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

The classic work of Peach et al. (1892, 1907) is first set of quality geologic maps depicting the geometry of the Moine and related crystalline thrusts, and the foreland fold-thrust belt (FFTB) beneath. Modern detailed geologic maps (e.g., M. P. Coward, unpublished) have facilitated more detailed analysis of the Moine thrust zone. C. W. Hayes (1891) was mapping at the same time in the Georgia Appalachians and thinking about the consequences of retrodeformation of thrusts. High quality geologic maps in the Northwest Highlands and in other FFTBs worldwide, along with modern digital seismic reflection data, permit almost quantitative resolution of 2D thrust geometry. These yield the common shortened wedge, thin-skinned, ramp-flat, listric configurations characteristic of thrust belts that propagated into a wedge-shaped platform sequence. FFTBs worldwide are commonly driven toward continental interiors by either large crystalline thrust sheets generated during continent-continent collision, composite terrane or arc-continent collision, or ophiolite obduction. Retrodeformation and attempts to balance portions of linear FFTBs is more readily attainable than in curved segments. Plane strain can reasonably be assumed in linear FFTBs, making 2D sections amenable to line and area balancing. These have a good chance of meeting Elliott’s (1983) minimal viability criterion. Sections in strongly to moderately curved FFTBs may individually appear restorable, but retrodeformation of 2D serial sections produces overlap of their hinterland ends, making the incompatibility problem obvious. Moreover, outward radiating displacement vectors suggest there should be along-strike stretching that increases toward the outer portions of arcuate FFTBs. Evidence other than across-strike joints and veins is frequently lacking to support a stretching mechanism. Balancing of curved FFTB segments thus becomes a 3D material balancing problem (Laubscher, 1988), with major components of nonplane strain. 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 challenges. The obvious solution is to employ Laubscher’s 3–D material balancing principles in both FFTBs and orogenic interiors. It may be that our principles of restroration are incorrect. Computer software exists that attempts 3–D balancing, but currently is limited because of difficulties of writing codes that can incorporate multiple rheologies (more than Coulomb) and varied material properties. Sophisticated finite-element codes that accommodate more than one 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 hand methods and obtaining enough field data. Possible solutions: (1) construct balanced 2–D cross sections through short, acrossand along-strike segments of FFTBs, and (2) construct and analyze displacement vector (particle trajectory) maps around curved segments of FFTBs, but finding enough quality displacement vectors that yield the regional vector field (slip lines) to permit 3–D balancing is difficult. Populations of usable structures are limited and unevenly distributed. Determination of regional displacement vectors remains the key starting point, however, because they track finite strain and provide paths for retrodeformation of curved segments of orogens.