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6 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

A mixed, unified forward/inverse framework for earthquake problems: fault implementation and coseismic slip estimate

SUMMARY We introduce a new finite-element (FE) based computational framework to solve forward and inverse elastic deformation problems for earthquake faulting via the adjoint method. Based on two advanced computational libraries, FEniCS and hIPPYlib for the forward and inverse problems, respectively, this framework is flexible, transparent and easily extensible. We represent a fault discontinuity through a mixed FE elasticity formulation, which approximates the stress with higher order accuracy and exposes the prescribed slip explicitly in the variational form without using conventional split node and decomposition discrete approaches. This also allows the first order optimality condition, that is the vanishing of the gradient, to be expressed in continuous form, which leads to consistent discretizations of all field variables, including the slip. We show comparisons with the standard, pure displacement formulation and a model containing an in-plane mode II crack, whose slip is prescribed via the split node technique. We demonstrate the potential of this new computational framework by performing a linear coseismic slip inversion through adjoint-based optimization methods, without requiring computation of elastic Green’s functions. Specifically, we consider a penalized least squares formulation, which in a Bayesian setting—under the assumption of Gaussian noise and prior—reflects the negative log of the posterior distribution. The comparison of the inversion results with a standard, linear inverse theory approach based on Okada’s solutions shows analogous results. Preliminary uncertainties are estimated via eigenvalue analysis of the Hessian of the penalized least squares objective function. Our implementation is fully open-source and Jupyter notebooks to reproduce our results are provided. The extension to a fully Bayesian framework for detailed uncertainty quantification and non-linear inversions, including for heterogeneous media earthquake problems, will be analysed in a forthcoming paper.

58 GEOSCIENCES↗
NASA NTRS1991

An assessment of the crustal remelting hypothesis for volcanism in the Freyja Montes deformation zone

The linear mountain belts of Ishtar Terra on Venus are notable for their topographic relief and slope and for the intensity of surface deformation. The mountains surround the highland plain Lakshmi Planum, the site of two major paterae and numerous other volcanic features and deposits, and evidence is widespread for volcanism within the mountains and in terrain immediately outward of the mountain belt units. While two hypotheses for magmatism can be distinguished on the basis of the chemistry of the melts, chemical data are presently lacking for the Ishtar region. The competing hypotheses for magmatism in Western Ishtar Terra can also be tested with thermal models, given a kinematic or dynamic model for the evolution of the region. The crustal remelting hypothesis is assessed, using the kinematic scenario of Head for the evolution of Freyja Montes. In that scenario, Freyja Montes formed by a sequence of large scale underthrusts of the lithosphere of the North Polar Plains beneath Ishtar Terra, with successive blocks of underthrust crust sutured in imbricate fashion onto the thickened crust of Lakshmi Planum and the mantle portion of underthrusting lithosphere episodically detached. The numerical experiments thus show that volcanic activity associated with the formation of the Frejya Montes deformation zone can be explained by crustal melting, due either to direct contact of crustal material with the hot asthenosphere or to heat generation in a thickened crustal layer.

Namiki, Noriyuki↗
NASA NTRS1987

Crustal deformation in Great California Earthquake cycles

A model in which coupling is described approximately through a generalized Elsasser model is proposed for computation of the periodic crustal deformation associated with repeated strike-slip earthquakes. The model is found to provide a more realistic physical description of tectonic loading than do simpler kinematic models. Parameters are chosen to model the 1857 and 1906 San Andreas ruptures, and predictions are found to be consistent with data on variations of contemporary surface strain and displacement rates as a function of distance from the 1857 and 1906 rupture traces. Results indicate that the asthenosphere appropriate to describe crustal deformation on the earthquake cycle time scale lies in the lower crust and perhaps the crust-mantle transition zone.

Li, Victor C.↗
NASA NTRS1989

Tests of crustal divergence models for Aphrodite Terra, Venus

This paper discusses the characteristics of Aphrodite Terra, the highland region of Venus which is considered to be a likely site of mantle upwelling, active volcanism, and extensional tectonics, and examines the relation of these features to three alternative kinematic models for the interaction of mantle convection with the surface. These the 'vertical tectonics' model, in which little horizontal surface displacement results from mantle flow; the 'plate divergence' model, in which shear strain from large horizontal displacements is accommodated only in narrow zones of deformation; and the 'distributed deformation' model, in which strain from large horizontal motions is broadly accommodated. No convincing observational evidence was found to support the rigid-plate divergence, while the evidence of large-scale horizontal motions of Aphrodite argues against purely vertical tectonics. A model is proposed, involving a broad disruption of a thin lithosphere. In such a model, lineaments are considered to be surface manifestations of mantle convective flow.

Grimm, Robert E.↗
NASA NTRS1994

Neotectonics of Asia: Thin-shell finite-element models with faults

As India pushed into and beneath the south margin of Asia in Cenozoic time, it added a great volume of crust, which may have been (1) emplaced locally beneath Tibet, (2) distributed as regional crustal thickening of Asia, (3) converted to mantle eclogite by high-pressure metamorphism, or (4) extruded eastward to increase the area of Asia. The amount of eastward extrusion is especially controversial: plane-stress computer models of finite strain in a continuum lithosphere show minimal escape, while laboratory and theoretical plane-strain models of finite strain in a faulted lithosphere show escape as the dominant mode. We suggest computing the present (or neo)tectonics by use of the known fault network and available data on fault activity, geodesy, and stress to select the best model. We apply a new thin-shell method which can represent a faulted lithosphere of realistic rheology on a sphere, and provided predictions of present velocities, fault slip rates, and stresses for various trial rheologies and boundary conditions. To minimize artificial boundaries, the models include all of Asia east of 40 deg E and span 100 deg on the globe. The primary unknowns are the friction coefficient of faults within Asia and the amounts of shear traction applied to Asia in the Himalayan and oceanic subduction zones at its margins. Data on Quaternary fault activity prove to be most useful in rating the models. Best results are obtained with a very low fault friction of 0.085. This major heterogeneity shows that unfaulted continum models cannot be expected to give accurate simulations of the orogeny. But, even with such weak faults, only a fraction of the internal deformation is expressed as fault slip; this means that rigid microplate models cannot represent the kinematics either. A universal feature of the better models is that eastern China and southeast Asia flow rapidly eastward with respect to Siberia. The rate of escape is very sensitive to the level of shear traction in the Pacific subduction zones, which is below 6 MPa. Because this flow occurs across a wide range of latitudes, the net eastward escape is greater than the rate of crustal addition in the Himalaya. The crustal budget is balanced by extension and thinning, primarily within the Tibetan plateau and the Baikal rift. The low level of deviation stresses in the best models suggests that topographic stress plays a major role in the orogeny; thus, we have to expect that different topography in the past may have been linked with fundamentally different modes of continental collision.

Kong, Xianghong↗
NASA NTRS1986

Crustal deformation in great California earthquake cycles

Periodic crustal deformation associated with repeated strike slip earthquakes is computed for the following model: A depth L (less than or similiar to H) extending downward from the Earth's surface at a transform boundary between uniform elastic lithospheric plates of thickness H is locked between earthquakes. It slips an amount consistent with remote plate velocity V sub pl after each lapse of earthquake cycle time T sub cy. Lower portions of the fault zone at the boundary slip continuously so as to maintain constant resistive shear stress. The plates are coupled at their base to a Maxwellian viscoelastic asthenosphere through which steady deep seated mantle motions, compatible with plate velocity, are transmitted to the surface plates. The coupling is described approximately through a generalized Elsasser model. It is argued that the model gives a more realistic physical description of tectonic loading, including the time dependence of deep slip and crustal stress build up throughout the earthquake cycle, than do simpler kinematic models in which loading is represented as imposed uniform dislocation slip on the fault below the locked zone.

Li, Victor C.↗