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Abstract Structural inversion of rifted basins is generally associated with surface uplift and denudation of the sedimentary infill, reflecting the active contractional deformation in the crust. However, worldwide examples of inverted rifts show contrasting basin-scale subsidence and widespread sedimentation patterns during basin inversion. By conducting a series of three-dimensional coupled geodynamic and surface processes models, we investigated the dynamic controls on these subsidence anomalies during the successive stages of rifting and basin inversion, and we propose a new evolutionary model for this process. Our models show that the inherited thermo-rheological properties of the lithosphere influence the initial strain localization and subsequent migration of crustal deformation during inversion. The sense of the vertical movements (i.e., uplift or subsidence), however, is not directly linked to the underlying crustal stress patterns; rather, it reflects the balance among contraction-induced tectonic uplift, postrift thermal subsidence of the inherited lithosphere, and sediment redistribution. Based on the interplay among the competing differential vertical movements with different amplitudes and wavelengths, inversion of rifted basins may lead to the growth of intraplate orogens, or the contraction-driven localized uplift may be hindered by the thermal sag effects of the inherited shallow lithosphere-asthenosphere boundary, resulting in basin-scale subsidence. In such basins, dating the first erosional surfaces and other unconformities may not provide accurate timing for the onset of inversion. 

In this paper, we consider the problem of optimizing the worst-case behavior of a partially observed system. All uncontrolled disturbances are modeled as finite-valued uncertain variables. Using the theory of cost distributions, we present a dynamic programming (DP) approach to compute a control strategy that minimizes the maximum possible total cost over a given time horizon. To improve the computational efficiency of the optimal DP, we introduce a general definition for information states and show that many information states constructed in previous research efforts are special cases of ours. Additionally, we define approximate information states and an approximate DP that can further improve computational tractability by conceding a bounded performance loss. We illustrate the utility of these results using a numerical example. 

SUMMARY To reach Earth’s surface, magma must ascend from the hot, ductile asthenosphere through cold and brittle rock in the lithosphere. It does so via fluid-filled fractures called dykes. While the continuum mechanics of ductile asthenosphere is well established, there has been little theoretical work on the cold and brittle regime where dyking and faulting occurs. Geodynamic models use plasticity to model fault-like behaviour; plasticity also shows promise for modelling dykes. Here we build on an existing model to develop a poro-viscoelastic–viscoplastic theory for two-phase flow across the lithosphere. Our theory addresses the deficiencies of previous work by incorporating (i) a hyperbolic yield surface, (ii) a plastic potential with control of dilatancy and (iii) a viscous regularization of plastic failure. We use analytical and numerical solutions to investigate the behaviour of this theory. Through idealized models and a comparison to linear elastic fracture mechanics, we demonstrate that this behaviour includes a continuum representation of dyking. Finally, we consider a model scenario reminiscent of continental rifting and demonstrate the consequences of dyke injection into the cold, upper lithosphere: a sharp reduction in the force required to rift. 

Contemporary autonomous vehicle (AV) benchmarks have advanced techniques for training 3D detectors, particularly on large-scale lidar data. Surprisingly, although semantic class labels naturally follow a long-tailed distribution, contemporary benchmarks focus on only a few common classes (e.g., pedestrian and car) and neglect many rare classes in-the-tail (e.g., debris and stroller). However, AVs must still detect rare classes to ensure safe operation. Moreover, semantic classes are often organized within a hierarchy, e.g., tail classes such as child and construction-worker are arguably subclasses of pedestrian. However, such hierarchical relationships are often ignored, which may lead to misleading estimates of performance and missed opportunities for algorithmic innovation. We address these challenges by formally studying the problem of Long-Tailed 3D Detection (LT3D), which evaluates on all classes, including those in-the-tail. We evaluate and innovate upon popular 3D detection codebases, such as CenterPoint and PointPillars, adapting them for LT3D. We develop hierarchical losses that promote feature sharing across common-vs-rare classes, as well as improved detection metrics that award partial credit to "reasonable" mistakes respecting the hierarchy (e.g., mistaking a child for an adult). Finally, we point out that fine-grained tail class accuracy is particularly improved via multimodal fusion of RGB images with LiDAR; simply put, small fine-grained classes are challenging to identify from sparse (lidar) geometry alone, suggesting that multimodal cues are crucial to long-tailed 3D detection. Our modifications improve accuracy by 5% AP on average for all classes, and dramatically improve AP for rare classes (e.g., stroller AP improves from 3.6 to 31.6)! Our code is available at this https URL. 

SUMMARY Physics-based simulations provide a path to overcome the lack of observational data hampering a holistic understanding of earthquake faulting and crustal deformation across the vastly varying space–time scales governing the seismic cycle. However, simulations of sequences of earthquakes and aseismic slip (SEAS) including the complex geometries and heterogeneities of the subsurface are challenging. We present a symmetric interior penalty discontinuous Galerkin (SIPG) method to perform SEAS simulations accounting for the aforementioned challenges. Due to the discontinuous nature of the approximation, the spatial discretization natively provides a means to impose boundary and interface conditions. The method accommodates 2-D and 3-D domains, is of arbitrary order, handles subelement variations in material properties and supports isoparametric elements, that is, high-order representations of the exterior boundaries, interior material interfaces and embedded faults. We provide an open-source reference implementation, Tandem, that utilizes highly efficient kernels for evaluating the SIPG linear and bilinear forms, is inherently parallel and well suited to perform high-resolution simulations on large-scale distributed memory architectures. Additional flexibility and efficiency is provided by optionally defining the displacement evaluation via a discrete Green’s function approach, exploiting advantages of both the boundary integral and volumetric methods. The optional discrete Green’s functions are evaluated once in a pre-computation stage using algorithmically optimal and scalable sparse parallel solvers and pre-conditioners. We illustrate the characteristics of the SIPG formulation via an extensive suite of verification problems (analytic, manufactured and code comparison) for elastostatic and quasi-dynamic problems. Our verification suite demonstrates that high-order convergence of the discrete solution can be achieved in space and time and highlights the benefits of using a high-order representation of the displacement, material properties and geometries. We apply Tandem to realistic demonstration models consisting of a 2-D SEAS multifault scenario on a shallowly dipping normal fault with four curved splay faults, and a 3-D intersecting multifault scenario of elastostatic instantaneous displacement of the 2019 Ridgecrest, CA, earthquake sequence. We exploit the curvilinear geometry representation in both application examples and elucidate the importance of accurate stress (or displacement gradient) representation on-fault. This study entails several methodological novelties. We derive a sharp bound on the smallest value of the SIPG penalty ensuring stability for isotropic, elastic materials; define a new flux to incorporate embedded faults in a standard SIPG scheme; employ a hybrid multilevel pre-conditioner for the discrete elasticity problem; and demonstrate that curvilinear elements are specifically beneficial for volumetric SEAS simulations. We show that our method can be applied for solving interesting geophysical problems using massively parallel computing. Finally, this is the first time a discontinuous Galerkin method is published for the numerical simulations of SEAS, opening new avenues to pursue extreme scale 3-D SEAS simulations in the future. 

Key Points The 15 January 2022 Hunga Tonga‐Hunga Ha'apai eruption had four episodic seismic subevents with similar waveforms within ∼300 s An unusual upward force jump‐started each subevent A magma hammer explains the force and estimates the subsurface magma mass flux which fits the vent discharge rate based on satellite data 

Abstract. Modelling the pressure in the Earth's interior is a common problem in Earth sciences. In this study we propose a method based on the conservation of the momentum of a fluid by using a hydrostatic scenario or a uniformly moving fluid to approximate the pressure. This results in a partial differential equation (PDE) that can be solved using classical numerical methods. In hydrostatic cases, the computed pressure is the lithostatic pressure. In non-hydrostatic cases, we show that this PDE-based approach better approximates the total pressure than the classical 1D depth-integrated approach. To illustrate the performance of this PDE-based formulation we present several hydrostatic and non-hydrostatic 2D models in which we compute the lithostatic pressure or an approximation of the total pressure, respectively. Moreover, we also present a 3D rift model that uses that approximated pressure as a time-dependent boundary condition to simulate far-field normal stresses. This model shows a high degree of non-cylindrical deformation, resulting from the stress boundary condition, that is accommodated by strike-slip shear zones. We compare the result of this numerical model with a traditional rift model employing free-slip boundary conditions to demonstrate the first-order implications of considering “open” boundary conditions in 3D thermo-mechanical rift models.