Bootstrapped total least squares orocline test: A robust method to quantify vertical-axis rotation patterns in orogens, with examples from the Cantabrian and Aegean oroclines

Abstract

Most mountain belts on Earth show some degree of curvature in plan view, from a slight bend to horseshoe shapes. Such curvatures may occur on different scales, from individual thrust sheets to entire plate boundaries. Curvature may be acquired by vertical-axis rotation during or after orogenesis, or reflect primary lateral variations in shortening directions or physiographical features. Quantifying the amount of vertical-axis rotations of plan-view curvature is therefore helpful to our understanding of orogenesis, geodynamics, and paleogeography. The orocline test assesses to what extent vertical-axis rotations have played a role in the acquisition of an orogen's curvature. The test quantifies through linear regression the relationships between changes in structural trends and the orientations of a geologic fabric. However, the current mathematical approaches to the orocline test show potential biases. In this paper we aim to overcome such biases by developing a novel orocline test that applies total least squares (TLS) regression combined with a novel approach to bootstrapping. This bootstrap TLS orocline test can be used with all types of directional data acquired from structural geology, paleomagnetism, or sedimentology. It quantifies, for the first time, secondary curvature with confidence bands. We also provide several graphical and analytical tests to evaluate the statistical significance of the result. An open source online application implementing this method is available for use on www.paleomagnetism.org. We illustrate the use of the methodology by reanalyzing published data sets from two well-known oroclines in the Cantrabrian (northwest Iberia) and Aegean (Greece) regions.

Late Paleozoic Iberian Orocline(s) and the Missing Shortening in the Core of Pangea. Paleomagnetism From the Iberian Range

“…Paleomagnetic results from the core and southern limb of the Central Iberian curve show an overall rotation that fits with the attitude of the southern limb of the Cantabrian Orocline (Pastor‐Galán, Groenewegen, et al, ; Pastor‐Galán et al, ; Pastor‐Galán, Gutiérrez‐Alonso, et al, ; Pastor‐Galán, Mulchrone, et al, ). However, the timing constraints provided by these results established that no differential rotation occurred younger than ca.…”

“…Following the global apparent polar wander path of Torsvik et al () calculated for Iberia (given in Koymans et al, ) such low paleolatitude (6.4°S) would only be expected for Iberia in middle–late Carboniferous times, during the waning stages of the Variscan orogeny. The Variscan orogeny produced pervasive remagnetizations in Iberia (e.g., Pastor‐Galán, Gutiérrez‐Alonso, et al, ; Pastor‐Galán, Mulchrone, et al, ; Weil et al, ). Therefore, we suggest a Late Mississippian–Early Pennsylvanian (middle Carboniferous) secondary origin for Component #2.…”

“…Orogenic bends are classified based on the kinematics of their curvature development (e.g., Johnston et al, ). Correlations between changes in the structural grain and paleomagnetic directions or rock fabrics are evaluated using an orocline test (e.g., Pastor‐Galán, Gutiérrez‐Alonso, et al, ; Pastor‐Galán, Mulchrone, et al, , and references therein), which distinguishes two end‐members: (1) primary bends, showing a slope ( m ) = 0, and (2) secondary oroclines, with m = 1. Intermediate relations (0 < m < 1) are known as progressive oroclines.…”

“…However, the timing constraints provided by these results established that no differential rotation occurred younger than ca. 318 Ma, and therefore, if the Central Iberian curve is oroclinal, then it must have become secondarily curved prior to ~318 Ma (Pastor‐Galán, Gutiérrez‐Alonso, et al, ; Pastor‐Galán, Mulchrone, et al, ).…”

The enigmatic curvature of Central Iberia and its puzzling kinematics

“…The test originally used a basic leastsquares (OLS) regression (Schwartz and Van der Voo, 1983) to estimate the slope (coded m in formulas), ideally between 0 and 1, which then is interpreted with respect to vertical-axis kinematics. More recently, Yonkee and Weil (2010b) and Pastor- Galán et al (2017a) introduced more robust statistics to estimate the slope and its uncertainty, considering and propagating errors of the input data. Primary orogenic bends show no change of paleomagnetic declination orientations with varying structural trend, and therefore the slope is expected to be 0.…”