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

Abstract

[1] 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 kilometerscale 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 smallscale 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. Citation: Yonkee, A., and A. B. Weil (2010), Quantifying vertical axis rotation in curved orogens: Correlating multiple data sets with a refined weighted least squares strike test, Tectonics, 29, TC3012,

The Ainsa Fold and thrust oblique zone of the central Pyrenees: Kinematics of a curved contractional system from paleomagnetic and structural data

“…A strike test has been performed in order to evaluate changes in the paleomagnetic data with respect to the structural trend (Figure and Table S2 in supporting information) [ Schwartz and Van der Voo , ; Eldredge et al ., ; Lowrie and Hirt , ; Yonkee and Weil , ]. Application of this test is not straightforward in the study area, regardless the significant amount of available paleomagnetic data and the pronounced change of strike of the Ainsa Oblique Zone structures with respect the regional Pyrenean structural trend (Figure ).…”

Oroclinal origin of the Simao Arc in the Shan-Thai Block inferred from the Cretaceous palaeomagnetic data

“…To judge kinematic models of oroclinal formations, an oroclinal test (Schwartz & Van der Voo 1983; Yonkee & Weil 2010) and a fold test (McFadden's 1990) are applied (Figs 7 and 8). At first, an amount of rotation in the study area is estimated and then reconstructed for bringing the arcuate shape in to straight bedding attitude.…”

Tectonic evolution of a Laramide transverse structural zone: Sweetwater Arch, south central Wyoming

“…Orientations of bedding, dominant fracture sets, and minor faults and slip lineations (best developed in the Alcova Limestone) were measured at each site following the approach of Yonkee and Weil [] and Weil et al . [].…”

“…Three-axis thermal demagnetization of IRM was performed on the other 10 specimens. Applied fields of 2.0, 0.5, and 0.15 T were imparted along the three mutually perpendicular axes of each core [Lowrie, 1990] Orientations of bedding, dominant fracture sets, and minor faults and slip lineations (best developed in the Alcova Limestone) were measured at each site following the approach of Yonkee and Weil [2010a] and Weil et al [2014]. Idealized maximum compressive stress (σ 1 ) vectors were estimated for minor faults using the method of Compton [1966] and a 25°fracture angle, with site mean σ 1 directions and α 95 confidence ellipses calculated from individual stress vectors using the orientation tensor.…”

“…These relations are interpreted to record Figure 16. Strike tests for LPS and paleomagnetic data from the Sweetwater Arch calculated using method of Yonkee and Weil [2010a]. Example error bars show measurement uncertainty and structural trend uncertainty.…”