A Superficial Working Guide to Deformations and Moduli

This is the first part of a guide to deformations and moduli, especially viewed from the perspective of algebraic surfaces (the simplest higher dimensional varieties). It contains also new results, regarding the question of local homeomorphism between Kuranishi and Teichmueller space, and a survey of new results with Ingrid Bauer, concerning the discrepancy between the deformation of the action of a group G on a minimal models S, respectively the deformation of the action of G on the canonical model X. Here Def(S) maps properly onto Def(X), but the same does not hold for pairs: Def(S,G) does not map properly onto Def(X,G). Indeed the connected components of Def(S), in the case of tertiary Burniat surfaces, only map to locally closed sets. The last section contains anew result on some surfaces whise Albanese map has generic degree equal to 2.Comment: 56 pages, revision to appear in the Handbook of Moduli, in honour of David Mumford, to be published by International press, editors Gavril Farkas and Ian Morrison. The former theorem 29 on moduli spaces for minimal surfaces has been correcte

Slip inversion along inner fore-arc faults, eastern Tohoku, Japan

The kinematics of deformation in the overriding plate of convergent margins may vary across timescales ranging from a single seismic cycle to many millions of years. In Northeast Japan, a network of active faults has accommodated contraction across the arc since the Pliocene, but several faults located along the inner fore arc experienced extensional aftershocks following the 2011 Tohoku-oki earthquake, opposite that predicted from the geologic record. This observation suggests that fore-arc faults may be favorable for stress triggering and slip inversion, but the geometry and deformation history of these fault systems are poorly constrained. Here we document the Neogene kinematics and subsurface geometry of three prominent fore-arc faults in Tohoku, Japan. Geologic mapping and dating of growth strata provide evidence for a 5.6–2.2 Ma initiation of Plio-Quaternary contraction along the Oritsume, Noheji, and Futaba Faults and an earlier phase of Miocene extension from 25 to 15 Ma along the Oritsume and Futaba Faults associated with the opening of the Sea of Japan. Kinematic modeling indicates that these faults have listric geometries, with ramps that dip ~40–65°W and sole into subhorizontal detachments at 6–10 km depth. These fault systems can experience both normal and thrust sense slip if they are mechanically weak relative to the surrounding crust. We suggest that the inversion history of Northeast Japan primed the fore arc with a network of weak faults mechanically and geometrically favorable for slip inversion over geologic timescales and in response to secular variations in stress state associated with the megathrust seismic cycle.Funding was provided by a grant from the National Science Foundation Tectonics Program grant EAR-0809939 to D.M.F. and E.K., Geologic Society of America Graduate Research Grants, and the P.D. Krynine Memorial Fund. The authors thank Gaku Kimura, Kyoko Tonegawa, Hiroko Watanabe, Jun Kameda, and Asuka Yamaguchi for scientific and logistical support, and Kristin Morell for comments on early versions of the manuscript. We also thank Yuzuru Yamamoto and Kohtaro Ujiie for their detailed reviews and suggestions for improvement to the manuscript. The authors acknowledge the use of the Move Software Suite granted by Midland Valley's Academic Software Initiative. Geologic, structural, stratigraphic, and chronologic data used herein are accessible in manuscript figures, and in the citations therein. Input geologic data for trishear kinematic modeling can be accessed in Table 1 and in the supporting information. (EAR-0809939 - National Science Foundation Tectonics Program grant; Geologic Society of America Graduate Research Grants; P.D. Krynine Memorial Fund

Buried shallow fault slip from the South Napa earthquake revealed by near-field geodesy.

Earthquake-related fault slip in the upper hundreds of meters of Earths surface has remained largely unstudied because of challenges measuring deformation in the near field of a fault rupture. We analyze centimeter-scale accuracy mobile laser scanning (MLS) data of deformed vine rows within ±300 m of the principal surface expression of the M (magnitude) 6.0 2014 South Napa earthquake. Rather than assuming surface displacement equivalence to fault slip, we invert the near-field data with a model that allows for, but does not require, the fault to be buried below the surface. The inversion maps the position on a preexisting fault plane of a slip front that terminates ~3 to 25 m below the surface coseismically and within a few hours postseismically. The lack of surface-breaching fault slip is verified by two trenches. We estimate near-surface slip ranging from ~0.5 to 1.25 m. Surface displacement can underestimate fault slip by as much as 30%. This implies that similar biases could be present in short-term geologic slip rates used in seismic hazard analyses. Along strike and downdip, we find deficits in slip: The along-strike deficit is erased after ~1 month by afterslip. We find no evidence of off-fault deformation and conclude that the downdip shallow slip deficit for this event is likely an artifact. As near-field geodetic data rapidly proliferate and will become commonplace, we suggest that analyses of near-surface fault rupture should also use more sophisticated mechanical models and subsurface geomechanical tests

DeformNet: Free-Form Deformation Network for 3D Shape Reconstruction from a Single Image

3D reconstruction from a single image is a key problem in multiple applications ranging from robotic manipulation to augmented reality. Prior methods have tackled this problem through generative models which predict 3D reconstructions as voxels or point clouds. However, these methods can be computationally expensive and miss fine details. We introduce a new differentiable layer for 3D data deformation and use it in DeformNet to learn a model for 3D reconstruction-through-deformation. DeformNet takes an image input, searches the nearest shape template from a database, and deforms the template to match the query image. We evaluate our approach on the ShapeNet dataset and show that - (a) the Free-Form Deformation layer is a powerful new building block for Deep Learning models that manipulate 3D data (b) DeformNet uses this FFD layer combined with shape retrieval for smooth and detail-preserving 3D reconstruction of qualitatively plausible point clouds with respect to a single query image (c) compared to other state-of-the-art 3D reconstruction methods, DeformNet quantitatively matches or outperforms their benchmarks by significant margins. For more information, visit: https://deformnet-site.github.io/DeformNet-website/ .Comment: 11 pages, 9 figures, NIP

GPS source solution of the 2004 Parkfield earthquake

We compute a series of finite-source parameter inversions of the fault rupture of the 2004 Parkfield earthquake based on 1 Hz GPS records only. We confirm that some of the co-seismic slip at shallow depth (<5 km) constrained by InSAR data processing results from early post-seismic deformation. We also show 1) that if located very close to the rupture, a GPS receiver can saturate while it remains possible to estimate the ground velocity (~1.2 m/s) near the fault, 2) that GPS waveforms inversions constrain that the slip distribution at depth even when GPS monuments are not located directly above the ruptured areas and 3) the slip distribution at depth from our best models agree with that recovered from strong motion data. The 95th percentile of the slip amplitudes for rupture velocities ranging from 2 to 5 km/s is, 55 +/- 6 cm.Comment: 24 pages including supp. material

Deformation Quantization of Nambu Mechanics

Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved most naturally, as illustrated on nonlinear $\sigma$-models, specifically for Chiral Models and de Sitter $N$-spheres. Classically, the dynamics of superintegrable models such as these is automatically also described by Nambu Brackets involving the extra symmetry invariants of them. The phase-space quantization worked out then leads to the quantization of the corresponding Nambu Brackets, validating Nambu's original proposal, despite excessive fears of inconsistency which have arisen over the years. This is a pedagogical talk based on hep-th/0205063 and hep-th/0212267, stressing points of interpretation and care needed in appreciating the consistency of Quantum Nambu Brackets in phase space. For a parallel discussion in Hilbert space, see T Curtright's contribution in these Proceedings [hep-th 0303088].Comment: Invited talk by the first author at the Coral Gables Conference (C02/12/11.2), Ft Lauderdale, Dec 2002. 14p, LateX2e, aipproc, amsfont