Artificial Neural Networks applied to estimate permeability, porosity and intrinsic attenuation using seismic attributes and well-log data Ursula Iturrarán-Viveros a, ⁎, Jorge O. Parra b a Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Escolar S/N, Coyoacán C.P., 04510 México D.F., Mexico b Southwest Research Institute, Division of Applied Physics, San Antonio Texas, USA abstract article info Article history: Received 11 January 2014 Accepted 5 May 2014 Available online 20 May 2014 Keywords: The Gamma test Seismic attributes Artificial Neural Networks Permeability Porosity Attenuation Permeability and porosity are two fundamental reservoir properties which relate to the amount of fluid contained in a reservoir and its ability to flow. The intrinsic attenuation is another important parameter since it is related to porosity, permeability, oil and gas saturation and these parameters significantly affect the seismic signature of a reservoir. We apply Artificial Neural Network (ANN) models to predict permeability (k) and porosity (ϕ) for a carbonate aquifer in southeastern Florida and to predict intrinsic attenuation (1/Q) for a sand–shale oil reservoir in northeast Texas. In this study, the Gamma test (a revolutionary estimator of the noise in a data set) has been used as a mathematically non-parametric nonlinear smooth modeling tool to choose the best input combination of seismic attributes to estimate k and ϕ, and the best combination of well-logs to estimate 1/Q. This saves time during the construction and training of ANN models and also sets a lower bound for the mean squared error to prevent over-training. The Neural Network method successfully delineates a highly permeable zone that corresponds to a high water production in the aquifer. The Gamma test found nonlinear relations that were not visible to linear regression allowing us to generalize the ANN estimations of k, ϕ and 1/Q for their respective sets of patterns that were not used during the learning phase. © 2014 Elsevier B.V. All rights reserved. 1. Introduction Artificial Neural Networks are mathematical tools design to perform complex pattern recognition tasks and they have been employed to quantify patterns and estimate parameters in many geophysical applications, see for example Poulton (2001), Sandham and Leggett (2003). Reservoir characterization is a process for quantitatively describing various reservoir properties in spatial variability using all the available field data. These properties have a significant impact on petroleum field operations and reservoir management. Committee of Neural Networks has been successfully used to estimate porosity and permeability form well logs, see Bhatt and Helle (2002) and Helle et al. (2001). We choose Artificial Neural Network models (ANNs) to estimate reservoir properties for two applications with two different data sets. In the first application, we integrate multi-attributes from surface seismic data with well-log permeability (k) and porosity (ϕ) to produce permeability and porosity images for a carbonate aquifer in southeastern Florida. The second application only involves well-log data from one well in an oil reservoir in northeast Texas and a reference estimation of the intrinsic attenuation (1/Q) extracted from sonic full- waveforms used to train an ANN. Similar to any other statistical and mathematical model, ANN models have also some disadvantages. Having a large number of input variables is one of the most common problems for their development because they are not engineered to eliminate superfluous inputs. It is critical to devise a systematic feature selection scheme that provides guidance on choosing the most representative features for estimation of petrophysical parameters. This paper presents an input feature selection scheme based on the Gamma test (GT), that saves time during the training phase of the ANNs and it sets a lower bound for Mean Square Errors (MSEs) to avoid over-fitting. The Gamma test is a mathematically proven smooth non-linear modeling tool with a wide variety of applications that helps modelers to choose the best input combination before calibrating and testing models, therefore it reduces the input selection uncertainty. Given a data set, the GT will be able to tell us how well we can predict k, ϕ and 1/Q using any model that is likely to be operating. It can delineate the complex non-linear relationships if there are any. There are other techniques to reduce the number of input variables such as multi-linear regression and principal component analysis (PCA), see Malhi and Gao (2004). However when using PCA we could not estimate a lower bound for the MSE, nor estimate the number of training samples needed to achieve a reasonable output. Studies in other fields show interesting comparisons between plain ANN, the GT-ANN and PCA- ANN. Findings favor GT-NN and PCA-NN over plain ANN, see Gholami and Moradzadeh (2011). In a different approach Díaz-Viera et al. (2006) use copulas to model permeability values associated with the Journal of Applied Geophysics 107 (2014) 45–54 ⁎ Corresponding author. Tel.: +52 55 56 22 54 11. E-mail addresses: ursula@ciencias.unam.mx (U. Iturrarán-Viveros), jparra@swri.org (J.O. Parra). http://dx.doi.org/10.1016/j.jappgeo.2014.05.010 0926-9851/© 2014 Elsevier B.V. All rights reserved. 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