Assessing uncertainties in balanced cross sections

Balanced structural cross sections are models that are fit to incomplete data. The models are under-constrained with respect to any particular two-dimensional line-length model, but enough data generally exists to yield a well-constrained area balance solution. Furthermore, the area balance encompasses all possible line-length solutions. Therefore, where the primary objective of section balancing is the determination of horizontal shortening magnitude, area balancing provides an analytical solution. We use this analytical solution to develop a comprehensive, robust analysis of the uncertainty in shortening estimates resulting from cross-section balancing. The analytical solution allows us to propagate errors formally on the input parameters — stratigraphic thicknesses, depth to decollement, eroded hanging wall cutoffs — through the equations and produce the resulting uncertainty on the magnitude of shortening. Balanced cross sections from the Subandean belt of the Central Andes are used to demonstrate the relative importance of stratigraphy and eroded hanging wall cutoffs in the contribution to the overall error.

► Prior to the current work, there existed no rigorous, quantitative evaluation of errors in balanced cross section except for a few models amenable to numerical simulation.
► We use analytical propagation of errors in area balancing, which accounts for all possible 2D kinematic fold-fault models, incorporates detailed deformation below the scale/resolution of the cross section, and is computationally simple.
► Using previously published cross sections from the Central Andes, we show that errors are substantially larger than implied in previous work.
► The single largest source of error is poorly known stratigraphic thicknesses. These are far more important than eroded hanging wall cutoffs or uncertainty about depth to decollement.