The numerical results are then analysed in terms of

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Unformatted text preview: Fig. 5 Transverse profiles of ZSALT(x) (the seashore is at left) : comparison of mean ZSALT (x) (shorewise average) with 100 distinct transects of ZSALT(x,yn) sampled at equally spaced shorewise positions (yn). Simulation grid : 1000x1000. Heterogeneity: σ = ln10 65 Modélisation stochastique de l'intrusion saline en 2D plan 66 Using a Taylor expansion cut off to 2nd order, yields: σφ ϕ ⎛1 ⎞ (45) Z ≈ 1 − φ 1 / 2 ⎜1 − τ 2 + O κ 3 ⎟ ; τ = ;κ= φ φ 8 ⎝ ⎠ We finally substitute Eq. (45) into Eq. (42) to calculate the standard deviation of Z. Neglecting 4 τ /64 and other “higher order terms” (“h.o.t.”), we obtain: 1 σφ (46) + h.o.t. σZ ≈ 2φ () This analytical expression can be used to predict σZ using either numerical estimates or theoretical spectral estimates of φ-statistics : the two procedures yield similar results (see comments about Fig. 6 further below). 6.2 Statistics of transformed potential via spectral theory We know need to determine the statistical moments of Φ, e.g. mean and variance. Two approaches are possible concerning the transformed potential Φ: a) Empirical evaluation of Φ-moments (sampling numerical simulation); b) Theoretical evaluation of Φ-moments (analytical spectral perturbation). Empirically, the first two lines in Tab...
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This document was uploaded on 01/19/2014.

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