The permeability of random two‐dimensional Poisson fracture networks can be studied using a model based on percolation theory and equivalent media theory. Such theories are usually applied on regular lattices where the lattice elements are present with probability p. In order to apply these theories to random systems, we (1) define the equivalent to the case where p = 1, (2) define p in terms of the statistical parameters of the random network, and (3) define the equivalent of the coordination number z. An upper bound for permeability equivalent to the case of p = 1 is found by calculating the permeability of the fracture network with the same linear fracture frequency and infinitely long fractures. The permeability of networks with the same linear fracture frequency and finite fractures can be normalized by this maximum. An equivalent for p is found as a function of the connectivity ζ, which is defined as the average number of intersections per fracture. This number can be calculated from the fracture density and distributions of fracture length and orientation. Then the equivalent p is defined by equating the average run length for a random network as a function of ζ to the average run length for a lattice as a function of p. The average run length in a random system is the average number of segments that a fracture is divided into by intersections with other fractures. In a lattice, it is the average number of bonds contiguous to a given bond. Also, an average coordination number can be calculated for the random systems as a function of ζ. Given these definitions of p and z, expressions for permeability are found based on percolation theory and equivalent media theory on regular lattices. When the expression for p is used to calculate the correlation length from percolation theory, an empirical formula for the size of the REV can be developed. To apply the models to random length systems, the expression for ζ must be modified to remove short fractures which do not contribute to flow. This leads to a quantitative prediction of how permeability decreases as one removes shorter fractures from a network. Numerical studies provide strong support for these models. These results also apply to the analogous electrical conduction problem.

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Feature selection is an important challenge in many classification problems, especially if the number of features greatly exceeds the number of examples available. We have developed a procedure--GenForest--which controls feature selection in random forests of decision trees by using a genetic algorithm. This approach was tested through our entry into the Comparative Evaluation of Prediction Algorithms 2006 (CoEPrA) competition (accessible online at: http://www.coepra.org). CoEPrA was a modeling competition organized to provide an objective testing for various classification and regression algorithms via the process of blind prediction. In the competition GenForest ranked 10/23, 5/16 and 9/16 on CoEPrA classification problems 1, 3 and 4, respectively, which involved the classification of type I MHC nonapeptides i.e. peptides containing nine amino acids. These problems each involved the classification of different sets of nonapeptides. Associated with each amino acid was a set of 643 features for a total of 5787 features per peptide. The method, its application to the CoEPrA datasets, and its performance in the competition are described.

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One way to estimate the hydrologic properties of heterogeneous geologic media is to invert well test data using multiple observation wells. Pressure transients observed during a well test are compared to the corresponding values obtained by numerically simulating the test using a mathematical model. The parameters of the mathematical model are varied and the simulation repeated until a satisfactory match to the observed pressure transients is obtained, at which point the model parameters are accepted as providing a possible representation of the hydrologic property distribution. Restricting the search to parameters that represent self‐similar (fractal) hydrologic property distributions can improve the inversion process. Far fewer parameters are needed to describe a hierarchical medium, improving the efficiency and robustness of the inversion. Additionally, each parameter set produces a hydrologic property distribution with a hierarchical structure, which mimics the multiple scales of heterogeneity often seen in natural geological media. The parameters varied during the inversion create fractal sets known as attractors, using an iterated function system (IFS). An attractor is mapped to a distribution of transmissivity and storativity in the mathematical model. Thus the IFS inverse method searches for the parameters of the IFS (typically tens of parameters) rather than the values of the hydrologic property distribution directly (typically hundreds to thousands of parameters). Application of the IFS inverse method to synthetic data shows that the method works well for simple heterogeneities. Application to field data from a sand/clay sedimentary sequence and a fractured granite produces reasonable results.

Abstract. We present a method for inverse modeling in hydrology that incorporates a physical understanding of the geological processes that form a hydrologic system. The method is based on constructing a stochastic model that is approximately representative of these geologic processes. This model provides a prior probability distribution for possible solutions to the inverse problem,. The uncertainty in the inverse solution is characterized by a conditional (posterior) probability distribution. A new stochastic simulation method, called conditional coding, approximately samples from this posterior distribution and allows study of solution uncertainty through Monte Carlo techniques. We examine a fracture-dominated flow system, but the method can potentially be applied to any system where formation processes are modeled with a stochastic simulation algorithm. based on geologic theory. We solve the inverse modeling problem by using this stochastic model to define a broad suite of possible spatial structures, and we then select samples from this suite that are consistent with (i.e., conditioned upon) the available hydraulic response data. The resulting solution is a model that is consistent with flow data and the geologic theory represented in the stochastic model. Our inverse modeling method is Bayesian, so we give a brief description of Bayesian theory and introduce some notation. In the Bayesian approach one first assumes that the unknown hydraulic geometry is randomly chosen from a given probability distribution of possible hydraulic geometries. This distribution is called the prior distribution or just the prior. Probabilities given by the prior can be represented with the notation P(X = X), where X represents the random hydraulic geometry and X is a particular geometry that X could equal. Before data are collected, the prior contains the only information about possible values for X, but after the data are taken some Xs will be more compatible with the data and so become more probable while other Xs are less compatible and less probable. Our Bayesian approach has two main components. First we define X using a physically based stochastic model that represents the geologic processes that form a hydraulic geometry; 3335