The utilization of soft transformation and genetic algorithm to model two sources of uncertainty of Indicator Kriging

Abstract

Abstract Indicator Kriging (IK) is a geostatistical method that uses observation points to quantify the probabilities at which a set of thresholds are exceeded at unmeasured points. To improve IK accuracy, the interpolation process should consider its uncertainty sources. By doing this, we also maintain its ability to provide the conditional cumulative distribution function (ccdf), which is a reliable measure of local uncertainty. This study modeled two IK uncertainty sources, i.e., measurement errors attached to observation points and subjective threshold choices. Soft Indicator Kriging (SIK), which uses a soft transformation for observation points, considers the measurement errors of these two sources. To select the thresholds objectively, a genetic algorithm (GA) was performed to obtain the optimum set of thresholds related to an objective function, which minimized the mean absolute error (MAE). The data used was a collection of 1889 gravitational acceleration points from Kordagh, Golestan, Iran. We used 95 points from those points to calculate the MAE values (jackknife). After applying GA to SIK and reaching the Genetic optimized Soft Indicator Kriging method (GSIK), our results showed a decrease in MAE (6.5925) compared to those of SIK and IK (8.4364 and 8.4366, respectively). Moreover, the coefficient of determination ( R 2 ) was used as another criterion to compare the methods. A more reliable method has a higher R 2 value; in this study, this value was 0.8683 for GSIK compared to those of SIK and IK (0.8423 and 0.8421, respectively). GSIK can improve the accuracy of the basic IK method.