Modelling Bedrock Topography

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.