Gridding of Geological Surfaces based on Equality-Inequality Constraints from Elevation Data and Trend Data

要旨

In the field of geology, many gridding algorithms have been proposed so far. However, most of all algorithms take into account only equality constraints from elevation data. In this paper, we propose a gridding algorithm taking into account equality-inequality constraints from elevation data and trend data. The algorithm is designed to approximate a surface by bi-cubic B-spline and to determine an optimal surface using the exterior penalty function method. The optimal surface is the smoothest one that satisfies the given constraints. Through griddings for simple data sets, it is confirmed that the algorithm enables us to use elevation data and trend data as equality-inequality constraints on geological surfaces. Additionally, through griddings for practical data, it is confirmed that the algorithm is useful to determine a form of geological boundary surface, and that we can obtain an optimal surface even if we have a large number of constraints. In conclusion, this algorithm is more practicable than the one proposed before.