USING SYNTHETIC GRIDS TO TEST THE EFFECTIVENESS OF SPATIAL INTERPOLATION ALGORITHMS USED FOR 3-DIMENSIONAL SUBSURFACE MODELING

There are many spatial interpolation algorithms that can be used to construct 3-D subsurface models but it is important to select the algorithm that most accurately models the available data. Unfortunately, testing the accuracy of different model outputs created with ‘real world’ data is extremely difficult due to output validation issues. An alternate approach to testing algorithm effectiveness utilizes a synthetic data set to compare two most commonly used spatial interpolation algorithms (Inverse Distance Weighting and Ordinary Kriging) under varying sampling scenarios. In this research, four synthetic grids were created with known values. The synthetic grids represent surfaces of varying complexity that may be commonly found in geological environments; 1) a simple, gently sloping surface, 2) a channelized surface with two isolated highs on either side, 3) a surface with multiple, interconnecting channels and 4) a surface crossed by a sinuous, meandering channel. In order to identify how both the number of data points and the sampling pattern impacted the effectiveness of each algorithm on the interpolation process each of the four synthetic grids were sampled at least 3 times using different numbers of sample points (e.g. 256, 100, and 64) in the following 4 sampling patterns; random, regular, clustered, and sparse. This produced 96 different output grid models that were then compared to the original grid surfaces in order to identify and calculate amounts of variation between the original and modeled surfaces.

Output accuracy and variability were quantified using a range of statistical tests including Root Mean Square Error (RMSE), relative RMSE, Mean Average Error, Bias Error, and Correlation Coefficient. The resulting values were compared and used to establish recommendations as to which algorithm performs most effectively in situations of differing topographic complexity and with different numbers and distributions of data points. Initial results indicate that Ordinary Kriging is not always more effective than Inverse Distance Weighting in predicting the form of a surface, particularly in models representing complex geological environments.