Stochastic inverse method for estimation of geostatistical representation of hydrogeologic stratigraphy using borehole logs and pressure observations |
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| Authors: | Dylan R Harp Velimir V Vesselinov |
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| Institution: | (1) Hydrology, Geochemistry, and Geology Group, Earth and Environmental Sciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA;(2) Department of Civil Engineering, University of New Mexico, Albuquerque, NM, USA |
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| Abstract: | An approach is presented for identifying statistical characteristics of stratigraphies from borehole and hydraulic data. The
approach employs a Markov-chain based geostatistical framework in a stochastic inversion. Borehole data provide information
on the stratigraphy while pressure and flux data provide information on the hydraulic performance of the medium. The use of
Markov-chain geostatistics as opposed to covariance-based geostatistics can provide a more easily interpreted model geologically
and geometrically. The approach hinges on the use of mean facies lengths (negative inverse auto-transition rates) and mean
transition lengths (inverse cross-transition rates) as adjustable parameters in the stochastic inversion. Along with an unconstrained
Markov-chain model, simplifying constraints to the Markov-chain model, including (1) proportionally-random and (2) symmetric
spatial correlations, are evaluated in the stochastic inversion. Sensitivity analyses indicate that the simplifying constraints
can facilitate the inversion at the cost of spatial correlation model generality. Inverse analyses demonstrate the feasibility
of this approach, indicating that despite some low parameter sensitivities, all adjustable parameters do converge for a sufficient
number of ensemble realizations towards their “true” values. This paper extends the approach presented in Harp et al. (doi:, 2008) to (1) statistically characterize the hydraulic response of a geostatistical model, thereby incorporating an uncertainty
analysis directly in the inverse method, (2) demonstrate that a gradient-based optimization strategy is sufficient, thereby
providing relative computational efficiency compared to global optimization strategies, (3) demonstrate that the approach
can be extended to a 3-D analysis, and (4) introduce the use of mean facies lengths and mean transition lengths as adjustable
parameters in a geostatistical inversion, thereby allowing the approach to be extended to greater than two category Markov-chain
models. |
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