Fragility and excluded minors

<p>Let Ɲ be a set of matroids. A matroid, M, is Ɲ -fragile, if for every element e, either M\e or M/e has no minor isomorphic to a member of Ɲ . This thesis gives new results in matroid representation theory that elucidate the relationship between Ɲ -fragile matroids and excluded minors. Let ℙ be a partial field, and let Ɲ be a set of strong stabilizers for ℙ. The first main result of this thesis establishes a relationship between Ɲ -fragile matroids and excluded minors for the class of ℙ-representable matroids. We prove that if an excluded minor M for the class of ℙ-representable matroids has a pair of elements a,b such that M\a,b is 3-connected with an Ɲ -minor, then either M is close to an Ɲ -minor or M\a,b is Ɲ -fragile. The result motivates a study of the structure of ℙ-representable Ɲ -fragile matroids. The matroids U₂,₅ and U₃,₅ are strong stabilizers for the U₂ and H₅ partial fields. The second main result of this thesis is a structural characterisation of the U₂- and H₅-representable {U₂,₅,U₃,₅}-fragile matroids. We prove that these matroids can be constructed from U₂,₅ and U₃,₅ by a sequence of moves, where, up to duality, each move consists of a parallel extension followed by a delta-wye or a generalised delta-wye exchange. Finally, we obtain a bound on the size of an excluded minor M for the class of U₂- or H₅-representable matroids with the property that M has a pair of elements a,b such that M\a,b is 3-connected with a {U₂,₅,U₃,₅}-minor. Our proof uses the first and second main results of this thesis.</p>

Fragility and excluded minors

<p>Let Ɲ be a set of matroids. A matroid, M, is Ɲ -fragile, if for every element e, either M\e or M/e has no minor isomorphic to a member of Ɲ . This thesis gives new results in matroid representation theory that elucidate the relationship between Ɲ -fragile matroids and excluded minors. Let ℙ be a partial field, and let Ɲ be a set of strong stabilizers for ℙ. The first main result of this thesis establishes a relationship between Ɲ -fragile matroids and excluded minors for the class of ℙ-representable matroids. We prove that if an excluded minor M for the class of ℙ-representable matroids has a pair of elements a,b such that M\a,b is 3-connected with an Ɲ -minor, then either M is close to an Ɲ -minor or M\a,b is Ɲ -fragile. The result motivates a study of the structure of ℙ-representable Ɲ -fragile matroids. The matroids U₂,₅ and U₃,₅ are strong stabilizers for the U₂ and H₅ partial fields. The second main result of this thesis is a structural characterisation of the U₂- and H₅-representable {U₂,₅,U₃,₅}-fragile matroids. We prove that these matroids can be constructed from U₂,₅ and U₃,₅ by a sequence of moves, where, up to duality, each move consists of a parallel extension followed by a delta-wye or a generalised delta-wye exchange. Finally, we obtain a bound on the size of an excluded minor M for the class of U₂- or H₅-representable matroids with the property that M has a pair of elements a,b such that M\a,b is 3-connected with a {U₂,₅,U₃,₅}-minor. Our proof uses the first and second main results of this thesis.</p>

Geometry, kinematics, and magnitude of extension across the Thakkhola Graben, Central Nepal Himalaya

The Thakkhola Graben has been a region of geologic inquiry for many decades. Although it is widely viewed to be in a class of structures that are important in accommodating the three-dimensional strain within the Himalayan thrust wedge, we still lack a detailed understanding of the total finite strain accommodated by graben-bounding faults, as well as their shape and cross-cutting relationships with structures deeper in the thrust wedge. Using geologic mapping and structural analysis, we show that a suite of pre-extensional shortening structures is offset by normal-oblique faults bounding the Thakkhola Graben that we use to define a piercing line. We calculate these faults to have accommodated 8.7 kilometers of vertical thinning, 7.2 kilometers of arc-perpendicular shear, and only 2.2 kilometers of arc-parallel extension. The magnitude of arc-parallel extension is quite low compared to extensional structures to the west in the Gurla Mandhata-Humla region. The cross-cutting relationships established in this study and timing constraints determined by previous works are consistent with a structural history of crustal thickening leading to foreland propagation of the locus of arc-perpendicular shortening contemporaneous with hinterland extension.

A thermal event in the Dolpo region (Nepal): a consequence of the shifting from orogen perpendicular to orogen parallel extension in central Himalaya?

In the Lower Dolpo Region (central Himalaya), structurally above the South Tibetan Detachment System (STDS), blastesis of static micas have been recognized. Nevertheless, until now, very little work has been done to constrain the tectonic meaning and the timing of this static mica growth. In this work we investigate samples from the STDS hanging wall, characterized by three populations of micas, defining (i) S1 and (ii) S2 foliations, and (iii) M3 static mineral growth cutting both foliations. New geochronological 40Ar/39Ar analyses on the microtexturally-different micas, complemented by microstructural and compositional data, allow to place temporal constraints on the static (re)crystallization at the STDS hanging wall. Results point out homogeneous chemical compositions and ages of micas within the investigated samples, irrespective of the structural positions. Phlogopite and muscovite on S1 and S2, and post-kinematic biotite yielded 40Ar/39Ar ages within 14-11 Ma with decreasing ages upward. We suggest that mica (re)crystallized under static conditions during a late thermal event at low structural levels (c. 15-18 km), after cessation of the ductile activity of the shear zone. We hypothesize that this later thermal event is kinematically linked to the switch from orogen perpendicular to orogen parallel extension in central Himalaya.Supplementary material: [Electron microprobe analyses of biotite and white mica] is available at https://doi.org/10.6084/m9.figshare.c.5509998Thematic collection: This article is part of the Isotopic Dating of Deformation collection available at: https://www.lyellcollection.org/cc/isotopic-dating-of-deformation

Temporal changes in pore fluid pressure during slow earthquake cycle estimated from foliation-parallel extension cracking

&lt;p&gt;Pore fluid pressure (P&lt;sub&gt;f&lt;/sub&gt;) is of great importance to understand slow earthquake mechanics. In this study, we estimated the pore fluid pressure during the formation of foliation-parallel quartz veins filling mode I cracks in the Makimine m&amp;#233;lange eastern Kyushu, SW Japan. The m&amp;#233;lange preserves quartz-filled shear veins, foliation-parallel extension veins and subvertical extension tension vein arrays. The coexistence of the crack-seal veins and viscously sheared veins (aperture width of a quartz vein: a few tens of microns) may represent episodic tremor and slow slip (Ujiie et al., 2018). The foliation-parallel extension cracks can function as the fluid pathway in the m&amp;#233;lange. We applied the stress tensor inversion approach proposed by Sato et al. (2013) to estimate stress regimes by using foliation-parallel extension vein orientations. The estimated stress is a reverse faulting stress regime with a sub-horizontal &amp;#963;&lt;sub&gt;1&lt;/sub&gt;-axis trending NNW&amp;#8211;SSE and a sub-vertical &amp;#963;&lt;sub&gt;3&lt;/sub&gt;-axis, and the driving pore fluid pressure ratio P* (P* = (P&lt;sub&gt;f&lt;/sub&gt; &amp;#8211; &amp;#963;&lt;sub&gt;3&lt;/sub&gt;) / (&amp;#963;&lt;sub&gt;1&lt;/sub&gt; &amp;#8211; &amp;#963;&lt;sub&gt;3&lt;/sub&gt;)) is ~0.1. When the pore fluid pressure exceeds &amp;#963;&lt;sub&gt;3&lt;/sub&gt;, veins filling mode I cracks are constructed (Jolly and Sanderson, 1997). The pore fluid pressure that exceeds &amp;#963;&lt;sub&gt;3&lt;/sub&gt; is the pore fluid overpressure &amp;#916;P&lt;sub&gt;f&lt;/sub&gt; (&amp;#916;P&lt;sub&gt;f&lt;/sub&gt; = P&lt;sub&gt;f&lt;/sub&gt; &amp;#8211; &amp;#963;&lt;sub&gt;3&lt;/sub&gt;). To estimate the pore fluid overpressure, we used the poro-elastic model for extension quartz vein formation (Gudmundsson, 1999). P&lt;sub&gt;f&lt;/sub&gt; and &amp;#916;P&lt;sub&gt;f&lt;/sub&gt; in the case of the Makimine m&amp;#233;lange are ~280 MPa and 80&amp;#8211;160 kPa (assuming depth = 10 km, density = 2800 kg/m&lt;sup&gt;3&lt;/sup&gt;, tensile strength = 1 MPa and Young&amp;#8217;s modulus = 7.5&amp;#8211;15 GPa). When the pore fluid overpressure is released, the cracks are closed and the reduction of pore fluid pressure is stopped (Otsubo et al., 2020). After the pore fluid overpressure is reduced, the normalized pore pressure ratio &amp;#955;* (&amp;#955;* = (P&lt;sub&gt;f&lt;/sub&gt; &amp;#8211; P&lt;sub&gt;h&lt;/sub&gt;) / (P&lt;sub&gt;l&lt;/sub&gt; &amp;#8211; P&lt;sub&gt;h&lt;/sub&gt;), P&lt;sub&gt;l&lt;/sub&gt;: lithostatic pressure; P&lt;sub&gt;h&lt;/sub&gt;: hydrostatic pressure) is ~1.01 (P&lt;sub&gt;f&lt;/sub&gt; &gt; P&lt;sub&gt;l&lt;/sub&gt;). The results indicate that the pore fluid pressure constantly maintains the lithostatic pressure during the extension cracking along the foliation.&lt;/p&gt;&lt;p&gt;References: Gudmundsson (1999) Geophys. Res. Lett., 26, 115&amp;#8211;118; Jolly and Sanderson (1997) Jour. Struct. Geol., 19, 887&amp;#8211;892; Otsubo et al. (2020) Sci. Rep., 10:12281; Palazzin et al. (2016) Tectonophysics, 687, 28&amp;#8211;43; Sato et al. (2013) Tectonophysics, 588, 69&amp;#8211;81; Ujiie et al. (2018) Geophys. Res. Lett., 45, 5371&amp;#8211;5379, https://doi.org/10.1029/2018GL078374.&lt;/p&gt;

Arc-arc collision in the Central Asian Orogenic Belt: insight from the eastern segment of the Irtysh Shear Zone, NW China.

&lt;p&gt;As the largest accretionary orogen, the Central Asian Orogenic Belt (CAOB) involved episodic accretion/collision of arc terranes or microcontinental blocks from Neoproterozoic to late Paleozoic. Understanding the time and processes of such collisional events is crucial for the tectonic reconstruction of the CAOB. Here we focus on the Irtysh Shear Zone that represents the suture of the Peri-Siberian orogenic system (Chinese Altai Orogen) with the Kazakhstan orogenic system/East Junggar Terrane. On a basis of a combined structural and chronological study along the eastern segment of the Irtysh Shear Zone (Qinghe area), we reconstructed the collisional processes of the Chinese Altai Orogen with an intra-oceanic island arc of the East Junggar Terrane. Our results show that the oceanic basin between the Chinese Altai Orogen and the East Junggar Terrane was completely consumed in the late Carboniferous. The following arc-arc collision was characterized by early stage of orogen-perpendicular contraction, followed by orogen-parallel extension and transpressional deformation. The orogen-parallel extension, which is demonstrated by originally sub-horizontal foliation and associated orogen-parallel stretching lineation, may have be responsible for Permian high-temperature metamorphism and extensive magmatism in the southern Chinese Altai. On a scale of the western CAOB, the sinistral kinematics of the Irtysh Shear Zone, together with dextral shearing farther south in the Tianshan, suggests eastward tectonic wedging in the Permian, possibly in response to the coeval convergence of the Siberian, Baltic, and Tarim cratons.&lt;/p&gt;&lt;p&gt;E-mail addresses: [email protected], [email protected] (P. Li).&lt;/p&gt;&lt;p&gt;Acknowledgements: this study was financially supported by the National Natural Science Foundation of China (41872222), the National Key Research and Development Program of China (2017YFC0601205), Hong Kong Research Grant Council (HKU17302317) and a project from Guangdong Province (2019QN01H101).&lt;/p&gt;

Strain partitioning around an indenter during oroclinal bending: kinematics of the Circum-Moesian fault system of the Carpatho-Balkanides

&lt;p&gt;The Carpatho-Balkanides of south-eastern Europe is a double 180&amp;#176; curved orogenic system. It is comprised of a foreland-convex orocline, situated in the north and east and a backarc-convex orocline situated in the south and west. The southern orocline of the Carpatho-Balkanides orogen formed during the Cretaceous closure of the Alpine Tethys Ocean and collision of the Dacia mega-unit with the Moesian Platform. Following the main orogen-building processes, the Carpathians subduction and Miocene slab retreat in the West and East Carpathians have driven the formation of the backarc-convex oroclinal bending in the south and west. The orocline formed during clockwise rotation of the Dacia mega-unit and coeval docking against the Moesian indenter. This oroclinal bending was associated with a Paleocene-Eocene orogen-parallel extension that exhumed the Danubian nappes of the South Carpathians and with a large late Oligocene &amp;#8211; middle Miocene Circum-Moesian fault system that affected the orogenic system surrounding the Moesian Platform along its southern, western and northern margins. This fault system is composed of various segments that have different and contrasting types of kinematics, which often formed coevally, indicating a large degree of strain partitioning during oroclinal bending. It includes the curved Cerna and Timok faults that cumulate up to 100 km of dextral offset, the lower offset Sokobanja-Zvonce and Rtanj-Pirot dextral strike-slip faults, associated with orogen parallel extension that controls numerous intra-montane basins and thrusting of the western Balkans units over the Moesian Platform. We have performed a field structural study in order to understand the mechanisms of deformation transfer and strain partitioning around the Moesian indenter during oroclinal bending by focusing on kinematics and geometry of large-scale faults within the Circum-Moesian fault system.&lt;/p&gt;&lt;p&gt;Our structural analysis shows that the major strike-slip faults are composed of multi-strand geometries associated with significant strain partitioning within tens to hundreds of metres wide deformation zones. Kinematics of the Circum-Moesian fault system changes from transtensional in the north, where the formation of numerous basins is controlled by the Cerna or Timok faults, to strike-slip and transpression in the south, where transcurrent offsets are gradually transferred to thrusting in the Balkanides. The characteristic feature of the whole system is splaying of major faults to facilitate movements around the Moesian indenter. Splaying towards the east connects the Circum-Moesian fault system with deformation observed in the Getic Depression in front of the South Carpathians, while in the south-west the Sokobanja-Zvonce and Rtanj-Pirot faults splay off the Timok Fault. These two faults are connected by coeval E-W oriented normal faults that control several intra-montane basins and accommodate orogen-parallel extension. We infer that all these deformations are driven by the roll-back of the Carpathians slab that exerts a northward pull on the upper Dacia plate in the Serbian Carpathians. However, the variability in deformation styles is controlled by geometry of the Moesian indenter and the distance to Moesia, as the rotation and northward displacements increase gradually to the north and west.&lt;/p&gt;