Our Local Average Subdivision (LAS) method is only used to generate the 2-D random field for 2D-Spatial Variability as stated in our theory manual, not for 1D Spatial Variability.
SVSLOPE uses Local Average Subdivision (LAS). This approach is a fast and accurate method of generating a homogeneous Gaussian scalar random process in one, two, or three dimensions. The resulting discrete process represent local average of a homogeneous random function defined by its mean and covariance function, the averaging being performed over incremental domains formed by different levels of discretization of the field. The approach is motivated first by the need to represent engineering properties as local averages (since many properties are not well defined at a point and show significant scale effect), and second to be able to easily condition the field to incorporate known data or change resolution within sub-regions.
In two dimensions, a rectangular domain is defined and the subdivision proceeds by dividing rectangles into 4 equal areas at each stage. In order to preserve the exact ‘within cell’ covariance structure, three random noises are added to three of the cell quadrants and the fourth quadrant is determined such that upwards averaging is preserved.
More details on this feature can be found in the slope stability theory manual 2021 Section 18.3.
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