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Abstract
Modeling the geometry and volumes of alluvial infill at the bottom of river valleys is essential for a better understanding of river dynamics and alluvial storage, which buffers sedimentary signal transmission from source to sink. This study introduces kriging methods for predicting alluvial thickness geometries in the valley bottom using random fields with nonstationary geometric anisotropies. These anisotropies are constructed based on the contours of the alluvial plain. The two methods (one based on covariance and the other on Stochastic Partial Differential Equations (SPDE)) are compared to kriging with stationary anisotropies. The main parameters are estimated by maximum likelihood and the different methods are tested using cross-validation. The methods incorporating nonstationary anisotropies exhibit lower uncertainties than the stationary anisotropy approach and produce patterns that align more realistically with river geomorphic and sedimentologic knowledge. Evidence of braided patterns, riffle-pool geometry related to meandering, and scouring at confluences is observed at the scale of the valley width. Finally, it is estimated that about 2.30 km3 of alluvium is currently stored in the studied Oise valley bottom. Although the method was applied to an alluvial setting, it could be easily adapted to other geological contexts where anisotropy fields can be estimated, such as faulted and folded structures, supergene mineralization or environmental context to track pollutants dissemination in rivers.
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