Estimation of sediment thickness by solving Poisson's equation with bedrock outcrops as boundary conditions

Abstract

Abstract Sediment thickness and bedrock topography are vital for the terrestrial hydrosphere. In this study, we estimated sediment thickness by using information from digital elevation models, geological maps, and public databases. We discuss two different approaches: First, the horizontal distances to the nearest bedrock outcrop were used as a secondary function in kriging and cokriging. Second, we applied Poisson's equation to estimate the local trend of the sediment thickness where bedrock outcrops were used as boundary conditions. Differences between point observations and the parabolic surface from Poisson's equation were minimized by inverse modelling. Ordinary kriging was applied to the residuals. These two approaches were evaluated with data from the Øvre Eiker, Norway. Estimates derived from Poisson's equation gave the smallest mean absolute error, and larger soil depths were reproduced better if the local trend was included in the estimation procedure. An independent cross-validation was undertaken. The results showed the best accuracy and precision for kriging on the residuals from Poisson's equation. Solutions of Poisson's equation are sensitive to the boundary conditions, which in this case were locations of the bedrock outcrops. Bedrock outcrops are available for direct observations; hence, the quality of the estimates can be improved by updating input from high-resolution mapping.