Stratigraphic uncertainty and errors in shortening from balanced sections in the North American Cordillera

Shortening from balanced cross sections is typically cited as a minimum estimate because of the uncertainty in the position of eroded hanging-wall cutoffs. We show here using area balancing that the single most significant source of error is that associated with the shape and thickness of the initial stratigraphic wedge involved in the deformation. New methods and software are introduced that, in combination with freely available scans of virtually all geologic maps published by the U.S. Geological Survey (USGS) and Geological Survey of Canada (GSC), allow one to make hundreds of map thickness measurements in just a few hours. These methods are applied to geologic maps and cross sections from the western North American Cordillera to determine the uncertainty of shortening in iconic cross sections by R.A. Price and P.R. Fermor, and by F. Royse. One-sigma stratigraphic thickness uncertainty, measured in homoclinal dip packages of prominent Paleozoic units within single thrust plates (and single quadrangles), ranges from 20% to 30% of average thickness in the Costigan and Sulfur Mountain plates in southern Canada and can be as high as 37% in the Darby and Absaroka plates of the Idaho-Wyoming (United States) thrust belt. Assuming that all individual Paleozoic units in the cross sections have similar errors, the entire Paleozoic section used in the area balancing would have 8%–11% uncertainty, assuming a normal or Gaussian distribution. Because the stratigraphic wedges in southern Canada and Idaho-Wyoming do not have a uniform original taper, our basic area balance underestimates shortening. By balancing the non-uniform taper back to a uniform taper, we can account for this discrepancy. Total shortening determined in this way is ∼104 ± 17 km, which is identical to that obtained by Price and Fermor. The Idaho-Wyoming section of Royse (with maps by the USGS) yields similarly large errors in shortening magnitude: 56 ± 10 km for the three frontal thrust faults. Of those errors, uncertainty in the shape and thickness of the initial stratigraphic wedge accounts for 56% and 70% of the total in southern Canada and western Wyoming, respectively. Eroded hanging-wall cutoffs account for just 15% in both areas, with the remainder coming from uncertainty in the subsurface geometry, including the position of the decollement.