Application of multi-fractal and Kriging interpolation method for the re-construction of strata

In order to generate 3-dimensional (3D) strata, a stratum data model of tri-prism based on borehole data is first presented, which is applicable in geologi- cal engineering and geotechnical engineering. Due to the local variance and spatial structure among attributes of boreholes, the geological properties at unknown lo- cation have to be estimated or interpolated by some special methods. However, classic statistical methods could not resolve such problem which includes selection of sample points, spatial estimation and comparison of bilateral data. A distance- weighted interpolation method for scattered borehole data points is proposed in this paper, which exploits the Kriging method in global geostatistics. On the premise that the distributed statistics characters of the spatial borehole data were obtained at first, accorded to the distributed statistics characters, the spatial interpolation was presenting successively. Moreover, multi-fractal is presented to depict the local singularity which should be ignored by sliding weighted average algorithm such as Kriging method. Case study shows that the generation of 3D strata by proposed interpolation methods could give a good result in global and local occasion.