Modeling of geological surfaces using finite elements. (English) Zbl 0815.65027

Springer, J.

Laurent, Pierre-Jean (ed.) et al., Wavelets, images, and surface fitting. Papers from the 2nd international conference on curves and surfaces, held in Chamonix-Mont-Blanc, France, June 10-16, 1993. Wellesley, MA: A K Peters. 467-474 (1994).

Summary: Geological surfaces are generally known incompletely and have to be reconstructed by use of interpolation methods. Some of these surfaces may be described by a continuous function \(z= u(x, y)\), where \(z\) is the vertical coordinate (depth). However, tectonic stresses cause discontinuities (faults) and complicated surfaces (folds).
In order to interpolate geological surfaces an algorithm is proposed which uses triangular finite elements. Among all functions satisfying the given constraints (\(u\) and possibly \(u_ x\) and \(u_ y\) at the data points) the sought function shall minimize an integral, the potential energy of a thin elastic plate.
For the entire collection see [Zbl 0805.00017].

MSC:

65D17	Computer-aided design (modeling of curves and surfaces)
65D05	Numerical interpolation
86A60	Geological problems

Keywords:

interpolation; geological surfaces; finite elements; thin elastic plate