The continuation parameter is chosen to be lnk the

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Unformatted text preview: = <dΦ/dx>, can be obtained from the exact analytical solution Φ(x) in a homogeneous aquifer, which corresponds to the asymptotic case σlnK → 0. Thus, asymptotically: (a )THEORY σ → 0: = a 0 + O (σ ) = 2 h0 + O (σ ε Lx ) (54) Table 2. Empirical and theoretical moments of the transformed potential ΦSALT(x,y). σ ln K 0 1 1.60 2.30 a = 1.54 ˆ a ≈ 1.54 ˆ a ≈ 1.40 ˆ a ≈ 1.33 ˆ σ Φ NUM σΦ = 0 ˆ σ Φ ≈ 17 ˆ σ Φ ≈ 27 ˆ σ Φ ≈ 42 ˆ σ Φ THEORY σΦ = 0 σ Φ ≈ 17 σ Φ ≈ 27.2 σ Φ ≈ 39.1 ˆ a NUM = dΦ dx To check whether “a” is nearly constant and close to its predicted value “a0”, consider the results summarized in Table 2. We conclude that the theoretical prediction of σΦ given by equation (52) with a ≈ a0 is robust. Finally - after some manipulations involving statistics from the Z-Φ transform (Eqs.(45),(46)) and the spectral solution for σΦ - one obtains, to first order: (a): σZSALT (x) ≈ c σlnK λlnK a or (b): σ ZSALT (x) ≈ c σ ln K λln K...
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This document was uploaded on 01/19/2014.

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