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Probability distributions for magnetotellurics

Description: Estimates of the magnetotelluric transfer functions can be viewed as ratios of two complex random variables. It is assumed that the numerator and denominator are governed approximately by a joint complex normal distribution. Under this assumption, probability distributions are obtained for the magnitude, squared magnitude, logarithm of the squared magnitude, and the phase of the estimates. Normal approximations to the distributions are obtained by calculating mean values and variances from error propagation, and the distributions are plotted with their normal approximations for different percentage errors in the numerator and denominator of the estimates, ranging from 10% to 75%. The distribution of the phase is approximated well by a normal distribution for the range of errors considered, while the distribution of the logarithm of the squared magnitude is approximated by a normal distribution for a much larger range of errors than is the distribution of the squared magnitude. The distribution of the squared magnitude is most sensitive to the presence of noise in the denominator of the estimate, in which case the true distribution deviates significantly from normal behavior as the percentage errors exceed 10%. In contrast, the normal approximation to the distribution of the logarithm of the magnitude is useful for errors as large as 75%.
Date: November 1, 1982
Creator: Stodt, John A.
Partner: UNT Libraries Government Documents Department

Application of automatic differentiation for the simulation of nonisothermal, multiphase flow in geothermal reservoirs

Description: Simulation of nonisothermal, multiphase flow through fractured geothermal reservoirs involves the solution of a system of strongly nonlinear algebraic equations. The Newton-Raphson method used to solve such a nonlinear system of equations requires the evaluation of a Jacobian matrix. In this paper we discuss automatic differentiation (AD) as a method for analytically computing the Jacobian matrix of derivatives. Robustness and efficiency of the AD-generated derivative codes are compared with a conventional derivative computation approach based on first-order finite differences.
Date: January 8, 2002
Creator: Kim, Jong G. & Finsterle, Stefan
Partner: UNT Libraries Government Documents Department

Estimation of hydrologic properties of heterogeneous geologic media with an inverse method based on iterated function systems

Description: The highly heterogeneous nature of most geologic media, coupled with the restricted view of the subsurface available through boreholes, makes it difficult to determine the spatial distribution of subsurface hydrologic properties. Without such a description one cannot predict how fluid flow or solute transport will occur through permeable geologic media, and these predictions are critically needed to address many important environmental problems, including toxic chemical spills, leaking underground storage tanks, and long-term radioactive waste isolation. A common concern of these problems is the possible existence of high-permeability pathways connecting the problem to the biosphere. An understanding of flow and transport behavior is also necessary to optimize energy extraction from petroleum or geothermal reservoirs, where identifying low-permeability barriers that compartmentalize reservoirs and hamper efficient resource utilization is a key problem. The present work describes the development and application of a new inverse method for determining the spatial distribution of hydrologic properties (permeability and specific storage) in heterogeneous geologic media, using pressure transients from interference well tests. The method employs fractal concepts to improve efficiency and reliability. It is applicable to any sort of heterogeneous geologic medium in which wells communicate with each other, whether it be porous, fractured, or a combination thereof. Application to field data from a shallow aquifer at Kesterson Reservoir agrees well with an independent analysis using traditional well-test analysis methods. Application to a series of interference tests conducted at the Gypsy Pilot Site produces a detailed picture of the subsurface, which compares favorably with cross-well seismic imaging studies. 53 refs.
Date: December 1, 1995
Creator: Doughty, C.
Partner: UNT Libraries Government Documents Department