功率谱密度函数的特征及其衰减形式。根据地震学的有关理论，提出了用四个参数控制幅值谱的均值随频率变化的函数形式并对拟合这些参数的