Modelling Bedrock Topography

Abstract

Abstract. The access to digital information from remote sensing; geological mapping; and public databases give an opportunity to express the surface of the bedrock as a mathematical estimation problem. We modelled the bedrock topography as a stochastic function in space. The function is given with high precision in areas where the bedrock is exposed to the surface, but unknown in areas covered by sediments except for a limited number of point information (viz boreholes; wells; geotechnical surveys). Two different approaches were evaluated to reveal the local trend of the bedrock surface: Firstly, we applied the statistical relation between the horizontal distance (L) to the nearest bedrock outcrop and the observed sediment depth (D) in boreholes. The relation between D and L was applied in ordinary kriging and cokriging to include the local trend in the estimation. Secondly, we applied inverse modelling of the Poisson s equation to model the local trend. After minimizing the difference between the point observations and the parabolic surface from the Poisson s equation, we did ordinary kriging of the residuals between the optimal parabolic function and the observations. These approaches were tested against observations from a test site. Estimates derived from the Poisson s equation gave a lowest mean absolute error for cross-validation by leaving one observation out. Ordinary kriging gave a least mean absolute error when an independent dataset was used for cross-validation. The results show that the extreme large soil depths were better reproduced if the local trend was included in the estimation procedure.