Inverse problem assisted multivariate geostatistical model for identification of transmissivity fields

Abstract

Groundwater models often require transmissivity (T) fields as an input. These T fields are commonly generated by performing univariate interpolation of the T data. This T data is derived from pumping tests and is generally limited due to the large costs and logistical requirements. Hence T fields generated using this limited data may not be representative for a whole study region. Groundwater models often require transmissivity (T) fields as an input. These T fields are commonly generated by performing univariate interpolation (using 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 logistical requirements. Hence, the T fields generated using this limited data may not be representative for the whole study region. This study presents a novel cokriging based methodology to generate credible T fields. Cokriging - a multivariate geostatistical interpolation method permits incorporation of additional correlated auxiliary variables for the generation of enhanced fields. Here abundantly available litholog derived saturated thickness data has been used as secondary (auxiliary) data given its correlation with the primary T data. Additionally, the proposed methodology addresses two operational problems of traditional cokriging procedure. The first operational problem is the poor estimation of variogram and cross-variogram parameters due to sparse T data. The second problem is the determination of relative contributions of primary and secondary variable in the estimation process. These two problems have been resolved by proposing a set of novel non-bias conditions, and linking the interpolator with a head based inverse problem solution for credible estimation of these parameters. The proposed methodology has been applied to Bist doab region in Punjab (India). Additionally, base line studies have been performed to elucidate the superiority of the proposed cokriging based methodology over kriging in terms of head reproducibility.