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1.
The paper discusses the smallest obtainable parameter errors (variances) in the interpretation with the least-squares method. Useful approximations of the sum of squares contained in the minimum error expressions are obtained using results of numerical integration. The approximations lead to especially simple results for long interpretation profiles, when the parameter errors are proportional to the square root of the point separation. Formulae are developed and examples shown for minimum error calculation in gravimetric interpretation with the cylindrical model and in magnetic interpretation with the two-dimensional plate model. Smallest errors are obtained when the interpretation profile is chosen around the anomaly maximum except for dip and depth extent interpretation of magnetic plates.  相似文献   

2.
Relative and cumulative analytical response functions have been widely used as a powerful tool for forward modelling and interpretation of measurements obtained by electromagnetic induction conductivity meters operating at low induction numbers for one‐dimensional layered earth models. These well‐known functions were derived and should be used for the instruments laid on the surface of the earth. In this paper, we extended the response functions and obtained new generalised analytical expressions, which can be used for instruments carried at any height from the surface. The proposed new equations were compared with numerically constructed functions, obtained using the full solution of Maxwell's equations, and proved to be in very good agreement at low induction numbers. Quantitative analyses of the behaviour of the relative response and the depth of investigation of electromagnetic induction instruments, when raised from the ground, could also be done using the generalised functions.  相似文献   

3.
The magnetic anomaly due to a uniformly magnetized vertical rectangular prism and that due to an arbitrary structure which can be divided into a number of such prisms are expressed in forms suitable for rapid computation. Both two-dimensional and three-dimensional cases are considered. The simplified expressions will find use in interpretation techniques where repeated computations have to be made of the anomaly due to prisms as in automated fitting of prism anomalies to observed magnetic anomalies using non-linear optimization techniques or related methods.  相似文献   

4.
An important aspect of any non-linear inversion method is the generation of a suitable or good initial model as this controls the rate of convergence and accuracy of the result. To overcome the problem, a numerical method is presented for direct interpretation of magnetotelluric sounding data based on the frequency-normalized impedance (FNI) function. The expressions used to calculate the parameters are developed, first for a two-layer case under the assumption that deeper layers do not contribute to the early part of the FNI curve, and they are then generalized for an n -layer situation. The parameters of the first layer are computed by using successive sample values and the final estimate is obtained from the arithmetic mean of selected values by excluding unacceptable results in the logarithmic space. The top layer is then removed using a reduction equation. The repetition of the procedure on successive branches of the FNI function gives successive layer parameters, the resistivity of the substratum being obtained at the final step, when the reduction equation becomes equal to the square root of that resistivity.   The proposed method can be used as a complementary method for iterative inversion as it creates an initial guess which is close to the optimal solution. The solution produced by the direct interpretation may also be modified by the interpreter to incorporate prior geological information before being input to iterative interpretation schemes.  相似文献   

5.
海底表面磁源瞬变响应建模及海水影响分析   总被引：11，自引：4，他引：7       下载免费PDF全文
刘长胜  林君 《地球物理学报》2006,49(6):1891-1898
根据电磁场理论,推导了磁偶源和接收点均位于海水中时层状海底模型的频域电磁场响应一般表达式,并通过此式,得到了海水为均匀半空间和有限海水深度两种情况下,垂直磁偶极装置、中心回线和重叠回线分别置于均匀半空间海底表面时的瞬变电磁响应（磁场和感应电压）表达式. 这些表达式将瞬变响应和海底的电导率等参数有机联系在一起,为海底瞬变电磁法的正演计算和反演解释提供了理论基础. 仿真计算表明,海水的存在不仅使得瞬变响应曲线形态发生变化,而且影响其对海底电导率的分辨能力.  相似文献   

6.
Book review     

This paper gives the expressions for the synoptic scale thermal winds when a full Coriolis force is considered. The atmosphere is assumed stratified with a steady density profile. It is also argued that the resulting expressions can be applied to atmospheric temperature maps obtained by standard infrared methods only if approximations are made. This paper augments the interpretation of the results obtained in a previous paper by the author and addresses comments made by J.-I. Yano in another paper of this journal.  相似文献   

7.
The existing expressions of elastic impedance,as the generalized form of acoustic impedance,represent the resistance of subsurface media to seismic waves of non-normal incidence,and thus include information on the shear-wave velocity.In this sense,conventional elastic impedance is an attribute of the seismic reflection and not an intrinsic physical property of the subsurface media.The derivation of these expressions shares the approximations made for reflectivity,such as weak impedance contrast andisotropic or weakly anisotropic media,which limits the accuracy of reflectivity reconstruction and seismic inversion.In this paper,we derive exact elastic impedance tensors of seismic P-and S-waves for isotropic media based on the stress-velocity law.Each componentof the impedance tensor represents a unique mechanical property of the medium.Approximations of P-wave elastic impedance tensor components are discussed for seismic inversion and interpretation.Application to synthetic data and real data shows the accuracy and robust interpretation capability of the derived elastic impedance in lithology characterizations.  相似文献   

8.
Matrix equations are derived to transform the resistivity sounding data obtained in one type of a four-electrode array to the corresponding resistivity sounding data that would be obtained using a different four-electrode array. These expressions are based primarily on recent work in which we have established a linear relation between the apparent resistivity and the kernel function by using a powerful exponential approximation for the kernel function. It is shown that the resistivity sounding data of two different four-electrode arrays have a linear relation through an essentially non-singular matrix operator and, as such, one is derivable from the other for a one-dimensional model and it can also be extended to two-dimensions. Some numerical examples considering synthetic data are presented which demonstrates the efficiency of the method in such transformations. Two published field examples are also considered for transformation giving a reliable interpretation.  相似文献   

9.
A model has been set up for the interpretation of geoelectrical sounding data for certain kinds of clay deposits containing gradually varying amounts of sand. The model assumes that in the so-called gradient layer, resistivity varies linearly with depth. Model calculations show how such a layer can be replaced by two homogeneous layers. An inversion procedure using the Marquardt algorithm has been developed for the interpretation of sounding data obtained with the Schlumberger array; it assumes a gradient layer beneath several covering layers. The procedure is demonstrated on two clay deposits. A comparison is made between the newly developed interpretation, the traditional approach using model curves, and computerized inversion for a homogeneous layer model.  相似文献   

10.
The voluminous gravity and magnetic data sets demand automatic interpretation techniques like Naudy, Euler and Werner deconvolution. Of these techniques, the Euler deconvolution has become a popular choice because the method assumes no particular geological model. However, the conventional approach to solving Euler equation requires tentative values of the structural index preventing it from being fully automatic and assumes a constant background that can be easily violated if the singular points are close to each other. We propose a possible solution to these problems by simultaneously estimating the source location, depth and structural index assuming nonlinear background. The Euler equation is solved in a nonlinear fashion using the optimization technique like conjugate gradient. This technique is applied to a published synthetic data set where the magnetic anomalies were modeled for a complex assemblage of simple magnetic bodies. The results for close by singular points are superior to those obtained by assuming linear background. We also applied the technique to a magnetic data set collected along the western continental margin of India. The results are in agreement with the regional magnetic interpretation and the bathymetric expressions.  相似文献   

11.
Summary The author proposes a new technique of magnetic interpretation in the case of a two-dimensional model, whereby six analytical expressions are deduced and computed forDH, DZ, PHB, PZB, AHB andAZB. These expressions denote the induced part of magnetic anomaly inH component, the induced part of anomaly inZ component, the permanent magnetization part ofH anomaly, the permanent magnetization part ofZ anomaly, the sum (DH+PHB), and the sum (DZ+PZB), respectively. The use of a series of these six curves taken together instead of the single profile curve, will improve the existing method of magnetic interpretation, reduce the uncertainties of the inverse problem, and provide a valuable tool for paleomagnetic studies of in situ older rocks commonly found in equatorial Africa. The resulting advantages outweigh the apparent increase in computation. This technique was applied to a field profile obtained across a subsurface dolerite vein, and the results agree with the theoretical predictions outlined.  相似文献   

12.
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   

13.
用地震反射波定量解释煤层厚度的方法   总被引：6，自引：0，他引：6  
一、引言 工业可采煤层厚度一般为1.5m,如何从地震资料上准确圈定1m厚的煤层边界、并定量解释煤层厚度、准确计算地质储量,国外一些学者研究了薄层地震反射波的动力学特征与薄层厚度的关系后,得出了不同的薄层垂直分辨率标准,Widess用零相位子波作实验时,发现当薄层厚度为λ/8(λ是地震子波的主波长)时,反射波形正好是入射波的导数,并可直观地鉴别顶底反射;Kallweit利用可控震源研究了薄层响应的频谱后,提出了分辨地震波的极限为1/(1.4f)(f为地震子波的上限频率),经主频换算后,此  相似文献   

14.
The fact that the geomagnetic potential, as well as magnetic induction and its gradient, can be represented with an arbitrary accuracy in the scope of multipole models has been justified programmatically and analytically. The obtained expressions are brief and can be utilized in analytical and computer-based studies using methods of computer algebra and numerical computations. Previously unknown analytical expressions for the components of the first seven multipole tensors, expressed in terms of the Gaussian coefficients, have been obtained for applied problems of space dynamics. An algorithm that makes it possible to construct analytical expressions for the arbitrary-order multipole tensor and magnetic induction vector components in any finite approximation has been developed.  相似文献   

15.
In this paper, the expressions for the induced voltage function V(T) and mutual impedance function Zm(T) have been derived for specific range of time T and specific values of induced polarization parameters a for ramp and saw-tooth type of current pulses. The computed results for various cases are also presented. The low values of induced polarization parameter a represent the medium possessing membrane polarization, whereas high values exhibit electrode polarization medium. The method has practical applicability and is best suited for the interpretation of transient electromagnetic fields over a polarizable half-space.  相似文献   

16.
A detailed analysis of the electromagnetic anomaly due to an elongated mineralized zone of low resistivity in presence of a fixed-transmitter (a long cable carrying an, alternating current IeIωt) is presented where (i) the host rock is not highly resistive and might contain some disseminated mineralization, (ii) the ore-body has an inhomogeneous conductivity, (iii) there is a contrast in magnetic properties of the ore-body and the host rocks, and (iv) source is close to the conducting system i.e., anomalous zone is lying shallow. The numerical computation of the generalized analytical expressions have been made. The selective screening behaviour of the cover is delineated and suitable frequency ranges for maximum detectability of a covered conductor have been obtained. A paradoxical decrease of the in-phase component of the response function with the increase of the core conductivity has been found for large conductivities of the cover. For moderate values of response parameter the inhomogeneity in the conductivity is found to significantly affect the induced field. The present analysis of the various features of the secondary field will aid to the existing interpretation sensitivity of the induction prospecting data for porphyry conducting ore deposits with zonal wall-rock alteration and sulphide distributions.  相似文献   

17.
The tools used in digital processsing have received little application, to date, to refraction seismic. It seems however that some problems encountered in the analysis of refraction records could be solved through techniques which are of common use in processing of reflection seismic data (correlation, stacking, f and k filtering). The experiments made with some of these techniques revealed the possibility of a more complete refraction record analysis, allowing the study of later arrivals. The interpretation of these records could also, to a fairly large extent, be automated by means of digital processing. While recording, some care ought to be taken to allow identification and interpretation by digital processing of as many events as possible. However, the results shown here have been obtained from fairly old analog records, for which no particular care had been taken, which makes it possible to complete and revise the interpretation of previous studies using the same processing techniques. Long line refraction shooting is justified for marine surveys in some areas, particularly where reflection is disturbed by singing; improvements in analysis and interpretation would therefore prove very useful for a faster and more thorough interpretation.  相似文献   

18.
Summary An algorithm, suitable for digital computer application, has been developed for rapid gravity interpretation of sedimentary basin. A discrete linear variable density contrast pattern over the constant density contrast has been preferred to obtain the structural configuration of the basin. The present algorithm, with slight modification, can be used for calculation of isostatic root increment below the mountain. An interpretation of the structure of Godavari Valley, India has been made using this algorithm.  相似文献   

19.
Summary The electromagnetic equations of Maxwell as well as the equations of fluid dynamics have been used to investigate the hydromagnetic flow due to the transient motion of a plane. The expressions for the velocity and skin-friction have been derived for small values of time by using Laplace transform techniques.  相似文献   

20.
The solution of a boundary value problem modelling a two-dimensional basin structure has been obtained by using the Schwartz-Christoffel conformal transformation technique and numerical methods of solving non-linear differential equations. Utilizing this solution, the telluric field and its first horizontal derivative have been theoretically computed for field directions perpendicular to the strike of the structure. On the basis of systematic analysis of a large number of such anomaly curves, two nomograms have been prepared to be used in the quantitative interpretation of telluric data. An interpretation procedure to evaluate the geometric parameters of the basin from the observed telluric data is outlined. This procedure is demonstrated on an actual field example.  相似文献   

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