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Most geostatistical methods rely on a global variogram model, assuming stationarity for the underlying random function. Applying stationary approaches in the case of large/complex areas, even locally with a moving neighbourhood, can lead to unsuitable estimates. Though preferable to some extent, non stationary approaches hardly handle prior knowledge nor reproduce precisely complex structures, such as local anisotropies, spatially varying small-scale structures or heterogeneity. The paper aims at presenting an innovative methodology, called M-GS (Moving-GeoStatistics), which is fully dedicated to the local optimization of parameters involved in variogram-based models. M-GS considers the structural and computational parameters as a set of dependant parameters to be spatially optimized. The optimization process, which may be guided by objective or subjective criteria, is carried out during a M-structural analysis phase that leads to a set of spatially variable structural and computational parameters. Thus, M-GS ensures a better adequacy between the geostatistical model and the data. 3 The methodology is applied for bathymetry mapping. The adequacy of the M-GS methodology is illustrated and compared with classical estimates for the Marenne-Oléron coast (West of France).

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