Fractal interrelationships between topography and structure

Abstract

Factal interrelationships between topography and structure are investigated in two areas of the North American central Appalachian Mountains: one in the intensely deformed Valley and Ridge province and the other in the relatively undeformed foreland area of the Appalachian Plateau province. In the Valley and Ridge province the fractal dimensions of topographic and structural relief vary systematically along the strike of major folds following a second-order polynominal trend. Cross-correlation of the fractal dimensions of topography to structure indicates that there is a significant positive correlation between the two. Fractal analysis of topography in the relatively undeformed foreland area of the Appalachian Plateau revealed no significant variation in the fractal characteristics of topography across the study area, consistent with the lack of near-surface structure. However, fractal analysis of deeper structures beneath the Plateau area undertaken using reflection seismic data revealed step-wise increases in fractal dimension from the deeply buried Precambrian basement to the near-surface. These vertical changes in fractal dimension can be related to the tectonic history of the area. Taken together, these studies indicate that fractal analysis provides a means to quantify and compare the influence of near-surface structure on topographic development and lateral and vertical structural variability. Fractal analysis provides a means to characterize the systematic changes in the complex patterns formed by topography and structure and the interrelationships between them. Similarity in their fractal characteristics implies similarity in the relative amplitude and abundance of different wavelength features in the topographic or structural profile. © 1998 John Wiley & Sons, Ltd.