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| Title: | Cosimulation of heads and log-transmissitvities using a numeral spectral-perturbation method: A new technique for obtaining stochastic predictions of groundwater flow through heterogenous porous media |
| Authors: | Zimmerman, D. |
| Issue Date: | 26-Aug-2009 |
| Abstract: | A new technique for obtaining stochastic predictions of groundwater flow through heterogeneous aquifer materials is presented. The aquifer properties are viewed as statistically homogeneous stochastic processes which are characterized by covariance functions. The governing stochastic stochastic differential equation for flow is written for mean-removed random variables whose joint distribution is assumed to be Gaussian. This transformed equation is then linearized by applying perturbation theory. Finally, spectral theory is used to obtain a relationship between the head spectrum and the logarithm of Transmissivity (InT) spectrum. Using this relationship, and algorithm is developed for generating discrete random fields of head and InT simultaneously. The probability behavior of the head process can then be estimated by computing its statistics over an ensemble of fields obtained through repeated application of the cogeneration algorithm. This cosimulation procedure is computationally much cheaper and faster than the standard sequential Monte Carlo method which involves solving a system of algebraic equations for each realization of the head field obtained. However, the method is restricted to relatively small input variance.
The theory is initially developed for the infinite domain problem in order to avoid complications arising from boundary conditions. It is then extended, using geostatistical methods, to enable the cosimultions to be conditioned on measurement of T and/or head, thus addressing the bounded domain problem.
The technique is demonstrated (without conditioning) for steady, confined flow in one and two-dimensional domains with unidirectional, linear mean hydraulic gradient. Practical aspects associated with compute implementation of the procedure are discussed in detail. The cogenerated fields are examined to determine under what conditions they preserve the proper statistical behavior and satisfy the mass conservation principle. |
| URI: | http://hdl.handle.net/10136/506 |
| Appears in Collections: | Independent Studies
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Files in This Item:
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| Zimmerman, D..pdf | | 5760Kb | Adobe PDF | View/Open |
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