Inversion of DC resistivity data using neural networks

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.     

Automatic 1D inversion of multifrequency airborne electromagnetic data with artificial neural networks: discussion and a case study

Artificial neural networks were used to implement an automatic inversion of frequency‐domain airborne electromagnetic (AEM) data that do not require a priori information about the survey area. Two classes of model, i.e. homogeneous half‐space models and horizontally layered half‐space models with two layers, are used in this 1D inversion, and for each data point the selection of the class of 1D model is performed prior to the inversion, also using an artificial neural network. The proposed inversion method was tested in a survey area situated in Austria, northwest of Vienna in the Bohemian Massif. The results of the inversion were compared with the geological setting, logging results, and seismic and gravimetric measurements. This comparison shows a good correlation between the AEM models and the known geological and geophysical data.     

1D inversion of DC resistivity data using a quality-based truncated SVD

Many DC resistivity inversion schemes use a combination of standard iterative least-squares and truncated singular value decomposition (SVD) to optimize the solution to the inverse problem. However, until quite recently, the truncation was done arbitrarily or by a trial-and-error procedure, due to the lack of workable guidance criteria for discarding small singular values. In this paper we present an inversion scheme which adopts a truncation criterion based on the optimization of the total model variance. This consists of two terms: (i) the term associated with the variance of statistically significant principal components, i.e. the standard model estimate variance, and (ii) the term associated with statistically insignificant principal components of the solution, i.e. the variance of the bias term. As an initial model for the start of iterations, we use a multilayered homogeneous half-space whose layer thicknesses increase logarithmically with depth to take into account the decrease of the resolution of the DC resistivity technique with depth. The present inversion scheme has been tested on synthetic and field data. The results of the tests show that the procedure works well and the convergence process is stable even in the most complicated cases. The fact that the truncation level in the SVD is determined intrinsically in the course of inversion proves to be a major advantage over other inversion schemes where it is set by the user.     

Magnetotelluric inversion using regularized Hopfield neural networks

Hopfield neural networks are massive parallel automata that support specific models and are adept in solving optimization problems. They suffer from a ‘rough’ solution space and convergence properties that are highly dependent on the starting model or prior. These detractions may be overcome by introducing regularization into the network in the form of local feedback smoothing. Application of regularized Hopfield networks to over 50 optimization test cases has yielded successful results, even with uniform (minimal information) priors. In particular, the non-linear, one- and two-dimensional magnetotelluric inverse problems have been solved by means of these regularized networks. The solutions compare favourably with those produced by other methods. Such regularized networks, with either hardware or programmed, parallel-computer implementation, can be extended to the problem of three-dimensional magnetotelluric inversion. Because neural networks are natural analog-to-digital converters, it is predicted that they will be the basic building blocks of future magnetotelluric instrumentation.     

Magnetotelluric inversion for azimuthally anisotropic resistivities employing artificial neural networks

An extension of an artificial neural network (ANN) approach to solve the magnetotelluric (MT) inverse problem for azimuthally anisotropic resistivities is presented and applied for a real dataset. Three different model classes, containing general 1-D and 2-D azimuthally anisotropic features, have been considered. For each model class, characteristics of three-layer feed forward ANNs trained through an error back propagation algorithm have been adjusted to approximate the inverse modeling function. It appears that, at least for synthetic models, reasonable results would be obtained by applying the amplitudes of the complex impedance tensor elements as inputs. Furthermore, the Levenberg-Marquart algorithm possesses optimal performance as a learning paradigm for this problem. The evaluation of applicability of the trained ANNs for unknown data sets excluded from the learning procedure reveals that the trained ANNs possess acceptable interpolation and extrapolation abilities to estimate model parameters accurately. This method was also successfully used for a field dataset wherein anisotropy had been previously recognized.     

基于主成分的时间域航空电磁数据神经网络反演仿真研究(英文)

传统上,时间域航空电磁数据通过拟合迭代反演计算得到大地模型,然而,由于航空电磁数据道间的较强相关性,导致病态反演,并引起超定问题;同时电磁数据的相关性使其与模型参数的映射关系复杂,增加了反演的复杂度。采用主成分分析法将航空电磁数据变换为正交的较少数量的主成分,不仅降低了数据道间的相关性,减小了数据量,同时压制了数据的不相关噪声。本文利用人工神经网络(ANN)逼近主成分与大地模型参数间的映射关系,避免了传统反演算法中雅克比矩阵的复杂计算。层状模型的主成分神经网络与数据神经网络的反演结果对比显示,主成分神经网络反演方法网络结构简单,训练步数少,反演结果好,特别是对于含噪数据。准二维模型的主成分ANN、数据ANN以及Zhody方法的反演结果显示了主成分神经网络具有更接近真实模型的反演效果,进一步证明了主成分神经网络反演方法适合海量航空电磁探测数据反演。     

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.     

Short term streamflow forecasting using artificial neural networks

The research described in this article investigates the utility of Artificial Neural Networks (ANNs) for short term forecasting of streamflow. The work explores the capabilities of ANNs and compares the performance of this tool to conventional approaches used to forecast streamflow. Several issues associated with the use of an ANN are examined including the type of input data and the number, and the size of hidden layer(s) to be included in the network. Perceived strengths of ANNs are the capability for representing complex, non-linear relationships as well as being able to model interaction effects. The application of the ANN approach is to a portion of the Winnipeg River system in Northwest Ontario, Canada. Forecasting was conducted on a catchment area of approximately 20 000 km². using quarter monthly time intervals. The results were most promising. A very close fit was obtained during the calibration (training) phase and the ANNs developed consistently outperformed a conventional model during the verification (testing) phase for all of the four forecast lead-times. The average improvement in the root mean squared error (RMSE) for the 8 years of test data varied from 5 cms in the four time step ahead forecasts to 12.1 cms in the two time step ahead forecasts.     

Fragility functions of blockwork wharves using artificial neural networks

The use of artificial neural networks in the general framework of a performance-based seismic vulnerability evaluation for earth retaining structures is presented. A blockwork wharf-foundation-backfill complex is modeled with advanced nonlinear 2D finite difference software, wherein liquefaction occurrence is explicitly accounted for. A simulation algorithm is adopted to sample geotechnical input parameters according to their statistical distribution, and extensive time histories analyses are then performed for several earthquake intensity levels. In the process, the seismic input is also considered as a random variable. A large dataset of virtual realizations of the behavior of different configurations under recorded ground motions is thus obtained, and an artificial neural network is implemented in order to find the unknown nonlinear relationships between seismic and geotechnical input data versus the expected performance of the facility. After this process, fragility curves are systematically derived by applying Monte Carlo simulation on the obtained correlations. The novel fragility functions herein proposed for blockwork wharves take into account different geometries, liquefaction occurrence and type of failure mechanism. Results confirm that the detrimental effects of liquefaction increase the probability of failure at all damage states. Moreover, it is also demonstrated that increasing the base width/height ratio results in higher failure probabilities for the horizontal sliding than for the tilting towards the sea.     

三维频率域航空电磁反演研究

航空电磁数据的三维解释由于数据量大需要有高效的反演算法作为支撑.本文利用两种目前主流的数值优化技术（非线性共轭梯度和有限内存的BFGS法）实现了三维频率域航空电磁反演,并进一步比较了两种方法的有效性和运算效率.在反演过程中,为了更好地反演异常体的空间位置,模型方差矩阵中的光滑系数在反演起始阶段取值较大;当数据拟合差下降趋于平缓时,再利用较小的光滑因子约束反演过程来实现聚焦和获得精确的反演结果.理论数据反演表明这两种优化策略具有相似的内存需求,但是有限内存的BFGS技术比非线性共轭梯度法在计算时间和模型反演分辨率上具有一定的优越性,因此有限内存BFGS法更适合于求解大规模三维反演问题. 模型试验进一步表明目前主流的迭代法求解技术不适合大规模航空电磁数据反演,未来移动平台多源电磁数据快速正反演可通过引入矩阵分解技术来实现.     

航空电磁拟三维模型空间约束反演

为了克服时间域航空电磁数据单点反演结果中常见的电阻率或层厚度横向突变造成数据难以解释的问题,通过引入双向约束实现航空电磁拟三维空间约束反演.除考虑沿测线方向相邻测点之间的横向约束外,同时还考虑了垂直测线方向测点在空间上的相互约束.为此,首先设计拟三维模型中固定层厚和可变层厚两种空间约束反演方案,然后通过在目标函数中引入沿测线和垂直测线方向上的模型参数约束矩阵,并使用L-BFGS算法使目标函数最小化,获得最优拟三维模型空间反演解.基于理论模型和实测数据反演,对单点反演与两种空间约束反演方案的有效性进行比较,证明本文空间约束反演算法对于噪声的压制效果好,反演的界面连续光滑,同时内存需求和反演时间少,是一种快速有效的反演策略.     

利用大地电磁三维反演方法获得二维剖面附近三维电阻率结构的可行性

大地电磁野外实测数据目前大多为二维剖面数据.如何反演这些二维剖面数据获得较为接近实际地电情况的结果,是多数大地电磁工作者关心的问题.我们通过对理论模型的三维响应进行分析和对合成数据及实测资料的反演结果进行对比研究,讨论了利用三维反演的方法来获得大地电磁二维剖面附近三维电阻率结构的可行性.结果表明:可用三维反演的方法来解释二维剖面数据.对大地电磁二维剖面的张量数据进行三维反演,不仅可以沿剖面获得较好的二维断面结果,还能够得到二维反演所不能获得的剖面附近的三维电阻率结构信息.合成数据的反演算例表明:对二维剖面数据进行三维反演时,对角元素对于圈定剖面附近三维异常体的空间分布具有独特作用,应尽量反演所有的张量元素.     

数据空间磁异常模量三维反演

强剩磁的存在通常导致了总磁化强度方向未知,进而影响了磁异常的反演和解释.磁异常模量是一种受磁化方向影响小的转换量,可以在强剩磁条件下通过反演三维磁化强度大小分布来推测场源分布状态.我们提出了一种数据空间磁异常模量反演算法来减少剩磁的影响.与标准的模型空间L2范数正则化反演方法相比,我们的方法有两个优点:一是无需搜索正则化参数(需要反复求解非线性反演问题),因而可以减少计算时间;二是反演结果更加聚焦,深度分辨率更高,我们对此进行了原因分析.通过模型和实测数据测试证明了该算法的有效性和更好的反演效果.     

Inversion of nuclear well-logging data using neural networks

This work looks at the application of neural networks in geophysical well‐logging problems and specifically their utilization for inversion of nuclear downhole data. Simulated neutron and γ‐ray fluxes at a given detector location within a neutron logging tool were inverted to obtain formation properties such as porosity, salinity and oil/water saturation. To achieve this, the forward particle‐radiation transport problem was first solved for different energy groups (47 neutron groups and 20 γ‐ray groups) using the multigroup code EVENT. A neural network for each of the neutron and γ‐ray energy groups was trained to re‐produce the detector fluxes using the forward modelling results from 504 scenarios. The networks were subsequently tested on unseen data sets and the unseen input parameters (formation properties) were then predicted using a global search procedure. The results obtained are very encouraging with formation properties being predicted to within 10% average relative error. The examples presented show that neural networks can be applied successfully to nuclear well‐logging problems. This enables the implementation of a fast inversion procedure, yielding quick and reliable values for unknown subsurface properties such as porosity, salinity and oil saturation.     

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.     

Multiobjective analysis of a public wellfield using artificial neural networks

As competition for increasingly scarce ground water resources grows, many decision makers may come to rely upon rigorous multiobjective techniques to help identify appropriate and defensible policies, particularly when disparate stakeholder groups are involved. In this study, decision analysis was conducted on a public water supply wellfield to balance water supply needs with well vulnerability to contamination from a nearby ground water contaminant plume. With few alternative water sources, decision makers must balance the conflicting objectives of maximizing water supply volume from noncontaminated wells while minimizing their vulnerability to contamination from the plume. Artificial neural networks (ANNs) were developed with simulation data from a numerical ground water flow model developed for the study area. The ANN-derived state transition equations were embedded into a multiobjective optimization model, from which the Pareto frontier or trade-off curve between water supply and wellfield vulnerability was identified. Relative preference values and power factors were assigned to the three stakeholders, namely the company whose waste contaminated the aquifer, the community supplied by the wells, and the water utility company that owns and operates the wells. A compromise pumping policy that effectively balances the two conflicting objectives in accordance with the preferences of the three stakeholder groups was then identified using various distance-based methods.     

建筑结构利用TLCD减振的神经网络智能控制

本文提出了建筑结构利用调谐液体柱型阻尼器（ＴＬＣＤ）减振的神经网络智能控制方法。首先阐述了确定ＴＬＣＤ半主动控制策略;然后利用ＢＰ人工神经网络方法计算并控制ＴＬＣＤ隔板孔洞的面积,以调节和控制阻尼比＆Ｔ,实现对建筑结构的智能控制。地震作用下的数值分析表明,本文所述的方法是十分有效的。     

利用人工神经网络预测电离层foF2参数

利用人工神经网络技术实现了电离层foF2参数提前1小时预测.从foF2时间序列本身的变化特征出发,根据时间序列相关分析结果确定网络输入参数.选用当前时刻foF2值,预测时刻前一天的foF2值,预测时刻前7天foF2平均值,当前时刻前7天foF2平均值,foF2的一阶差分及表示当前时刻t的变量共六个参数作为神经网络输入,下一时刻值作为神经网络输出.对于太阳活动高年平均预测相对误差小于6%,均方根误差小于0.6 MHz,太阳活动低年平均预测相对误差小于10%,均方根误差小于0.5 MHz     

Fracture-frequency prediction from borehole wireline logs using artificial neural networks

Borehole-wall imaging is currently the most reliable means of mapping discontinuities within boreholes. As these imaging techniques are expensive and thus not always included in a logging run, a method of predicting fracture frequency directly from traditional logging tool responses would be very useful and cost effective. Artificial neural networks (ANNs) show great potential in this area. ANNs are computational systems that attempt to mimic natural biological neural networks. They have the ability to recognize patterns and develop their own generalizations about a given data set. Neural networks are trained on data sets for which the solution is known and tested on data not previously seen in order to validate the network result. We show that artificial neural networks, due to their pattern recognition capabilities, are able to assess the signal strength of fracture-related heterogeneity in a borehole log and thus fracture frequency within a borehole. A combination of wireline logs (neutron porosity, bulk density, P-sonic, S-sonic, deep resistivity and shallow resistivity) were used as input parameters to the ANN. Fracture frequency calculated from borehole televiewer data was used as the single output parameter. The ANN was trained using a back-propagation algorithm with a momentum learning function. In addition to fracture frequency within a single borehole, an ANN trained on a subset of boreholes in an area could be used for prediction over the entire set of boreholes, thus allowing the lateral correlation of fracture zones.