Mapping Curvilinear Structures with Local Anisotropy Kriging

Abstract

Interpolating geo-data with curvilinear structures using geostatistics is often disappointing. Channels, for example, become disconnected sets of lakes when interpolated from point data. In order to improve the interpolation of geological structures (e.g., curvilinear structures), we present a new form of kriging, local anisotropy kriging (LAK). Local anisotropy kriging combines a gradient algorithm from image analysis with kriging in an iterative way. After an initial standard kriging interpolation, the gradient algorithm determines the local anisotropy for each cell in the grid using a search area around the cell. Subsequently, kriging is carried out with the spatially varying anisotropy. The anisotropy calculation and subsequent kriging steps will then succeed until the result is satisfactory in the way of reproducing the curvilinear structures. Depending on the size of the search area more or less detail in the geological structures can be reproduced with LAK. Using test examples we show that LAK interpolates data with curvilinear structures more realistically than standard kriging. In a real world case, using bathymetric data of the Oosterschelde estuary, LAK also proves to be quantitatively superior to standard kriging. Absolute interpolation errors are decreased by 23%. Local anisotropy kriging only uses information from point data, which makes the method very objective, it only presents “what the data can tell.”