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1.
O. KOEFOED 《Geophysical Prospecting》1970,18(4):564-570
In a previous publication (Koefoed 1968) a function called the “raised kernel function” has been introduced as an intermediate function in the interpretation of resistivity sounding data, and methods have been described both for the determination of the raised kernel function from the apparent resistivity function, and for the determination of the layer distribution from the raised kernel function. In the present paper a procedure is described by which the second step in this interpretation method–i.e. the determination of the layer distribution from the raised kernel function–is considerably accelerated. This gain in interpretation speed is attained by the use of a standard graph for a function which defines the reduction of the raised kernel function to a lower boundary plane. 相似文献
2.
We start from the Hankel transform of Stefanescu's integral written in the convolutionintegral form suggested by Ghosh (1971). In this way it is possible to obtain the kernel function by the linear electric filter theory. Ghosh worked out the sets of filter coefficients in frequency domain and showed the very low content of high frequencies of apparent resistivity curves. Vertical soundings in the field measure a series of apparent resistivity values at a constant increment Δx of the logarithm of electrode spacing. Without loss of information we obtain the filter coefficient series by digital convolution of the Bessel function of exponential argument with sine function of the appropriate argument. With a series of forty-one values we obtain the kernel functions from the resistivity curves to an accuracy of better than 0.5%. With the digital method it is possible to calculate easily the filter coefficients for any electrode arrangement and any cut-off frequency. 相似文献
3.
SIEW HUNG CHAN 《Geophysical Prospecting》1970,18(2):215-235
This paper describes certain procedures for deriving from the apparent resistivity data as measured by the Wenner electrode configuration two functions, known as the kernel and the associated kernel respectively, both of which are functions dependent on the layer resistivities and thicknesses. It is shown that the solution of the integral equation for the Wenner electrode configuration leads directly to the associated kernel, from which an integral expression expressing the kernel explicitly in terms of the apparent resistivity function can be derived. The kernel is related to the associated kernel by a simple functional equation where K1(λ) is the kernel and B1(λ) the associated kernel. Composite numerical quadrature formulas and also integration formulas based on partial approximation of the integrand by a parabolic arc within a small interval are developed for the calculation of the kernel and the associated kernel from apparent resistivity data. Both techniques of integration require knowledge of the values of the apparent resistivity function at points lying between the input data points. It is shown that such unknown values of the apparent resistivity function can satisfactorily be obtained by interpolation using the least-squares method. The least-squares method involves the approximation of the observed set of apparent resistivity data by orthogonal polynomials generated by Forsythe's method (Forsythe 1956). Values of the kernel and of the associated kernel obtained by numerical integration compare favourably with the corresponding theoretical values of these functions. 相似文献
4.
A simple unified equation of apparent resistivity for a general four-electrode array is developed. The main idea is the analytical integration of the Stefanescu expression for potential over a layered earth by writing an exponential approximation for the kernel function. Finally a matrix equation is developed to estimate the kernel function from observed apparent resistivity values. The general equation automatically reduces to the particular configuration once the electrode separations are modified suitably. Examples for Schlumberger and Wenner configurations are numerically calculated to estimate the precision of the method. Good results in a short execution time are obtained, irrespective of the shape of the apparent resistivity curve. Finally, the full interpretation of one theoretical resistivity curve and two field resistivity curves is demonstrated. The more stable ridge-regression estimation method is used in the identification of layer parameters from the kernel function. 相似文献
5.
从横向均匀介质满足的基本方程出发,得到视电阻率核函数的一阶非线性微分方程,通过方程求解,并利用滤波系数法容易得到电阻率随深度任意变化的视电阻率问题。当各层介质电性结构随深度呈指数变化时,还可得到各层之间核函数的递推关系,这对实际介质的正反演问题都有重要意义和应用价值。 相似文献
6.
Parts of the consecutive apparent resistivity monitoring stations of China have recorded clear diurnal variations. The relative amplitudes of diurnal variations at these stations range from 1.3‰ to 5.8‰. The daily accuracies of apparent resistivity observation are better than 1‰, because the background electromagnetic noise is rather low at these stations. Therefore, the diurnal variations of apparent resistivity recorded at these stations are real phenomena. The diurnal variation shapes can be divided into two opposite types according to their characteristics. One type is that the apparent resistivity data decreases during the daytime but increases during the nighttime(Type 1). The other type is the apparent resistivity data increases during the daytime but decreases during the nighttime(Type 2). There is a correspondence between the diurnal and annual variation patterns of apparent resistivity. For the monitoring direction with diurnal variation of Type 1, the apparent resistivity decreases in summer and increases in winter. However, for the monitoring direction with diurnal variation of Type 2, the apparent resistivity increases in summer and decreases in winter.
We take an analysis on the mechanism of apparent resistivity diurnal variation, combining the influence factors of water-bearing medium's resistivity, the electric structure of stations, and the apparent resistivity sensitivity coefficient(SC)theory. Intuitively, diurnal variation of apparent resistivity is caused by diurnal variation of medium resistivity in the measured area. The diurnal variation of medium resistivity will inevitably be caused by the factors with diurnal variation. Among the possible factors, there is diural variation in earth tide and temperature.
Our analysis displays that apparent resistivity diurnal variation is not caused by the usually-believed earth tide, but by the ground temperature difference between daytime and nighttime. The earth tide strain is too small to cause remarkable effects on the apparent resistivity data. On the other hand, the daily tide strain has two peak-valley variations, and its phase and amplitude has a period of approximate 28 days. However, the apparent resistivity data do not show these corresponding features to earth tide. Furthermore, the detection range of current apparent resistivity stations is within a depth of several hundred meters. Within this depth range, the medium deformation caused by solid tide can be regarded as uniform change. Therefore, all monitoring directions and all stations will have the same pattern of diurnal variation.
In general, the temperature increases in the daytime but decreases in the nighttime. For most water-bearing rock and soil medium, its resistivity decreases as temperature increases and increases as temperature decreases. Diurnal temperature difference affects about 0.4m of soil depth. Therefore, resistivity of this surface thin soil layer decreases in the daytime while increases in the nighttime. Under layered medium model, SC of each layer represents its contribution to the apparent resistivity. For the stations with positive SC of surface layer, apparent resistivity decreases in the daytime but increases in the nighttime. While for the stations with negative SC of surface layer, apparent resistivity diurnal variations display the opposite shape. 相似文献
7.
RAKESH KUMAR 《Geophysical Prospecting》1974,22(2):224-237
This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940). 相似文献
8.
D. P. GHOSH 《Geophysical Prospecting》1971,19(2):192-217
Koefoed has given practical procedures of obtaining the layer parameters directly from the apparent resistivity sounding measurements by using the raised kernel function H(λ) as the intermediate step. However, it is felt that the first step of his method—namely the derivation of the H curve from the apparent resistivity curve—is relatively lengthy. In this paper a method is proposed of determining the resistivity transform T(λ), a function directly related to H(λ), from the resistivity field curve. It is shown that the apparent resistivity and the resistivity transform functions are linearily related to each other such that the principle of linear electric filter theory could be applied to obtain the latter from the former. Separate sets of filter coefficients have been worked out for the Schlumberger and the Wenner form of field procedures. The practical process of deriving the T curve simply amounts to running a weighted average of the sampled apparent resistivity field data with the pre-determined coefficients. The whole process could be graphically performed within an quarter of an hour with an accuracy of about 2%. 相似文献
9.
O. KOEFOED 《Geophysical Prospecting》1966,14(1):71-79
In a previous paper by the present author a method was developed for direct interpretation of resistivity observations made with a Schlumberger electrode configuration. This method consisted of two steps. The first of these was to derive the kernel function in the integral expression for the apparent resistivity from the observed data; the second step was to derive the resistivity stratification from this kernel function. The first of these two steps depends on the electrode configuration that has been used. In the present paper the above mentioned method is modified so as to make it apply to a Wenner electrode configuration. The procedure is indicated by which the method may be adapted to any other electrode configuration in which the distances between the electrodes are finite. The second step in the interpretation, i.e. the derivation of the resistivity stratification from the kernel function, is independent of the electrode configuration used, and therefore needs no further discussion in the present context. 相似文献
10.
A method to calculate the resistivity transform of Schlumberger VES curves has been developed. It consists in approximating the field apparent resistivity data by utilizing a linear combination of simple functions, which must satisfy the following requirements: (i) they must be suitable for fitting the resistivity data; (ii) once the fitting function has been obtained they allow the kernel to be determined in an analytic way. The fitting operation is carried out by the least mean squares method, which also accomplishes a useful smoothing of the field curve (and therefore a partial noise filtering). It gives the possibility of assigning different weights to the apparent resistivity values to be approximated according to their different reliability. For several examples (theoretical resistivity curves in order to estimate the precision of the method and with field data to verify the practicality) yield good results with short execution time independent of shape the apparent resistivity curve. 相似文献
11.
A method for the automatic inversion of resistivity soundings is presented. The procedure consists of two main stages. First, application of linear filters which transforms the apparent resistivity curve into the kernel function, and vice versa. In the second stage the first and second derivatives of the kernel function are calculated and used in a second-order modified Newton-Raphson iterative fitting procedure. The model obtained is optimal in the least squares sense. The method has been tried on some field examples and produced resistivity models which show a good agreement with the geological well logs. 相似文献
12.
D. P. GHOSH 《Geophysical Prospecting》1971,19(4):769-775
In this paper a fast method is developed for computing apparent resistivity curves for known layer configurations. The method is based on the application of a linear filter to determine the apparent resistivity curve from, the kernel function. 相似文献
13.
地电阻率多极距观测的目的是借助对观测数据的反演获得地下介质中不同层位真电阻率的变化.本文以3层结构为例,对地电阻率多极距观测的一维反演的效果进行了初步地理论研究.首先研究了一维地电阻率结构下观测数据一维反演的模拟效果,得到了各层电阻率值,且与真电阻率值很接近,说明在地下电性结构为一维的情况下,电阻率多极距观测可以区分出不同地层的电阻率变化.其次,考虑到台址下电阻率结构的复杂性,研究了上两层界面存在起伏的情况下,多极距观测数据一维反演的效果,结果显示:当电阻率变化较小时,各层反演得到的电阻率的变化与真电阻率十分符合;当上两层介质的电阻率变化较大时,各层反演得到的电阻率出现畸变,与真实电阻率的变化情况存在一定差别,表明浅层电阻率变化达到一定程度后将会影响对深部电阻率变化情况的正确判断.一般情况下,观测的时间间隔越短,则连续两次观测时段内各层介质的电阻率变化越小,因此缩短多极距观测的时间间隔可能是避免出现上述畸变现象的有效观测手段. 相似文献
14.
EDWARD SZARANIEC 《Geophysical Prospecting》1970,18(1):1-13
Direct interpretation methods of resistivity curves are discussed, which use the kernel function of the apparent resistivity. This function results from the consideration of the problem of diverse electrodes configurations. Several expressions for the determination of the kernel function of the potential from the kernel function of the apparent resistivity are given. 相似文献
15.
HANS A. MEINARDUS 《Geophysical Prospecting》1970,18(3):415-433
The digital computer technique described for interpreting resistivity soundings over a horizontally stratified earth requires two steps. First, the kernel function is evaluated numerically from the inverse Hankel transform of the observed apparent resistivity curve. Special attention is given to the inversion of resistivity data recorded over a section with a resistant basement. The second step consists in the least-squares estimation of layer resistivities and thicknesses from the kernel function. For the case of S or T-equivalent beds only one layer-parameter can be obtained, either the longitudinal conductance, or the transverse resistance respectively. Two examples given in the paper show that a wide tolerance is permitted for Choosing the starting values of the layering parameters in the successive approximation procedure. Another important feature for practical applications is good convergence of the iterations. The method is probably best suited for interpreting profiles of electrical soundings with the purpose of mapping approximately horizontal interfaces at depth. 相似文献
16.
A. T. BASOKUR 《Geophysical Prospecting》1984,32(6):1131-1146
A numerical method is presented for direct interpretation of resistivity sounding measurements. The early part of the resistivity transform curve derived from field observations by standard methods is approximated by a two-layer curve. The resistivity of the first layer is determined from the arithmetic mean of the successive computations which are carried on each of three successive discrete values of the resistivity transform curve. Using this mean value of the resistivity, the thickness of the first layer is computed from the sample values in pairs of the resistivity transform curve. After these determinations, the top layer is removed by Pekeris's reduction equation. The parameters of the second layer are obtained from the discrete values of the reduced transform curve (which corresponds to the second part of the resistivity transform curve) by the same procedure as described for the first layer. The same computational scheme is repeated until the parameters of all intermediate layers are obtained. The resistivity of the substratum is determined from the reduction equation. 相似文献
17.
The temporal variation in a soil moisture profile can be studied using resistivity sounding data acquired at different times. The layered earth model based estimation of soil moisture from apparent resistivity data is a two-step non-linear inversion. Firstly, the apparent resistivity data are inverted to derive the layer resistivity variations and thicknesses and, secondly, the moisture content is estimated from these layer resistivity variations using a calibration equation. The soil moisture–resistivity problem was studied using the one-dimensional formulation of resistivity problem. A generalized geoelectric earth model was considered to simulate the soil moisture distribution and its temporal variation in the unsaturated zone. An algorithm (RESMOS) for the interpretation of the apparent resistivity data in terms of soil moisture variations through this two-step inversion process is reported. 相似文献
18.
本文针对多辐射场源地空瞬变电磁法理论,建立了相应的多分量全域视电阻率定义方法.分析了利用磁场强度进行多辐射场源地空系统全域视电阻率定义的优点,针对磁场强度的各个分量,提出了各自的全域视电阻率算法,实现了多分量、全时域、全空域视电阻率计算,并分析了偏移距对全域视电阻率的影响.通过调整源的相对位置及电流方向等参数,多辐射源瞬变电磁地空系统不仅可以加强不同分量信号强度,削弱随机干扰,还可更好地分辨地下异常体的位置.通过对所设计模型的处理,证实了多辐射场源地空系统多分量全域视电阻率算法的有效性,也验证了多辐射场源地空系统的优势. 相似文献
19.
本文根据视电阻率定义的原则,以及用不同的场量定义的视电阻率效果不同这一事实,提出一种新的全波视电阻率定义.在全区同时用均匀大地上电磁场的三个分量来分区定义祝电阻率.在远区视电阻率由磁场的水平分量求出,在近区由磁场的垂直分量或其实分量定义,而在过渡区则由电场的水平分量确定.用这种方法定义的视电阻率为电磁响应的单值函数,它随频率变化的曲线显著改善,能直观地反映地层电阻率随深度的变化,数值比较接近地层的真电阻率值,假极值效应明显压低.在计算中用切比雪夫多项式分段拟合均匀大地电磁响应的反函数,并给出一套系数,由此算出的视电阻率误差小于1％. 相似文献
20.
本文研究了三层介质中膨胀球模拟震源的应力、应变场以及由这个应力、应变场产生的电阻率变化量和地表视电阻率变化的关系。结果表明,对于一定强度的“震源”,在地电装置探测范围内的应力场随具有不同弹性参数的层位有显著的变化;而应变场却看不出有明显的突变;由地表视电阻率变化量的计算结果揭示了地电异常受台站介质电性结构与力学结构的综合影响。因此作为预报地震的地电阻率法一方面要寻找具有高电阻率——应变灵敏度岩层的台址,另一方面台址的视电阻率变化对各层真电阻率变化要具有好的响应。 相似文献