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.     

GEOPHYSICAL ANOMALY INTERPRETATION OF POTENTIAL FIELDS BY MEANS OF SINGULAR POINTS METHOD AND FILTERING*

The calculation of potential field anomalies on different levels below the measuring level permits to localize the singular points related to the sources of anomalies. It is possible to achieve considerable improvement of the resolution of this method

• 1) filtering of analytical downward continuation,
• 2) the use of the magnitude of the gravitational vector,
• 3) calculation of physe changes.

The numerical examples confirm these assumptions.     

测定浅震震源参数的宏观方法

本文提出了利用等震线测定地震断层面的走向、倾向、倾角和破裂长度等震源参数的宏观方法。用这种方法测定了35个地震（1830年—1973年）的参数,其结果与用微观方法得到的结果进行了比较,二者基本一致。 关于破裂方式对等震线的影响问题,本文也进行了初步的讨论。     

测定浅震震源参数的宏观方法

本文提出了利用等震线测定地震断层面的走向、倾向、倾角和破裂长度等震源参数的宏观方法。用这种方法测定了35个地震（1830年-1973年）的参数,其结果与用微观方法得到的结果进行了比较,二者基本一致。 关于破裂方式对等震线的影响问题,本文也进行了初步的讨论。     

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.     

MATHEMATICAL DENOTATION OF STANDARD-GRAPHS FOR RESISTIVITY PROSPECTING IN VIEW OF THEIR CALCULATION BY MEANS OF A DIGITAL COMPUTER*

This paper is the follow-up of an earlier paper by the same author on the calculation of standard-graphs for horizontally stratified subsoils. The method which was developed in that earlier paper was destined for handwork; it was laid down in master-tables. The present paper deals with the presentation of similar methods to the computer expert in purely mathematical denotation. Two different denotations are described for the calculation of the image pole strengths involved. The first denotation is an improved version of Watsons formulae; it gives the total strengths. The second denotation preserves the character of successive approximations as described in the previous paper. Both denotations have been worked out until a six layer resistivity profile, but actually there is no limitation to the number of layers. There is no restriction to the resistivities of any layer. The only condition is now that all interface depths must be integers. This paper is followed by a paper on the relevant computer program by Argelo in this same issue     

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.     

ON THE INTERPRETATION OF RESISTIVITY SOUNDINGS BY THE LEAST-SQUARES METHOD*

An interactive least-squares method for the interpretation of VES curves was proposed by Johansen (1977). The method permits one to select some parameters (thicknesses and/or resistivities of individual layers) and to change the rest in such a way that the interpreted model approaches the measured data. This note suggests a modification of Johansen's method, in which not only the individual parameters can be selected but also linear combinations of parameters—in particular, the sum of thicknesses of several layers.     

PROSPECTING BY THE GEOTHERMIG METHOD*

A high sensitivity thermometer using a thermistor sensing element was designed for practical measurements in the field. The most suitable procedures for the elimination of diurnal and seasonal variation of temperature, the influence of vegetation cover and of other effects were investigated. Positive results of geothermic measurements have been acquired on sulfide deposits. By far the most important results of geothermic measurements have been obtained in hydrogeological problems, e.g. the investigation of circulation of underground water. In the case of prospection for cold mineral waters the combination of geothermic measurements with gasometric analyses is very useful. As the classical domain for geothermic investigation, prospection for hot water is to be mentioned.     

INVESTIGATION OF THE SEISMIC RESPONSE OF CYCLICALLY LAYERED CARBONIFEROUS ROCK BY MEANS OF SYNTHETIC SEISMOGRAMS *

Seismic exploration for coal as well as basic scientific research indicate the existence of unsolved problems. These problems arise partly because the requirements are different from those in exploration for gas and oil and are partly due to the geological situation. The medium to be investigated is composed of cyclically changing layers with extremely high velocity and density contrast. Furthermore, the structure of the carboniferous rock is highly fractured and folded. This leads to difficulties in interpreting the seismic response of carboniferous rock. To overcome these difficulties synthetic seismograms are a useful tool. Calculating synthetic seismograms the carboniferous rock has been modelled as a sequence of seams and rock. The following results have been obtained

• (i) A single seam gives rise to a distinct reflection signal even for a thickness of 1/50 of the wavelenght.
• (ii) Individual reflections are not visible from a sequence of layers containing a great number of seams and interfaces. Due to constructive interference only a few high amplitudes appear. These high amplitudes are labelled “interference reflections”.
• (iii) With increasing travel time the interference reflections are mainly composed of short lag multiples such that the primary reflections have no significant influence.
• (iv) The sequence of seams acts on the reflected seismic signal as a high pass filter and on the transmitted signal as a low pass filter. The cut-off frequencies are determined by the average seam thickness, and the steepness of the slopes increases with increasing number of seams.
• (v) The interference reflections can be used for determining the geological structure at least for the upper part of the sequence.

     

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.     

DETERMINATION OF RESISTIVITY SOUNDING FILTERS BY THE WIENER-HOPF LEAST-SQUARES METHOD*

It has been found that the Wiener-Hopf least-squares method is a very successful tool for the determination of resistivity sounding filters. The values of the individual filter coefficients differ quite appreciably from those obtained by the Ghosh procedure. These differences in the filter coefficients, however, have only a negligible effect on the output of the filter. It seems that these differences in the coefficients correspond to a filter function of a rather narrow frequency band around the Nyquist frequency, which is only very weakly present in the input and output functions.     

利用不完全Cholesky共轭梯度法求解点源三维地电场

点源三维地电场的求解是一大型数值计算问题．本文用有限差分方法求解,最后形成一个线性方程组Ax＝b,这里A是大型稀疏的带状对称矩阵．解大型稀疏方程组的完全Cholesky分解直接算法,一般要求巨大的机器内存来存储系数矩阵A,而且计算速度极慢．因此引入不完全Cholesky共轭梯度（ICCG）算法及按行索引的稀疏存储模式,充分利用A的稀疏性,使得计算速度大大提高,而内存要求则大大减少,因此ICCG算法是地电三维正演的强有力工具．     

利用不完全Cholesky共轭梯度法求解点源三维地电场

点源三维地电场的求解是一大型数值计算问题．本文用有限差分方法求解,最后形成一个线性方程组Ax＝b,这里A是大型稀疏的带状对称矩阵．解大型稀疏方程组的完全Cholesky分解直接算法,一般要求巨大的机器内存来存储系数矩阵A,而且计算速度极慢．因此引入不完全Cholesky共轭梯度（ICCG）算法及按行索引的稀疏存储模式,充分利用A的稀疏性,使得计算速度大大提高,而内存要求则大大减少,因此ICCG算法是地电三维正演的强有力工具．     

DEPTH ESTIMATION OF MAGNETIC SOURCES BY MEANS OF FOURIER AMPLITUDE SPECTRA*

The Fourier transform of a square-shaped section of a magnetic survey, digitized in a square grid, forms a rectangular matrix of coefficients which can be condensed to a series of average amplitudes dependent only on their frequency and no longer on the direction of the respective partial waves. These average amplitudes together represent a spectrum which–when plotted in a semilogarithmic coordinate system (log amplitude versus frequency)–often shows straight segments which decrease with increasing frequency. By continuing the given field downwards these straight segments become horizontal at a certain depth, the so-called “white depth”. This white depth may be used as a first estimate for the depth of magnetic sources producing the respective part of the field. It is shown that the sources which correspond to such use of the white depth can be expected to be “randomly distributed with some positive autocorrelation”. As an example for such a depth estimation the interpretation of the aeromagnetic survey of NW-Germany by a relief in 8–16 km depth is given. The relief divides the subsurface in an upper nonmagnetic layer and a lower layer with magnetization M= 2 Am^?1.     

NEW ASPECTS IN THE INVERSION OF GRAVITY PROFILES BY POLYNOMIAL METHOD*

The gravity anomaly caused by a deviation of a density interface that is of constant profile but finite extension (a so-called 2 1/2-dimensional structure) can be expressed in polynomial form that can be inverted. Numerical experiments with synthetic structures show the viability of this inversion method.     

DIRECT LOCATION OF OIL AND GAS BY THE SEISMIC REFLECTION METHOD*

The seismic velocity of sedimentary rocks is determined by the porosity, the velocity in the matrix and that in the fluid. The last two are known experimentally. The velocity can be measured from the surface. By applying the time average equation we can find the porosity. If the only difference at two points is the nature of the fluid in one layer, the ratio of the reflectivities of the layer at these points determines the nature of the fluid; this ratio is equal to the ratio of the amplitudes at these points. The size of the reservoir can then be found. The method can be applied to both oil exploration and production. It is more accurate in the latter case because more information is available than in the former case. The method is also more effective in developing discovered fields than the conventional method of relying only on the geological structural configurations.     

MAGNETOTELLURIC MODELLING BY THE FINITE ELEMENT METHOD*

The finite element method, here viewed as a special case of the Galerkin projective method, is applied to the modelling of magnetotelluric problems, and its adaptation to geological profiles is outlined. A novel method for obtaining surface field values, involving matrix representation of the normal derivative operator, is presented in detail. Results obtained by this method are compared with well-known infinite series solutions for the vertical fault and the outcropping dyke. Two profiles containing sulphide zones are also modelled, the results being compared with field data; satisfactory agreement is obtained.     

利用模糊方法识别地震前兆的讨论

当前,在对地震信息还没有一个清晰地识别判定的情况下,地震预报是一件难事,一般传统数学计算方法都将感到困难。本文就利用模糊方法识别地震前兆问题作一些初步讨论。模糊集合的特性是以“亦此亦彼”的原则来确定研究对象与集合从属关系。一个模糊概念虽没有明确的外延,但只要指定U中各个元素对它的符合程度,这个模糊概念也就得到一     

用地形变资料预报地震的初次尝试

1976年8月23日松潘、平武之间发生了第二次7.2级地震。震前我们曾根据地形变资料作了预报,现分述如下: 资料介绍这次地震前松潘与新庄短水准都有明显趋势异常。松潘短水准从75年3月开始,异常持续了24个月,幅度为5.2毫米,是正常值的2.6倍。新庄短水准异常从75年11月开始,持续了13个月,最大幅度3.8毫米,是正常值的2.7倍(图1、2)。