Non-stationary variogram models for geostatistical sampling optimisation: An empirical investigation using elevation data

A problem with use of the geostatistical Kriging error for optimal sampling design is that the design does not adapt locally to the character of spatial variation. This is because a stationary variogram or covariance function is a parameter of the geostatistical model. The objective of this paper was to investigate the utility of non-stationary geostatistics for optimal sampling design. First, a contour data set of Wiltshire was split into 25 equal sub-regions and a local variogram was predicted for each. These variograms were fitted with models and the coefficients used in Kriging to select optimal sample spacings for each sub-region. Large differences existed between the designs for the whole region (based on the global variogram) and for the sub-regions (based on the local variograms). Second, a segmentation approach was used to divide a digital terrain model into separate segments. Segment-based variograms were predicted and fitted with models. Optimal sample spacings were then determined for the whole region and for the sub-regions. It was demonstrated that the global design was inadequate, grossly over-sampling some segments while under-sampling others.

A Geostatistical Investigation into Changing Permeability of Sandstones During Weathering Simulations

The ability to predict the behavior of masonry materials is crucial to conserve building stone. Natural stone, such as sandstone, is not immune from the processes of weathering in the built environment and suffers from decay by granular disintegration, contour scaling, and multiple flaking. Spatial variation of rock properties is a major contributing factor to inconsistent responses to weathering. This has implications for moisture movement and salt input and output and storage, and results in unpredictability in the decay dynamics of masonry materials. This article explores the use of variography and kriging to investigate the spatial interactions between the trigger factors of stone decay, in particular, permeability and its effect on salt penetration. Sandstone blocks were used to represent fresh building stones from a weathering perspective and gave baseline characteristics for the interpretation of subsequent deterioration and decay pathways. Simulated weathering trials involved preloading a sandstone block with salt and subjecting a separate block to 20 cycles of a weathering trial designed to simulate a temperate weathering regime. Geostatistical analysis indicated differences in the spatial variation of permeability of the fresh rock and that subjected to the weathering regimes. Spatial prediction and visualization showed differences in the spatial continuity of permeability in a horizontal and vertical direction through the preloaded block after salt weathering. Continual wetting with salt and alternate heating increased permeability in a vertical direction, enabling the ingress and movement of salt and moisture more effectively through the stone.