More Like this

1. Magmatism controls global oceanic transform fault topography

   https://doi.org/10.1038/s41467-024-46197-9  

   Tian, Xiaochuan; Behn, Mark D; Ito, Garrett; Schierjott, Jana C; Kaus, Boris_J P; Popov, Anton A (December 2024, Nature Communications)

   Abstract Oceanic transform faults play an essential role in plate tectonics. Yet to date, there is no unifying explanation for the global trend in broad-scale transform fault topography, ranging from deep valleys to shallow topographic highs. Using three-dimensional numerical models, we find that spreading-rate dependent magmatism within the transform domain exerts a first-order control on the observed spectrum of transform fault depths. Low-rate magmatism results in deep transform valleys caused by transform-parallel tectonic stretching; intermediate-rate magmatism fully accommodates far-field stretching, but strike-slip motion induces across-transform tension, producing transform strength dependent shallow valleys; high-rate magmatism produces elevated transform zones due to local compression. Our models also address the observation that fracture zones are consistently shallower than their adjacent transform fault zones. These results suggest that plate motion change is not a necessary condition for reproducing oceanic transform topography and that oceanic transform faults are not simple conservative strike-slip plate boundaries. 

   more » « less
2. The tensorial X-ray transform on asymptotically conic spaces

   https://doi.org/10.3934/ipi.2024001  

   Jia, Qiuye; Vasy, András (January 2024, Inverse Problems and Imaging)

   In this paper we show the invertibility of the geodesic X-ray transform on one forms and 2-tensors on asymptotically conic manifolds, up to the natural obstruction, allowing existence of certain kinds of conjugate points. We use the 1-cusp pseudodifferential operator algebra and its semiclassical foliation version introduced and used by Vasy and Zachos, who showed the same type invertibility on functions. The complication of the invertibility of the tensorial X-ray transform, compared with X-ray transform on functions, is caused by the natural kernel of the transform consisting of ‘potential tensors’. We overcome this by arranging a modified solenoidal gauge condition, under which we have the invertibility of the X-ray transform. 

   more » « less
3. Quantitative Uniqueness Properties for L 2 Functions with Fast Decaying, or Sparsely Supported, Fourier Transform

   https://doi.org/10.1093/imrn/rnab075  

   Jaye, Benjamin; Mitkovski, Mishko (April 2021, International Mathematics Research Notices)

   null (Ed.)

   Abstract This paper builds upon two key principles behind the Bourgain–Dyatlov quantitative uniqueness theorem for functions with Fourier transform supported in an Ahlfors regular set. We first provide a characterization of when a quantitative uniqueness theorem holds for functions with very quickly decaying Fourier transform, thereby providing an extension of the classical Paneah–Logvinenko–Sereda theorem. Secondly, we derive a transference result which converts a quantitative uniqueness theorem for functions with fast decaying Fourier transform to one for functions with Fourier transform supported on a fractal set. In addition to recovering the result of Bourgain–Dyatlov, we obtain analogous uniqueness results for denser fractals. 

   more » « less
4. Geometric scattering on measure spaces

   https://doi.org/10.1016/j.acha.2024.101635  

   Chew, Joyce; Hirn, Matthew; Krishnaswamy, Smita; Needell, Deanna; Perlmutter, Michael; Steach, Holly; Viswanath, Siddharth; Wu, Hau-Tieng (May 2024, Applied and Computational Harmonic Analysis)

   The scattering transform is a multilayered, wavelet-based transform initially introduced as a mathematical model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks’ stability and invariance properties. In subsequent years, there has been widespread interest in extending the success of CNNs to data sets with non- Euclidean structure, such as graphs and manifolds, leading to the emerging field of geometric deep learning. In order to improve our understanding of the architectures used in this new field, several papers have proposed generalizations of the scattering transform for non-Euclidean data structures such as undirected graphs and compact Riemannian manifolds without boundary. Analogous to the original scattering transform, these works prove that these variants of the scattering transform have desirable stability and invariance properties and aim to improve our understanding of the neural networks used in geometric deep learning. In this paper, we introduce a general, unified model for geometric scattering on measure spaces. Our proposed framework includes previous work on compact Riemannian manifolds without boundary and undirected graphs as special cases but also applies to more general settings such as directed graphs, signed graphs, and manifolds with boundary. We propose a new criterion that identifies to which groups a useful representation should be invariant and show that this criterion is sufficient to guarantee that the scattering transform has desirable stability and invariance properties. Additionally, we consider finite measure spaces that are obtained from randomly sampling an unknown manifold. We propose two methods for constructing a data-driven graph on which the associated graph scattering transform approximates the scattering transform on the underlying manifold. Moreover, we use a diffusion-maps based approach to prove quantitative estimates on the rate of convergence of one of these approximations as the number of sample points tends to infinity. Lastly, we showcase the utility of our method on spherical images, a directed graph stochastic block model, and on high-dimensional single-cell data. 

   more » « less
5. How transform fault shear influences where detachment faults form near mid-ocean ridges

   https://doi.org/10.1038/s41598-023-35714-3  

   Schierjott, Jana C.; Ito, Garrett; Behn, Mark D.; Tian, Xiaochuan; Morrow, Thomas; Kaus, Boris J.; Escartín, Javier (December 2023, Scientific Reports)

   Abstract Oceanic detachment faults represent an end-member form of seafloor creation, associated with relatively weak magmatism at slow-spreading mid-ocean ridges. We use 3-D numerical models to investigate the underlying mechanisms for why detachment faults predominantly form on the transform side (inside corner) of a ridge-transform intersection as opposed to the fracture zone side (outside corner). One hypothesis for this behavior is that the slipping, and hence weaker, transform fault allows for the detachment fault to form on the inside corner, and a stronger fracture zone prevents the detachment fault from forming on the outside corner. However, the results of our numerical models, which simulate different frictional strengths in the transform and fracture zone, do not support the first hypothesis. Instead, the model results, combined with evidence from rock physics experiments, suggest that shear-stress on transform fault generates excess lithospheric tension that promotes detachment faulting on the inside corner. 

   more » « less