EVALUATING THE ACCURACY OF LINEAR AND GEOSTATISTICAL INTERPOLATION METHODS IN SUBSURFACE MAPPING

The methods by which we model the Earth’s subsurface will always necessitate some form of interpolation; however the way in which we estimate these unknowns and the accuracy with which we can make these predictions has been improved. Further, inaccurate interpolation of subsurface geology can lead to wasted money and resources. This study seeks to compare the results of both linear and geostatistical interpolation methods utilizing a large sampling of boreholes drilled for a subsurface rock investigation at our study site in coastal Central America.

One way to determine the accuracy of an interpolated surface is to compare the values from the surface to additional values collected in the field. In this study, we divide a total population of nearly 500 borings into two parts; a random sampling of 75% of the borings are used as an input to each of the interpolated surfaces, and the remaining 25% are used to assess the surface’s accuracy. The linear interpolation method takes the larger 75% sampling of points, generates a triangulated irregular network (TIN), and converts the TIN to a raster. The same 75% sampling are also used to develop a surface through kriging interpolation, a geostatistical method. We then compare each interpolated surface to the values from the remaining 25% sample not used to generate the surface. The accuracy of each surface will be determined through the use of a three-dimensional root mean square error (RMSE) method. This workflow is used to create multiple iterations of each surface using a different random sampling every time and allowing summary statistics to be evaluated rigorously and consistently across the study.