Abstract
The steady state two dimensional groundwater flow equation with constant transmissivities was studied by Whittle in 1954 as a stochastic Laplace equation. He showed that the correlation function consisted of a modified Bessel function of the second kind, order 1, multiplied by its argument. This paper uses this pioneering work of Whittle to fit an aquifer head field to unequally spaced observations by maximum likelihood. Observational error is also included in the model. Both the isotropic and anisotropic cases are considered. The fitted field is then calculated on a two dimensional grid together with its standard deviation. The method is closely related to the use of two-dimensional splines for fitting surfaces to irregularly spaced observations.
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Jones, R.H. Fitting a stochastic partial differential equation to aquifer data. Stochastic Hydrol Hydraul 3, 85–96 (1989). https://doi.org/10.1007/BF01544074
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DOI: https://doi.org/10.1007/BF01544074