Interpretation of self-potential anomalies of some simple geometric bodies

Summary An entirely new procedure for interpreting selfpotential anomalies of spheres, rods and dipping sheets is presented. The anomaly of a sphere is divided into two parts — the anomaly of odd symmetry and the anomaly of even symmetry — from which the depth can be obtained by fitting them with the master curves. The self-potential anomalies of a finite rod are transformed to the anomalies of a veritcal sheet, for which standard curves are presented. The case of a sheet was divided into three parts; (a) finite line of poles; (b) infinite double line of poles and (c) finite double line of poles. For the first case logarithmic curves were prepared and presented; by their comparison with the field profile, different parameters can be obtained. In the second case, a geometrical construction is provided to obtain the various values. In the third case, the anomalies of finite sheet (finite double line of poles) are transformed into those due to an infinite double line of poles for interpretation.     

概率神经网络技术在煤田地震反演中的应用研究

实现从构造勘探向岩性勘探阶段的转变,是煤田地震勘探亟待解决的重要问题。其中,地震反演技术是岩性勘探的一种重要手段。为了规避常规反演方法的固有限制,利用概率神经网络技术预测井数据和地震数据之间的非线性关系,得到密度数据体和速度数据体,并获得相应的波阻抗数据体。对某矿区的实际地震资料采用该技术进行岩性反演,得到了较为准确的波阻抗数据体,为岩性解释提供了不可或缺的资料。     

Quantitative interpretation of self potential anomalies of some specific geometric bodies

Summary Some direct and quantitative methods of SP anomalies caused by some specific geometric bodies have been developed in this paper. The models of current sources which have been considered are i) single pole, ii) a doublet, iii) a pair of single point poles separated by a horizontal distance, iv) single finite line pole, v) single infinite line pole and vi) two similar double infinite vertical line poles separated by a horizontal distance.     

Inversion of gravity and magnetic anomalies over some bodies of simple geometric shape

The general expression for gravity and magnetic anomalies over thin sheets and sloping contacts may be expressed as a polynomial of the formFx ²+C₁Fx+C₂F+C₃x³+C₄x²+C₅x+C₆. The initial parameters of the source are obtained from the coefficientsC ₁, C₂,..., C₆ which may be solved by inverting a 6×6 matrix. The initial parameters are modified by successive iteration process using the difference formula until the root mean square error between the observed and calculated anomalies is a minimum. The regional background which may be in the form of a polynomial is estimated by the computer itself. This method is applied on a number of field anomalies and is found to yield reliable estimates of depth and other parameters of the source.     

电阻率二维神经网络反演

由于非线性特性地球物理反演一直以来都是一个比较困难的问题. 近十年来,非线性反演方法如人工神经网络、遗传算法在地球物理数据解释中得到越来越多的应用,但目前基本仍限于一维反演问题. 对于二维反问题,反演参数较多,神经网络反演运用较少. 本文利用BP神经网络优化方法,实现了电阻率二维非线性反演. 与传统线性化的迭代反演比较,神经网络反演能够克服传统方法的不足、获得更好的反演结果.     

Analysis of magnetic anomalies due to some two-dimensional bodies using the Mellin transform

An interpretation technique using the Mellin transform is suggested for the analysis of magnetic anomalies due to some two-dimensional structures namely (i) a vertical sheet of both finite and infinite depth extent, (ii) a thick dyke and (iii) a horizontal circular cylinder. The Mellin transformed magnetic anomalies resemble gamma functions which are amenable to an easy interpretation. This procedure is illustrated with a small number of synthetic examples in each case. The practicality of the method is exemplified with the well-known vertical magnetic anomalies of Kursk (USSR) in the case of an infinite sheet model and Karimnagar magnetic anomaly (India) in the case of a horizontal circular cylinder. The results are compared with the techniques already available and found to be reliable.     

3-D inversion of borehole-to-surface electrical data using a back-propagation neural network

The “fluid-flow tomography”, an advanced technique for geoelectrical survey based on the conventional mise-à-la-masse measurement, has been developed by Exploration Geophysics Laboratory at the Kyushu University. This technique is proposed to monitor fluid-flow behavior during water injection and production in a geothermal field. However data processing of this technique is very costly. In this light, this paper will discuss the solution to cost reduction by applying a neural network in the data processing. A case study in the Takigami geothermal field in Japan will be used to illustrate this. The achieved neural network in this case study is three-layered and feed-forward. The most successful learning algorithm in this network is the Resilient Propagation (RPROP). Consequently, the study advances the pragmatism of the “fluid-flow tomography” technique which can be widely used for geothermal fields. Accuracy of the solution is then verified by using root mean square (RMS) misfit error as an indicator.     

Characteristic curves for the inversion of magnetic anomalies of spherical ore bodies

Characteristic curves are presented for interpreting vertical and total components of the anomalous magnetic field caused by spherical ore bodies. The curves use characteristic distances which are easy to measure on an anomaly profile. The method is fast, and does not require prior knowledge of the base level or the origin. Inversion with the characteristic curves is demonstrated on two field examples and the curves computed for the estimated parameters match well the field curves.     

Interpretation of gravity and magnetic anomalies caused due to spherical bodies

Summary The method of continuation has been used to obtain the master curves for gravity and magnetic anomalies caused by spherical bodies. The procedure to calculate the depth of burial and radius of spherical bodies has been outlined.     

人工神经网络系统在接收函数反演中的应用

为使接收函数的反演更为简便,本文提出了一种基于人工神经网络误差反传(BP)算法的接收函数反演新方法,该方法采用人工神经网络反演系统,避免了接收函数反演过程中复杂的地震响应计算及耗时的雅可比矩阵计算,只需经过学习训练就能够解决复杂的实际问题,而且具有记忆功能,这使接收函数的反演工作具有延续性和可继承性.理论数据的反演计算结果表明,该方法是切实可行的.     

Walsh spectra of gravity anomalies over some simple sources

Walsh transform of gravity anomalies over a point mass, a horizontal and a vertical line mass have been computed to obtain a cyclic shift invariant differential energy density (DED) function. Quantitative relations between DED spectral characteristics with depth to centroid/top of the source have been established. The effects of profile length, sampling interval, random noise and zero padding have been investigated. Applicability of the proposed method has been evaluated through two field examples.     

Interpretations of self potential anomalies due to localised causative bodies

Summary Some direct methods of interpretation of SP anomalies that may arise from localised causative bodies have been developed in this paper. The models of the current sources that have been considered here are the cases of 1. single vertical dipole, 2. a pair of similar and similarly situated vertical dipoles and 3. an inclined dipole. A set of three master curves has been prepared in terms of which the interpretation in the first and the third case is complete. With an additional assumption that the distance between the dipoles is small, the second case also is completely solved with the help of the same set of master curves.Published under the kind permission of the Director General, Geological Survey of India, Calcutta.     

Interpretation of magnetic anomalies using a genetic algorithm

A genetic algorithm (GA) is an artificial intelligence method used for optimization. We applied a GA to the inversion of magnetic anomalies over a thick dike. Inversion of nonlinear geophysical problems using a GA has advantages because it does not require model gradients or well-defined initial model parameters. The evolution process consists of selection, crossover, and mutation genetic operators that look for the best fit to the observed data and a solution consisting of plausible compact sources. The efficiency of a GA on both synthetic and real magnetic anomalies of dikes by estimating model parameters, such as depth to the top of the dike (H), the half-width of the dike (B), the distance from the origin to the reference point (D), the dip of the thick dike (δ), and the susceptibility contrast (k), has been shown. For the synthetic anomaly case, it has been considered for both noise-free and noisy magnetic data. In the real case, the vertical magnetic anomaly from the Pima copper mine in Arizona, USA, and the vertical magnetic anomaly in the Bayburt–Sar?han skarn zone in northeastern Turkey have been inverted and interpreted. We compared the estimated parameters with the results of conventional inversion methods used in previous studies. We can conclude that the GA method used in this study is a useful tool for evaluating magnetic anomalies for dike models.     

基于BP神经网络的波阻抗反演及应用

人工神经网络是近期发展最快的人工智能领域研究成果之一.本文在介绍BP神经网络的有关原理的基础上,提出一种基于BP神经网络模型的波阻抗反演方法,该方法克服了常规基于模型的波阻抗反演方法严重依赖于初始模型的选择和易陷入局部最优等局限性.利用该方法对实际地震剖面进行了波阻抗参数反演处理,结果表明人工神经网络方法在波阻抗反演中的应用是可行的并且是有效的.     

Interpretation of magnetic anomalies of dikes using correlation factors

The magnetic anomaly due to a buried dike consists of the sum of two easily separated elementary functions. These functions, which have simple symmetry, are called even and odd functions. The correlation factors (r _0,1 for the even andr _0,2 for the odd function) between least-squares residual anomalies from even and odd functions are computed. Correlation values are used to determine the depth to the top and the half-width of the dike. The method also includes the determination of the index parameter and the amplitude coefficient. The validity of the method is tested against a theoretical and a field example where the parameters of the latter were determined by other investigators in comparing the results.     

Non-linear inversion of resistivity profiling data for some regular geometrical bodies1

The inversion of resistivity profiling data involves estimation of the spatial distribution of resistivities and thicknesses of rock layers from the apparent resistivity data values measured in the field as a function of electrode separation. The drawbacks of using traditional curve-matching techniques to solve this inverse problem have been overcome by iterative linear techniques but these require good starting models even if the shape of the causative body is asssumed known. In spite of the recent developments in inversion techniques, no robust method exists for the inversion of resistivity profiling data for the simple model of dikes and spheres which are the classical models of geophysical prospecting. We apply three different non-linear inversion schemes to invert synthetic resistivity profiling data for the classical models embedded in a uniform matrix of contrasting resistivity. The three non-linear algorithms used are called the Metropolis simulated annealing (SA), very fast simulated annealing (VFSA) and a genetic algorithm (GA). We compare the performance of the three algorithms using synthetic data for an outcropping vertical dike model. Although all three methods were successful in obtaining optimal solutions for arbitrary starting models, VFSA proved to be computationally the most efficient.     

Artificial neural network forward modelling and inversion of electrokinetic logging data

An artificial neural network method is proposed as a computationally economic alternative to numerical simulation by the Biot theory for predicting borehole seismoelectric measurements given a set of formation properties. Borehole seismoelectric measurements are simulated using a finite element forward model, which solves the Biot equations together with an equation for the streaming potential. The results show that the neural network method successfully predicts the streaming potentials at each detector, even when the input pressures are contaminated with 10% Gaussian noise. A fast inversion methodology is subsequently developed in order to predict subsurface material properties such as porosity and permeability from streaming potential measurements. The predicted permeability and porosity results indicate that the method predictions are more accurate for the permeability predictions, with the inverted permeabilities being in excellent agreement with the actual permeabilities. This approach was finally verified by using data from a field experiment. The predicted permeability results seem to predict the basic trends in permeabilities from a packer test. As expected from synthetic results, the predicted porosity is less accurate. Investigations are also carried out to predict the zeta potential. The predicted zeta potentials are in agreement with values obtained through experimental self potential measurements.     

Prediction of variations from Polar Cap indices using time-delay neural network

The hourly averaged Polar Cap (PC) index was used as the input parameter for the ring current index D_st variation forecasting. The PC index is known to describe well the principal features of the interplanetary magnetic field as well as the total energy input to the magnetosphere. This allowed us to design a neural network that was able to forecast the D_st variations 1 h ahead. 1995 PC and D_st data sets were used for training and testing and 1997 data sets were used for validation. From 15 moderate and strong geomagnetic storms observed during 1997, 10 were successfully forecasted. In 3 cases the observed minimum D_st value was less than the predicted value, and only in 3 cases the neural network was not able to reproduce the features of the geomagnetic storm.     

3D inversion of DC data using artificial neural networks

In this paper, we investigate the applicability of artificial neural networks in inverting three-dimensional DC resistivity imaging data. The model used to produce synthetic data for training the artificial neural network (ANN) system was a homogeneous medium of resistivity 100 Ωm with an embedded anomalous body of resistivity 1000 Ωm. The different sizes for anomalous body were selected and their location was changed to different positions within the homogeneous model mesh elements. The 3D data set was generated using a finite element forward modeling code through standard 3D modeling software. We investigated different learning paradigms in the training process of the neural network. Resilient propagation was more efficient than any other paradigm. We studied the effect of the data type used on neural network inversion and found that the use of location and the apparent resistivity of data points as the input and corresponding true resistivity as the output of networks produces satisfactory results. We also investigated the effect of the training data pool volume on the inversion properties. We created several synthetic data sets to study the interpolation and extrapolation properties of the ANN. The range of 100–1000 Ωm was divided into six resistivity values as the background resistivity and different resistivity values were also used for the anomalous body. Results from numerous neural network tests indicate that the neural network possesses sufficient interpolation and extrapolation abilities with the selected volume of training data. The trained network was also applied on a real field dataset, collected by a pole-pole array using a square grid (8 ×8) with a 2-m electrode spacing. The inversion results demonstrate that the trained network was able to invert three-dimensional electrical resistivity imaging data. The interpreted results of neural network also agree with the known information about the investigation area.     

Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks

Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α _k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.