A general approach for porosity estimation using artificial neural network method: a case study from Kansas gas field

This study aims to design a back-propagation artificial neural network (BP-ANN) to estimate the reliable porosity values from the well log data taken from Kansas gas field in the USA. In order to estimate the porosity, a neural network approach is applied, which uses as input sonic, density and resistivity log data, which are known to affect the porosity. This network easily sets up a relationship between the input data and the output parameters without having prior knowledge of petrophysical properties, such as porefluid type or matrix material type. The results obtained from the empirical relationship are compared with those from the neural network and a good correlation is observed. Thus, the ANN technique could be used to predict the porosity from other well log data.     

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.     

Committee neural networks for porosity and permeability prediction from well logs

Neural computing has moved beyond simple demonstration to more significant applications. Encouraged by recent developments in artificial neural network (ANN) modelling techniques, we have developed committee machine (CM) networks for converting well logs to porosity and permeability, and have applied the networks to real well data from the North Sea. Simple three‐layer back‐propagation ANNs constitute the blocks of a modular system where the porosity ANN uses sonic, density and resistivity logs for input. The permeability ANN is slightly more complex, with four inputs (density, gamma ray, neutron porosity and sonic). The optimum size of the hidden layer, the number of training data required, and alternative training techniques have been investigated using synthetic logs. For both networks an optimal number of neurons in the hidden layer is in the range 8–10. With a lower number of hidden units the network fails to represent the problem, and for higher complexity overfitting becomes a problem when data are noisy. A sufficient number of training samples for the porosity ANN is around 150, while the permeability ANN requires twice as many in order to keep network errors well below the errors in core data. For the porosity ANN the overtraining strategy is the suitable technique for bias reduction and an unconstrained optimal linear combination (OLC) is the best method of combining the CM output. For permeability, on the other hand, the combination of overtraining and OLC does not work. Error reduction by validation, simple averaging combined with range‐splitting provides the required accuracy. The accuracy of the resulting CM is restricted only by the accuracy of the real data. The ANN approach is shown to be superior to multiple linear regression techniques even with minor non‐linearity in the background model.     

Testing bedload transport formulae using morphologic transport estimates and field data: lower Fraser River,British Columbia

Morphologic transport estimates available for a 65‐km stretch of Fraser River over the period 1952–1999 provide a unique opportunity to evaluate the performance of bedload transport formulae for a large river over decadal time scales. Formulae tested in this paper include the original and rational versions of the Bagnold formula, the Meyer‐Peter and Muller formula and a stream power correlation. The generalized approach adopted herein does not account for spatial variability in flow, bed structure and channel morphology. However, river managers and engineers, as well as those studying rivers within the context of long‐term landscape change, may find this approach satisfactory as it has minimal data requirements and provides a level of process specification that may be commensurable with longer time scales. Hydraulic geometry equations for width and depth are defined using morphologic maps based on aerial photography and bathymetric survey data. Comparison of transport predictions with bedload transport measurements completed at Mission indicates that the original Bagnold formula most closely approximates the main trends in the field data. Sensitivity analyses are conducted to evaluate the impact of inaccuracies in input variables width, depth, slope and grain size on transport predictions. The formulae differ in their sensitivity to input variables and between reaches. Average annual bedload transport predictions for the four formulae show that they vary between each other as well as from the morphologic transport estimates. The original Bagnold and Meyer‐Peter and Muller formulae provide the best transport predictions, although the former underestimates while the latter overestimates transport rates. Based on our findings, an error margin of up to an order of magnitude can be expected when adopting generalized approaches for the prediction of bedload transport. Copyright © 2005 John Wiley & Sons, Ltd.     

Improved normalization of time‐lapse seismic data using normalized root mean square repeatability data to improve automatic production and seismic history matching in the Nelson field

Updating of reservoir models by history matching of 4D seismic data along with production data gives us a better understanding of changes to the reservoir, reduces risk in forecasting and leads to better management decisions. This process of seismic history matching requires an accurate representation of predicted and observed data so that they can be compared quantitatively when using automated inversion. Observed seismic data is often obtained as a relative measure of the reservoir state or its change, however. The data, usually attribute maps, need to be calibrated to be compared to predictions. In this paper we describe an alternative approach where we normalize the data by scaling to the model data in regions where predictions are good. To remove measurements of high uncertainty and make normalization more effective, we use a measure of repeatability of the monitor surveys to filter the observed time‐lapse data. We apply this approach to the Nelson field. We normalize the 4D signature based on deriving a least squares regression equation between the observed and synthetic data which consist of attributes representing measured acoustic impedances and predictions from the model. Two regression equations are derived as part of the analysis. For one, the whole 4D signature map of the reservoir is used while in the second, 4D seismic data is used from the vicinity of wells with a good production match. The repeatability of time‐lapse seismic data is assessed using the normalized root mean square of measurements outside of the reservoir. Where normalized root mean square is high, observations and predictions are ignored. Net: gross and permeability are modified to improve the match. The best results are obtained by using the normalized root mean square filtered maps of the 4D signature which better constrain normalization. The misfit of the first six years of history data is reduced by 55 per cent while the forecast of the following three years is reduced by 29 per cent. The well based normalization uses fewer data when repeatability is used as a filter and the result is poorer. The value of seismic data is demonstrated from production matching only where the history and forecast misfit reductions are 45% and 20% respectively while the seismic misfit increases by 5%. In the best case using seismic data, it dropped by 6%. We conclude that normalization with repeatability based filtering is a useful approach in the absence of full calibration and improves the reliability of seismic data.     

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。     

Optimal selection of artificial neural network parameters for the prediction of a karstic aquifer's response

The simulation of karstic aquifers is difficult using traditional groundwater numerical simulators, as the exact knowledge of the hydraulic characteristics of the physical system in small scale is rarely available and the numerical simulators produce results of limited reliability. In the present work, artificial neural networks (ANNs) are utilized to predict the response of a karstic aquifer, using the hydraulic head change per time step rather than the hydraulic head itself as output parameter of the network. As it will be demonstrated, in the first case a better approximation of the physical system's response is achieved as the change of the hydraulic head is more naturally connected to the input parameters of the network, which model the aquatic equilibrium of the system. The correlation of rainfall and hydraulic head change per time step was initially used to determine the time lag of the rainfall input data, which represents the time needed by the rainfall to percolate and reach the water table. In a second step, a differential evolution (DE) algorithm is utilized for the optimal selection of rainfall time lag as well as ANN's architecture and training parameters. Although a time consuming procedure, the improvement obtained suggests that the empirical determination of the ANN parameters and structure is not always sufficient and an optimization procedure, which minimizes the training and evaluation errors of the ANN, may provide substantially better simulation results. The optimized networks were finally used for midterm predictions (30 to 90 days ahead) of the hydraulic head, showing the ability of the ANN with hydraulic head change as output parameter to provide predictions with high accuracy at the end of the considered time period. Copyright © 2009 John Wiley & Sons, Ltd.     

Modelling evaporation using an artificial neural network algorithm

This paper investigates the prediction of Class A pan evaporation using the artificial neural network (ANN) technique. The ANN back propagation algorithm has been evaluated for its applicability for predicting evaporation from minimum climatic data. Four combinations of input data were considered and the resulting values of evaporation were analysed and compared with those of existing models. The results from this study suggest that the neural computing technique could be employed successfully in modelling the evaporation process from the available climatic data set. However, an analysis of the residuals from the ANN models developed revealed that the models showed significant error in predictions during the validation, implying loss of generalization properties of ANN models unless trained carefully. The study indicated that evaporation values could be reasonably estimated using temperature data only through the ANN technique. This would be of much use in instances where data availability is limited. Copyright © 2002 John Wiley & Sons, Ltd.     

Artificial neural networks for daily rainfall—runoff modelling

Abstract

The application of artificial neural network (ANN) methodology for modelling daily flows during monsoon flood events for a large size catchment of the Narmada River in Madhya Pradesh (India) is presented. The spatial variation of rainfall is accounted for by subdividing the catchment and treating the average rainfall of each subcatchment as a parallel and separate lumped input to the model. A linear multiple-input single-output (MISO) model coupled with the ANN is shown to provide a better representation of the rainfall-runoff relationship in such large size catchments compared with linear and nonlinear MISO models. The present model provides a systematic approach for runoff estimation and represents improvement in prediction accuracy over the other models studied herein.     

An ANN‐based model for spatiotemporal groundwater level forecasting

This paper evaluates the feasibility of using an artificial neural network (ANN) methodology for estimating the groundwater levels in some piezometers placed in an aquifer in north‐western Iran. This aquifer is multilayer and has a high groundwater level in urban areas. Spatiotemporal groundwater level simulation in a multilayer aquifer is regarded as difficult in hydrogeology due to the complexity of the different aquifer materials. In the present research the performance of different neural networks for groundwater level forecasting is examined in order to identify an optimal ANN architecture that can simulate the piezometers water levels. Six different types of network architectures and training algorithms are investigated and compared in terms of model prediction efficiency and accuracy. The results of different experiments show that accurate predictions can be achieved with a standard feedforward neural network trained usung the Levenberg–Marquardt algorithm. The structure and spatial regressions of the ANN parameters (weights and biases) are then used for spatiotemporal model presentation. The efficiency of the spatio‐temporal ANN (STANN) model is compared with two hybrid neural‐geostatistics (NG) and multivariate time series‐geostatistics (TSG) models. It is found in this study that the ANNs provide the most accurate predictions in comparison with the other models. Based on the nonlinear intrinsic ANN approach, the developed STANN model gives acceptable results for the Tabriz multilayer aquifer. Copyright © 2008 John Wiley & Sons, Ltd.     

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.     

Uncertainty assessment and optimization of hydrological model with the Shuffled Complex Evolution Metropolis algorithm: an application to artificial neural network rainfall-runoff model

Assessment of parameter and predictive uncertainty of hydrologic models is an essential part in the field of hydrology. However, during the past decades, research related to hydrologic model uncertainty is mostly done with conceptual models. As is accepted that uncertainty in model predictions arises from measurement errors associated with the system input and output, from model structural errors and from problems with parameter estimation. Unfortunately, non-conceptual models, such as black-box models, also suffer from these problems. In this paper, we take the artificial neural network (ANN) rainfall-runoff model as an example, and the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) is employed to analysis the parameter and predictive uncertainty of this model. Furthermore, based on the results of uncertainty assessment, we finally arrive at a simpler incomplete-connection artificial neural network (ICANN) model as well as with better performance compared to original ANN rainfall-runoff model. These results not only indicate that SCEM-UA can be a useful tool for uncertainty analysis of ANN model, but also prove that uncertainty does exist in ANN rainfall-runoff model. Additionally, in some way, it presents that the ICANN model is with smaller uncertainty than the original ANN model.     

Rainfall‐runoff modelling using artificial neural networks technique: a Blue Nile catchment case study

A rainfall‐runoff model based on an artificial neural network (ANN) is presented for the Blue Nile catchment. The best geometry of the ANN rainfall‐runoff model in terms of number of hidden layers and nodes is identified through a sensitivity analysis. The Blue Nile catchment (about 300 000 km²) in the Nile basin is selected here as a case study. The catchment is classified into seven subcatchments, and the mean areal precipitation over those subcatchments is computed as a main input to the ANN model. The available daily data (1992–99) are divided into two sets for model calibration (1992–96) and for validation (1997–99). The results of the ANN model are compared with one of physical distributed rainfall‐runoff models that apply hydraulic and hydrologic fundamental equations in a grid base. The results over the case study area and the comparative analysis with the physically based distributed model show that the ANN technique has great potential in simulating the rainfall‐runoff process adequately. Because the available record used in the calibration of the ANN model is too short, the ANN model is biased compared with the distributed model, especially for high flows. Copyright © 2005 John Wiley & Sons, Ltd.     

Forecasting flows in Apalachicola River using neural networks

Forecasting river flow is important to water resources management and planning. In this study, an artificial neural network (ANN) model was successfully developed to forecast river flow in Apalachicola River. The model used a feed‐forward, back‐propagation network structure with an optimized conjugated training algorithm. Using long‐term observations of rainfall and river flow during 1939–2000, the ANN model was satisfactorily trained and verified. Model predictions of river flow match well with the observations. The correlation coefficients between forecasting and observation for daily, monthly, quarterly and yearly flow forecasting are 0·98, 0·95, 0·91 and 0·83, respectively. Results of the forecasted flow rates from the ANN model were compared with those from a traditional autoregressive integrated moving average (ARIMA) forecasting model. Results indicate that the ANN model provides better accuracy in forecasting river flow than does the ARIMA model. Copyright © 2004 John Wiley & Sons, Ltd.     

A systematic approach to the input determination for neural network rainfall–runoff models

Input determination has a great influence on the performance of artificial neural network (ANN) rainfall–runoff models. To improve the performance of ANN models, a systematic approach to the input determination for ANN models is proposed. In the proposed approach, the irrelevant inputs are removed. Then an adequate ANN model, which only includes highly relevant inputs, is constructed. Unlike the trial‐and‐error procedure, the proposed approach is more systematic and avoids unnecessary trials. To demonstrate the effectiveness of the proposed approach, an application to actual typhoon events is presented. The results show that the proposed ANN model, which is constructed by the proposed approach, has advantages over those obtained by the trial‐and‐error procedure. The proposed ANN model has a simpler architecture, needs less training time, and performs better. The proposed ANN model is recommended as an alternative to existing rainfall–runoff ANN models. Copyright © 2007 John Wiley & Sons, Ltd.     

Monthly streamflow forecasting using neuro-wavelet techniques and input analysis

ABSTRACT

Combinations of low-frequency components (also known as approximations) resulting from the wavelet decomposition are tested as inputs to an artificial neural network (ANN) in a hybrid approach, and compared to classical ANN models for flow forecasting for 1, 3, 6 and 12 months ahead. In addition, the inputs are rewritten in terms of the flow, revealing what type of information was being provided to the network, in order to understand the effect of the approximations on the forecasting performance. The results show that the hybrid approach improved the accuracy of all tested models, especially for 1, 3 and 6 months ahead. The input analyses show that high-frequency components are more important for shorter forecast horizons, while for longer horizons, they may worsen the model accuracy.     

Probabilistic and ensemble simulation approaches for input uncertainty quantification of artificial neural network hydrological models

Artificial neural network (ANN) has been demonstrated to be a promising modelling tool for the improved prediction/forecasting of hydrological variables. However, the quantification of uncertainty in ANN is a major issue, as high uncertainty would hinder the reliable application of these models. While several sources have been ascribed, the quantification of input uncertainty in ANN has received little attention. The reason is that each measured input quantity is likely to vary uniquely, which prevents quantification of a reliable prediction uncertainty. In this paper, an optimization method, which integrates probabilistic and ensemble simulation approaches, is proposed for the quantification of input uncertainty of ANN models. The proposed approach is demonstrated through rainfall-runoff modelling for the Leaf River watershed, USA. The results suggest that ignoring explicit quantification of input uncertainty leads to under/over estimation of model prediction uncertainty. It also facilitates identification of appropriate model parameters for better characterizing the hydrological processes.     

Porosity and permeability prediction from wireline logs using artificial neural networks: a North Sea case study

Estimations of porosity and permeability from well logs are important yet difficult tasks encountered in geophysical formation evaluation and reservoir engineering. Motivated by recent results of artificial neural network (ANN) modelling offshore eastern Canada, we have developed neural nets for converting well logs in the North Sea to porosity and permeability. We use two separate back-propagation ANNs (BP-ANNs) to model porosity and permeability. The porosity ANN is a simple three-layer network using sonic, density and resistivity logs for input. The permeability ANN is slightly more complex with four inputs (density, gamma ray, neutron porosity and sonic) and more neurons in the hidden layer to account for the increased complexity in the relationships. The networks, initially developed for basin-scale problems, perform sufficiently accurately to meet normal requirements in reservoir engineering when applied to Jurassic reservoirs in the Viking Graben area. The mean difference between the predicted porosity and helium porosity from core plugs is less than 0.01 fractional units. For the permeability network a mean difference of approximately 400 mD is mainly due to minor core-log depth mismatch in the heterogeneous parts of the reservoir and lack of adequate overburden corrections to the core permeability. A major advantage is that no a priori knowledge of the rock material and pore fluids is required. Real-time conversion based on measurements while drilling (MWD) is thus an obvious application.     

Spatial variability of precipitation regimes over Turkey

Abstract

This study aims to predict the daily precipitation from meteorological data from Turkey using the wavelet—neural network method, which combines two methods: discrete wavelet transform (DWT) and artificial neural networks (ANN). The wavelet—ANN model provides a good fit with the observed data, in particular for zero precipitation in the summer months, and for the peaks in the testing period. The results indicate that wavelet—ANN model estimations are significantly superior to those obtained by either a conventional ANN model or a multi linear regression model. In particular, the improvement provided by the new approach in estimating the peak values had a noticeably high positive effect on the performance evaluation criteria. Inclusion of the summed sub-series in the ANN input layer brings a new perspective to the discussions related to the physics involved in the ANN structure.     

Test of statistical means for the extrapolation of soil depth point information using overlays of spatial environmental data and bootstrapping techniques

Hydrological modelling depends highly on the accuracy and uncertainty of model input parameters such as soil properties. Since most of these data are field surveyed, geostatistical techniques such as kriging, classification and regression trees or more sophisticated soil‐landscape models need to be applied to interpolate point information to the area. Most of the existing interpolation techniques require a random or regular distribution of points within the study area but are not adequate to satisfactorily interpolate soil catena or transect data. The soil landscape model presented in this study is predicting soil information from transect or catena point data using a statistical mean (arithmetic, geometric and harmonic mean) to calculate the soil information based on class means of merged spatial explanatory variables. A data set of 226 soil depth measurements covering a range of 0–6·5 m was used to test the model. The point data were sampled along four transects in the Stubbetorp catchment, SE‐Sweden. We overlaid a geomorphology map (8 classes) with digital elevation model‐derived topographic index maps (2–9 classes) to estimate the range of error the model produces with changing sample size and input maps. The accuracy of the soil depth predictions was estimated with the root mean square error (RMSE) based on a testing and training data set. RMSE ranged generally between 0·73 and 0·83 m ± 0·013 m depending on the amount of classes the merged layers had, but were smallest for a map combination with a low number of classes predicted with the harmonic mean (RMSE = 0·46 m). The results show that the prediction accuracy of this method depends on the number of point values in the sample, the value range of the measured attribute and the initial correlations between point values and explanatory variables, but suggests that the model approach is in general scale invariant. Copyright © 2009 John Wiley & Sons, Ltd.