Using paleomagnetism to test rolling hinge behaviour of an active low angle normal fault, Papua New Guinea

<p>Metamorphic core complexes (MCC) are widespread in extensional tectonic environments. Despite their significant contribution to extension in rifts, little is known about the origin and evolution of metamorphic core complexes. Particular controversy regards the origin of the typically shallowly dipping (<30°) detachment fault that bounds the footwall core of metamorphic rocks. According to Andersonian faulting theory, normal faults should initiate at a dip of ~60° and frictionally lock up and stop slipping at dips of <30°. One possible solution to this problem is a rolling hinge evolution for the fault. In this scenario the fault initiates at a steep dip of ~60° and evolves to a shallower dip during slip due to the rebound of the footwall in response to progressive unloading as the hangingwall is removed (Wernicke & Axen, 1988; Buck, 1988; Hamilton, 1988). Large rotations of the footwall, indicative of rolling hinge style deformation, may conceivably be measured by comparing the remanent paleomagnetic vector of the footwall rocks with the expected direction of the geomagnetic field at the site where the remanent magnetization was acquired. Using these techniques, large rotations of footwall rocks consistent with rolling hinge style deformation have been demonstrated for the footwalls of oceanic core complexes (Garcés & Gee, 2006; Zhao & Tominaga, 2009; Morris et al., 2009; MacLeod et al., 2011), but not for continental MCCs. In this study we attempt to test, using the remanent magnetization of the footwall rocks, whether rolling hinge style rotations have affected the footwall of the Mai’iu fault, Papua New Guinea. The Mai’iu fault, located in the continental Woodlark Rift, is a rapidly slipping (~1 cm/yr) (Wallace et al., 2014; Webber et al., 2018), shallowly-dipping (<22° at the surface) normal fault (Spencer, 2010; Little et al., 2019) responsible for the Pliocene-Recent exhumation of the domed Suckling-Dayman MCC, which is comprised mostly of Goropu Metabasalt. The remanent magnetization of forty-four samples of footwall Goropu Metabasalt were measured for this study. Close to the fault trace (<1.5 km) a moderately inclined, northerly trending, normal component of magnetic remanence is preserved (Dec: 351.1°, Inc: -35.7°, α₉₅: 6.8°, N= 18 sites). Farther to the south, and up-dip of the fault trace (>1.5 km to 10 km from the fault trace) a normal component is observed in the lower blocking temperature range (Dec: 347.2°, Inc: -41.7°, α₉₅: 9.4°, N= 7 sites) (up to 300-400°C) that we interpret to be equivalent to the normal component present in samples closer to the fault trace. The maximum (un)blocking temperature to which the normal component is carried decreases with increasing distance up-dip and away from the fault trace. In the higher blocking temperature range a southerly trending, reversed component of magnetization is preserved that is more steeply inclined than the component mentioned above (Dec: 177.2°, Inc: 57.1°, α₉₅: 7.3°, N= 8 sites). We interpret the moderately-inclined normal component in both regions to be a recent component of magnetization to have been acquired during the exhumation of the Goropu Metabasalt over the last 780,000 years (Brunhes chron). The origin of the older, reversed component is less clear; however, we prefer the interpretation that this component is also an exhumational overprint that was acquired between 2,600,000-780,000 years ago during the Matuyama chron. Comparison of the direction of the average normal component of both Group 1 and Group 2 samples (Dec: 350.6°, Inc: -37.1°, α₉₅: 5.4°, N= 25 sites) with the expected direction of the geomagnetic field at the paleomagnetic sampling locality indicates that 23.9 ± 2.6° (1σ) of back-rotation about a sub-horizontal axis sub-parallel to fault strike has affected the footwall of the Mai’iu fault. Taking into account the known dip of the fault at the surface of <20-22°, this rotation value implies an original fault dip at depth of 41.3-48.5° that is inherited from a paleo-subduction zone. This result is remarkably consistent with other estimates of the original fault dip: for example, geologically observed fault-bedding cut-off angles on an upper plate imbricate (rider) block imply an original fault dip of ~40-49° (Little et al., 2019). Also, microseismicity between 10-25 km depth implies a modern dip there of 30-40° (Eilon et al., 2015; Abers et al., 2016). This study is the first of its kind to use paleomagnetism to demonstrate that substantial rolling hinge style rotations have affected the footwall of a continental MCC.</p>

Using paleomagnetism to test rolling hinge behaviour of an active low angle normal fault, Papua New Guinea

<p>Metamorphic core complexes (MCC) are widespread in extensional tectonic environments. Despite their significant contribution to extension in rifts, little is known about the origin and evolution of metamorphic core complexes. Particular controversy regards the origin of the typically shallowly dipping (<30°) detachment fault that bounds the footwall core of metamorphic rocks. According to Andersonian faulting theory, normal faults should initiate at a dip of ~60° and frictionally lock up and stop slipping at dips of <30°. One possible solution to this problem is a rolling hinge evolution for the fault. In this scenario the fault initiates at a steep dip of ~60° and evolves to a shallower dip during slip due to the rebound of the footwall in response to progressive unloading as the hangingwall is removed (Wernicke & Axen, 1988; Buck, 1988; Hamilton, 1988). Large rotations of the footwall, indicative of rolling hinge style deformation, may conceivably be measured by comparing the remanent paleomagnetic vector of the footwall rocks with the expected direction of the geomagnetic field at the site where the remanent magnetization was acquired. Using these techniques, large rotations of footwall rocks consistent with rolling hinge style deformation have been demonstrated for the footwalls of oceanic core complexes (Garcés & Gee, 2006; Zhao & Tominaga, 2009; Morris et al., 2009; MacLeod et al., 2011), but not for continental MCCs. In this study we attempt to test, using the remanent magnetization of the footwall rocks, whether rolling hinge style rotations have affected the footwall of the Mai’iu fault, Papua New Guinea. The Mai’iu fault, located in the continental Woodlark Rift, is a rapidly slipping (~1 cm/yr) (Wallace et al., 2014; Webber et al., 2018), shallowly-dipping (<22° at the surface) normal fault (Spencer, 2010; Little et al., 2019) responsible for the Pliocene-Recent exhumation of the domed Suckling-Dayman MCC, which is comprised mostly of Goropu Metabasalt. The remanent magnetization of forty-four samples of footwall Goropu Metabasalt were measured for this study. Close to the fault trace (<1.5 km) a moderately inclined, northerly trending, normal component of magnetic remanence is preserved (Dec: 351.1°, Inc: -35.7°, α₉₅: 6.8°, N= 18 sites). Farther to the south, and up-dip of the fault trace (>1.5 km to 10 km from the fault trace) a normal component is observed in the lower blocking temperature range (Dec: 347.2°, Inc: -41.7°, α₉₅: 9.4°, N= 7 sites) (up to 300-400°C) that we interpret to be equivalent to the normal component present in samples closer to the fault trace. The maximum (un)blocking temperature to which the normal component is carried decreases with increasing distance up-dip and away from the fault trace. In the higher blocking temperature range a southerly trending, reversed component of magnetization is preserved that is more steeply inclined than the component mentioned above (Dec: 177.2°, Inc: 57.1°, α₉₅: 7.3°, N= 8 sites). We interpret the moderately-inclined normal component in both regions to be a recent component of magnetization to have been acquired during the exhumation of the Goropu Metabasalt over the last 780,000 years (Brunhes chron). The origin of the older, reversed component is less clear; however, we prefer the interpretation that this component is also an exhumational overprint that was acquired between 2,600,000-780,000 years ago during the Matuyama chron. Comparison of the direction of the average normal component of both Group 1 and Group 2 samples (Dec: 350.6°, Inc: -37.1°, α₉₅: 5.4°, N= 25 sites) with the expected direction of the geomagnetic field at the paleomagnetic sampling locality indicates that 23.9 ± 2.6° (1σ) of back-rotation about a sub-horizontal axis sub-parallel to fault strike has affected the footwall of the Mai’iu fault. Taking into account the known dip of the fault at the surface of <20-22°, this rotation value implies an original fault dip at depth of 41.3-48.5° that is inherited from a paleo-subduction zone. This result is remarkably consistent with other estimates of the original fault dip: for example, geologically observed fault-bedding cut-off angles on an upper plate imbricate (rider) block imply an original fault dip of ~40-49° (Little et al., 2019). Also, microseismicity between 10-25 km depth implies a modern dip there of 30-40° (Eilon et al., 2015; Abers et al., 2016). This study is the first of its kind to use paleomagnetism to demonstrate that substantial rolling hinge style rotations have affected the footwall of a continental MCC.</p>

Strain accuracy enhancement of stereo digital image correlation for objects deformation with large rotations

We propose a full-field stereo digital image correlation (DIC) strain measurement method in order to overcome the poor accuracy while measuring the deformation under large rotations. Such drawback comes from the missing of considering rotation movements of the deformed objects when calculating their strain values. To address that, we first used a DIC matching algorithm combined with rotated subset and feature point detection to obtain displacement fields. By employing a singular value decomposition (SVD) method, we then can calculate rotation matrices of the strain windows before and after deformations. Finally, in order to eliminate the strain errors caused by rotation, we introduced the rotation matrices into the classical pointwise least square (PLS) DIC strain calculation method. Both numerical simulations and experiments are performed, and the accuracy and effectiveness of the proposed method are confirmed by the experimental results.

Investigation of a novel 2R1T parallel mechanism and construction of its variants

A 3-RRPRR variable spherical symmetrical parallel mechanism (PM) with arc-shaped sliding pairs and no parasitic motion is presented, exhibiting two rotational and one translational (2R1T) degrees of freedom. Three limbs are symmetrically distributed between the base and end-effector; upper and lower parts of each limb are mirror symmetrical around the middle. The geometry, mobility, forward/inverse kinematics, workspace, and parasitic motion of the mechanism are analyzed, showing its ability to achieve large rotations around a continuous rotation axis. Finally, a structure synthesis strategy for variable spherical symmetrical PM is proposed, and several limb types meeting the conditions are obtained.

BEAM ELEMENT UNDER FINITE ROTATIONS

The present work focuses on the 2-D formulation of a nonlinear beam model for slender structures that can exhibit large rotations of the cross sections while remaining in the small-strain regime. Bernoulli-Euler hypothesis that plane sections remain plane and perpendicular to the deformed beam centerline is combined with a linear elastic stress-strain law.The formulation is based on the integrated form of equilibrium equations and leads to a set of three first-order differential equations for the displacements and rotation, which are numerically integrated using a special version of the shooting method. The element has been implemented into an open-source finite element code to ease computations involving more complex structures. Numerical examples show a favorable comparison with standard beam elements formulated in the finite-strain framework and with analytical solutions.

Analysis of the Nonlinear Response of Piezo-Micromirrors with the Harmonic Balance Method

In this work, we address the simulation and testing of MEMS micromirrors with hardening and softening behaviour excited with patches of piezoelectric materials. The forces exerted by the piezoelectric patches are modelled by means of the theory of ferroelectrics developed by Landau–Devonshire and are based on the experimentally measured polarisation hysteresis loops. The large rotations experienced by the mirrors also induce geometrical nonlinearities in the formulation up to cubic order. The solution of the proposed model is performed by discretising the device geometry using the Finite Element Method, and the resulting large system of coupled differential equations is solved by means of the Harmonic Balance Method. Numerical results were validated with experimental data collected on the devices.