A fast technique for the inversion of data from resistivity tomography surveys has been developed. This technique is based on the smoothness‐constrained, least‐squares method, and it produces a 2-D subsurface model that is free of distortions in the apparent resistivity pseudosection caused by the electrode array geometry used. A homogeneous earth model is used as the starting model for which the apparent resistivity partial derivative values can be calculated analytically. Tests with a variety of models and data from field surveys show that this technique is insensitive to random noise, provided a sufficiently large damping factor is used, and that it can resolve structures that cause overlapping anomalies in the pseudosection. On a 33 MHz 80486DX microcomputer, it takes about 5 s to process a single data set.

This paper is a philosophical exploration of adaptive pattern recognition paradigms for geophysical data inversion, aimed at overcoming many of the problems faced by current inversion methods. APR (adaptive pattern recognition) methods are based upon encoding exemplar patterns in such a way that their features can be used to classify subsequent test patterns. These paradigms are adaptive in that they learn from experience and are capable of inferring rules to deal with incomplete data. APR paradigms can also be highly effective in dealing with noise and other data distortions through the use of exemplars which characterize such distortions. Rather than merely seeking to reduce the point by point mismatch between data and model curves, effective APR paradigms would match patterns by establishing a feature vocabulary and inferring rules to weight the relative importance of these features in interpreting data. They have the advantage that prototype data sets can include analogue modelling data and field survey data rather than being restricted to models for which a numerical forward model can be calculated. The success of this approach to inversion will depend upon the effectiveness of replacing continuous parameter estimation with microclassification (discretized parameter estimation). Once the viability of APR schemes has been established for inverting data from individual geophysical methods, the task of joint interpretation of data from different geophysical survey methods could be accomplished in an optimum fashion by using hierarchical adaptive schemes.

Artificial neural systems have been used in a variety of problems in the fields of science and engineering. Here we describe a study of the applicability of neural networks to solving some geophysical inverse problems. In particular, we study the problem of obtaining formation resistivities and layer thicknesses from vertical electrical sounding (VES) data and that of obtaining 1D velocity models from seismic waveform data. We use a two‐layer feedforward neural network (FNN) that is trained to predict earth models from measured data. Part of the interest in using FNNs for geophysical inversion is that they are adaptive systems that perform a non‐linear mapping between two sets of data from a given domain. In both of our applications, we train FNNs using synthetic data as input to the networks and a layer parametrization of the models as the network output. The earth models used for network training are drawn from an ensemble of random models within some prespecified parameter limits. For network training we use the back‐propagation algorithm and a hybrid back‐propagation–simulated‐annealing method for the VES and seismic inverse problems, respectively. Other fundamental issues for obtaining accurate model parameter estimates using trained FNNs are the size of the training data, the network configuration, the description of the data and the model parametrization. Our simulations indicate that FNNs, if adequately trained, produce reasonably accurate earth models when observed data are input to the FNNs.

The inversion of geoelectrical resistivity data is a difficult task due to its non‐linear nature. In this work, the neural network (NN) approach is studied to solve both 1D and 2D resistivity inverse problems. The efficiency of a widespread, supervised training network, the back‐propagation technique and its applicability to the resistivity problem, is investigated. Several NN paradigms have been tried on a basis of trial‐and‐error for two types of data set. In the 1D problem, the batch back‐propagation paradigm was efficient while another paradigm, called resilient propagation, was used in the 2D problem. The network was trained with synthetic examples and tested on another set of synthetic data as well as on the field data. The neural network gave a result highly correlated with that of conventional serial algorithms. It proved to be a fast, accurate and objective method for depth and resistivity estimation of both 1D and 2D DC resistivity data. The main advantage of using NN for resistivity inversion is that once the network has been trained it can perform the inversion of any vertical electrical sounding data set very rapidly.

. Koyna region is well-known for its triggered seismic activities since the hazardous earthquake of M=6.3 occurred around the Koyna reservoir on 10 December 1967. Understanding the shallow distribution of resistivity pattern in such a seismically critical area is vital for mapping faults, fractures and lineaments. However, deducing true resistivity distribution from the apparent resistivity data lacks precise information due to intrinsic non-linearity in the data structures. Here we present a new technique based on the Bayesian neural network (BNN) theory using the concept of Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) simulation scheme. The new method is applied to invert one and two-dimensional Direct Current (DC) vertical electrical sounding (VES) data acquired around the Koyna region in India. Prior to apply the method on actual resistivity data, the new method was tested for simulating synthetic signal. In this approach the objective/cost function is optimized following the Hybrid Monte Carlo (HMC)/Markov Chain Monte Carlo (MCMC) sampling based algorithm and each trajectory was updated by approximating the Hamiltonian differential equations through a leapfrog discretization scheme. The stability of the new inversion technique was tested in presence of correlated red noise and uncertainty of the result was estimated using the BNN code. The estimated true resistivity distribution was compared with the results of singular value decomposition (SVD)-based conventional resistivity inversion results. Comparative results based on the HMC-based Bayesian Neural Network are in good agreement with the existing model results, however in some cases, it also provides more detail and precise results, which appears to be justified with local geological and structural details. The new BNN approach based on HMC is faster and proved to be a promising inversion scheme to interpret complex and non-linear resistivity problems. The HMC-based BNN results are quite useful for the interpretation of fractures and lineaments in seismically active region.\n

为满足地球物理资料反演解释的高精度、快速、稳定的要求，本文结合免疫遗传算法寻优速度快和BP神经网络反演不依赖初始模型等优点，设计了一种将BP神经网络和免疫遗传算法进行有机结合的全局优化反演策略，并将该策略成功地应用于二维高密度电法数据反演.利用免疫遗传算法（Immune Genetic Algorithm，简称IGA）对神经网络的反演参数进行同步优化，提高了电阻率反演的精度.仿真和实验结果验证设计的全局优化反演策略取得了较好的效果，通过与线性反演方法和BP法以及遗传神经网络法等反演方法进行比较，得出该方法具有反演精度更高，反演时间更短等显著优势的结论.

In recent years, electrical tomography, namely, electrical resistance tomography (ERT), has emerged as a viable approach to detecting, localizing and reconstructing structural cracking patterns in concrete structures. High-fidelity ERT reconstructions, however, often require computationally expensive optimization regimes and complex constraining and regularization schemes, which impedes pragmatic implementation in Structural Health Monitoring frameworks. To address this challenge, this article proposes the use of predictive deep neural networks to directly and rapidly solve an analogous ERT inverse problem. Specifically, the use of cross-entropy loss is used in optimizing networks forming a nonlinear mapping from ERT voltage measurements to binary probabilistic spatial crack distributions (cracked/not cracked). In this effort, artificial neural networks and convolutional neural networks are first trained using simulated electrical data. Following, the feasibility of the predictive networks is tested and affirmed using experimental and simulated data considering flexural and shear cracking patterns observed from reinforced concrete elements.

It is well known that the addition of noise to the input data of a neural network during training can, in some circumstances, lead to significant improvements in generalization performance. Previous work has shown that such training with noise is equivalent to a form of regularization in which an extra term is added to the error function. However, the regularization term, which involves second derivatives of the error function, is not bounded below, and so can lead to difficulties if used directly in a learning algorithm based on error minimization. In this paper we show that for the purposes of network training, the regularization term can be reduced to a positive semi-definite form that involves only first derivatives of the network mapping. For a sum-of-squares error function, the regularization term belongs to the class of generalized Tikhonov regularizers. Direct minimization of the regularized error function provides a practical alternative to training with noise.

We study the effects of adding noise to the inputs, outputs, weight connections, and weight changes of multilayer feedforward neural networks during backpropagation training. We rigorously derive and analyze the objective functions that are minimized by the noise-affected training processes. We show that input noise and weight noise encourage the neural-network output to be a smooth function of the input or its weights, respectively. In the weak-noise limit, noise added to the output of the neural networks only changes the objective function by a constant. Hence, it cannot improve generalization. Input noise introduces penalty terms in the objective function that are related to, but distinct from, those found in the regularization approaches. Simulations have been performed on a regression and a classification problem to further substantiate our analysis. Input noise is found to be effective in improving the generalization performance for both problems. However, weight noise is found to be effective in improving the generalization performance only for the classification problem. Other forms of noise have practically no effect on generalization.