Geo-Modelling and Geo-Informatics

   doi:10.3850/978-981-07-0188-8_P100

ABSTRACT

In the interpolation of spatial data, as the difference of distance, sparse extent, direction and data values among the sampling points, it requires interpolation and extrapolation for the unknown spatial characteristics outside of the sampling points. The traditional methods of mathematical statistics did not be good at selecting sampling point solution, spatial anisotropic estimating and spatial analysis among the sampling point’s data. Based on the geostatistical method, this paper carries out spatial interpolation based on variability characteristics of spatial data on different orientation. This paper also put to use Multi Fractal theory with Kriging interpolation method to overcome the local smooth defects of semi-variation function and Kriging linear equations. Multi Fractal theory improve the smooth distribution of spatial variability by Kriging interpolation method and measure the local singularity of spatial data distribution based on filtering of spatial self-similarity. Finally, according to an example of reconstruction of three-dimensional digital strata based on drilling information of engineering geology, the method is verified to obtain good interpolation results and solve the spatial distribution of the local singularity.

Keywords: Spatial interpolation, Kriging, Multi fractal, Local singularity.

© 2012 by Geotechnical Society of Singapore (GeoSS)