Quantifying vertical axis rotation in curved orogens: Correlating multiple data sets with a refined weighted least squares strike test

Abstract

Map‐scale curvature is a fundamental feature of most contractional orogenic belts and is central to understanding the kinematic and dynamic evolution of mountain systems. Paleomagnetic analysis, combined with detailed structural studies, is the most robust means of quantifying vertical axis rotations that produce curvature over a range of temporal and spatial scales. This paper explores how vertical axis rotations can best be evaluated for multiple data sets by applying a weighted least squares method to the classic strike test. This refined method provides measures of best fit slope, confidence interval, and goodness of fit between map‐scale structural trend, paleomagnetic rotations, and deformation fabric orientations. Structural trend is estimated by averaging fold axial trace, formation contact, and bed strike data over kilometer‐scale areas. Paleomagnetic and deformation fabric site‐mean orientations and measurement uncertainties are estimated using vector and bootstrap statistics. Weighting factors are estimated from combined measurement uncertainty, structural noise related to small‐scale block rotation and stress/strain refraction, and variations in restoration paths. The number of sites needed to obtain a significant confidence interval in strike test slope is a function of combined uncertainty in paleomagnetic or deformation fabric directions and the total range in structural trend around a curved orogen. Improved estimates of strike test slope and rotation thus require systematic sampling with a wide distribution of sites, evaluation of appropriate weighting factors, and statistical analysis. A case study is presented that highlights application of this refined method to paleomagnetic and deformation fabric data sets from the Wyoming salient of the Sevier thrust belt. Paleomagnetic data yield a strike test slope of 0.76 ± 0.11, indicating that the Wyoming salient is a progressive arc, with ∼3/4 secondary curvature related to vertical axis rotation synchronous with large‐scale thrusting and ∼1/4 initial curvature. Finite strain, anisotropy of magnetic susceptibility, and mesoscopic structural orientations, which are related to early layer‐parallel shortening, all yield strike test slopes of ∼0.9 ± 0.1. Comparing these slopes with paleomagnetic results indicates that deformation fabrics had initial curvature and thus cannot be used alone to accurately estimate rotations. By integrating systematic paleomagnetic and structural data using statistical analysis, curvature models for the Wyoming salient are closely constrained.