Inverse problem assisted multivariate geostatistical model for identification of transmissivity fields - Kapoor, Aditya; Kashyap, Deepak (Frontiers in Water, 2024)
Groundwater models often require transmissivity (T) fields as an input. These T fields are commonly generated by performing univariate interpolation (kriging, IDW etc.) of the T data. This T data is derived from pumping tests and is generally limited due to the large costs and man-power requirements associated with the pumping tests. Hence T fields generated using this limited data may not be presentative for a whole study region.This study presents a novel cokriging based methodology to enhance the reliability of T fields.Cokriging -a multivariate geostatistical interpolation method permits incorporation of additional correlated auxiliary variables for the generation of credible fields. Here abundantly available saturated thickness (B) data has been used as secondary (auxiliary) data because of its correlation with the primary T data. Additionally, the proposed methodology addresses two operational problems related to cokriging. First operational problem is the poor estimation of variogram and cross-variogram parameters due to sparse data. Second problem is determining the relative contributions of primary and secondary variable in the estimation process. These two problems have been solved by proposing novel non-bias conditions and linking the interpolator with a head based inverse problem solution for credible estimation of these parameters.