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Toward a solution of the 3D balancing problem in curved segments of orogens

Abstract Sections in strongly to moderately curved foreland fold-thrust belts may be restorable, but retrodeformation of two-dimensional (2D) serial sections produces overlap of their hinterland ends, making the incompatibility problem obvious. Outward-radiating displacement vectors predict along-strike stretching that increases toward the outer portions of arcuate foreland fold-thrust belts. Balancing of curved foreland fold-thrust belts becomes a three-dimensional (3D) material balance problem, involving non-plane strain. We propose a technique that will solve the 3D balancing problem if: (1) boundary pin lines, consisting of strike-boundary and normal-boundary lines, are present and identifiable; (2) a set of constant-length lines can be defined; (3) a set of section lines is constructed normal to tectonic strike; and (4) a set of boundary and internal constant-area regions is defined. This technique recognizes as false the unstated assumption that the deformed and undeformed state coordinate frames are identical. Accordingly, the displacement vector field of curved orogens does not parallel the deformed state strike normals. Instead, physically possible displacement vector fields require body rotations about a set of vertical axes during deformation, indicating that, during deformation, out-of-plane motions occur normal to the deformed-state strike normals relative to the external deformed-state coordinate frame. The final position of the plane strain surfaces parallels the deformed-state position of the strike normals, because they rotate into this position.