PROBLEMS INHERENT WITH 2D BALANCED CROSS SECTIONS

Retrodeforming geologic cross sections has taken place since the late 19th Century, mostly in foreland fold-thrust belts (FTBs). Assumption of plane strain is necessary retrodeform or construct balanced sections, and is probably valid in linear segments of FTBs (Zagros, Bolivian Andes, Alberta Rockies, Urals, Pyrenees), and in short segments of any FTB. In strongly (Ligurian Alps, Cantabrian Mountains) to moderately curved (southern/central Appalachians, Jura, Scottish Caledonides) thrust belts, however, incompatibilities arise that prevent the section construction process from meeting Elliott's minimal viability criterion. Retrodeformation of radiating 2–D sections produces overlap of their hinterland ends, making the incompatibility problem obvious. Various 2–D solutions have been proposed, but they generally fail. Retrodeformation of 2–D cross sections through plastic thrust sheets in the internides of orogens presents even greater difficulties; Ramsay has questioned the validity at all of constructing cross sections here. The obvious solution is to employ Laubscher's principles of 3–D material balancing in both FTBs and the interiors of mountain chains. Some computer software exists for use on personal computers that attempts 3–D balancing, but currently has major limitations because of the difficulties of writing codes that can incorporate more than one rheology (usually Coulomb) and varied material properties. Sophisticated finite-element codes that accommodate >1 rheology and a host of parameters are currently limited to 2–D. Current reality is the recognition that 3–D material balancing is needed, but we still are limited to almost hand methods to accomplish this. Possible solutions: (1) construct balanced 2–D cross sections through short, along-strike segments of FTBs; (2) conduct regional finite strain analysis to test for along-strike extension; and (3) construct and analyze displacement vector maps around curved segments of FTBs.