An Eulerian approach to the problem of structural cross-section balancing

Abstract

In continuum mechanics, a deformation process can be described either using a Lagrangian reference frame or an Eulerian reference frame. The problem of balancing and restoration of cross- sections traditionally has been approached using the former reference frame in which the observer moves with the rocks as they deform. Under such reference frame an observer is only aware of changes in geometrical relationships among geological markers (distortion field). Geologists in turn use this information to build a model of the subsurface geometry that satisfies the stratigraphic principles of continuity of strata and bed area at a given time in the geologic past (cross section restoration). At the same time, the amount of area contained in the balanced and restored cross-section must be the same because mass must be conserved. Using classical results from continuum mechanics, this paper shows that the problem of balancing and restoration of cross-sections can also be characterized by the velocity field of the deformation process. This requires, however, using an Eulerian reference frame in which the observer remains stationary.