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    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.

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  2. Abstract

    Physics‐based simulations of earthquake ground motion are useful to complement recorded ground motions. However, the computational expense of performing numerical simulations hinders their applicability to tasks that require real‐time solutions or ensembles of solutions for different earthquake sources. To enable rapid physics‐based solutions, we present a reduced‐order modeling approach based on interpolated proper orthogonal decomposition (POD) to predict peak ground velocities (PGVs). As a demonstrator, we consider PGVs from regional 3D wave propagation simulations at the location of the 2008MW5.4 Chino Hills earthquake using double‐couple sources with varying depth and focal mechanisms. These simulations resolve frequencies ≤1.0 Hz and include topography, viscoelastic attenuation, and S‐wave speeds ≥500 m/s. We evaluate the accuracy of the interpolated POD reduced‐order model (ROM) as a function of the approximation method. Comparing the radial basis function (RBF), multilayer perceptron neural network, random forest, andk‐nearest neighbor, we find that the RBF interpolation gives the lowest error (≈0.1 cm/s) when tested against an independent data set. We also find that evaluating the ROM is 107–108times faster than the wave propagation simulations. We use the ROM to generate PGV maps for 1 million different focal mechanisms, in which we identify potentially damaging ground motions and quantify correlations between focal mechanism, depth, and accuracy of the predicted PGV. Our results demonstrate that the ROM can rapidly and accurately approximate the PGV from wave propagation simulations with variable source properties, topography, and complex subsurface structure.

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  3. Abstract

    The Húsavík‐Flatey Fault Zone (HFFZ) is the largest strike‐slip fault in Iceland and poses a high seismic risk to coastal communities. To investigate physics‐based constraints on earthquake hazards, we construct three fault system models of varying geometric complexity and model 79 3‐D multi‐fault dynamic rupture scenarios in the HFFZ. By assuming a simple regional prestress and varying hypocenter locations, we analyze the rupture dynamics, fault interactions, and the associated ground motions up to 2.5 Hz. All models account for regional seismotectonics, topo‐bathymetry, 3‐D subsurface velocity, viscoelastic attenuation, and off‐fault plasticity, and we explore the effect of fault roughness. The rupture scenarios obey earthquake scaling relations and predict magnitudes comparable to those of historical events. We show how fault system geometry and segmentation, hypocenter location, and prestress can affect the potential for rupture cascading, leading to varying slip distributions across different portions of the fault system. Our earthquake scenarios yield spatially heterogeneous near‐field ground motions modulated by geometric complexities, topography, and rupture directivity, particularly in the near‐field. The average ground motion attenuation characteristics of dynamic rupture scenarios of comparable magnitudes and mean stress drop are independent of variations in source complexity, magnitude‐consistent and in good agreement with the latest regional empirical ground motion models. However, physics‐based ground motion variability changes considerably with fault‐distance and increases for unilateral compared to bilateral ruptures. Systematic variations in physics‐based near‐fault ground motions provide important insights into the mechanics and potential earthquake hazard of large strike‐slip fault systems, such as the HFFZ.

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    Tsunami generation by offshore earthquakes is a problem of scientific interest and practical relevance, and one that requires numerical modelling for data interpretation and hazard assessment. Most numerical models utilize two-step methods with one-way coupling between separate earthquake and tsunami models, based on approximations that might limit the applicability and accuracy of the resulting solution. In particular, standard methods focus exclusively on tsunami wave modelling, neglecting larger amplitude ocean acoustic and seismic waves that are superimposed on tsunami waves in the source region. In this study, we compare four earthquake-tsunami modelling methods. We identify dimensionless parameters to quantitatively approximate dominant wave modes in the earthquake-tsunami source region, highlighting how the method assumptions affect the results and discuss which methods are appropriate for various applications such as interpretation of data from offshore instruments in the source region. Most methods couple a 3-D solid earth model, which provides the seismic wavefield or at least the static elastic displacements, with a 2-D depth-averaged shallow water tsunami model. Assuming the ocean is incompressible and tsunami propagation is negligible over the earthquake duration leads to the instantaneous source method, which equates the static earthquake seafloor uplift with the initial tsunami sea surface height. For longer duration earthquakes, it is appropriate to follow the time-dependent source method, which uses time-dependent earthquake seafloor velocity as a forcing term in the tsunami mass balance. Neither method captures ocean acoustic or seismic waves, motivating more advanced methods that capture the full wavefield. The superposition method of Saito et al. solves the 3-D elastic and acoustic equations to model the seismic wavefield and response of a compressible ocean without gravity. Then, changes in sea surface height from the zero-gravity solution are used as a forcing term in a separate tsunami simulation, typically run with a shallow water solver. A superposition of the earthquake and tsunami solutions provides an approximation to the complete wavefield. This method is algorithmically a two-step method. The complete wavefield is captured in the fully coupled method, which utilizes a coupled solid Earth and compressible ocean model with gravity. The fully coupled method, recently incorporated into the 3-D open-source code SeisSol, simultaneously solves earthquake rupture, seismic waves and ocean response (including gravity). We show that the superposition method emerges as an approximation to the fully coupled method subject to often well-justified assumptions. Furthermore, using the fully coupled method, we examine how the source spectrum and ocean depth influence the expression of oceanic Rayleigh waves. Understanding the range of validity of each method, as well as its computational expense, facilitates the selection of modelling methods for the accurate assessment of earthquake and tsunami hazards and the interpretation of data from offshore instruments.

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  5. Abstract

    Advances in physics‐based earthquake simulations, utilizing high‐performance computing, have been exploited to better understand the generation and characteristics of the high‐frequency seismic wavefield. However, direct comparison to ground motion observations of a specific earthquake is challenging. We here propose a new approach to simulate data‐fused broadband ground motion synthetics using 3D dynamic rupture modeling of the 2016Mw6.2 Amatrice, Italy earthquake. We augment a smooth, best‐fitting model from Bayesian dynamic rupture source inversion of strong‐motion data (<1 Hz) with fractal fault roughness, frictional heterogeneities, viscoelastic attenuation, and topography. The required consistency to match long periods allows us to quantify the role of small‐scale dynamic source heterogeneities, such as the 3D roughness drag, from observational broadband seismic waveforms. We demonstrate that 3D data‐constrained fully dynamic rupture synthetics show good agreement with various observed ground‐motion metrics up to ∼5 Hz and are an important avenue toward non‐ergodic, physics‐based seismic hazard assessment.

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  6. Abstract

    Detailed imaging of accretionary wedges reveals splay fault networks that could pose a significant tsunami hazard. However, the dynamics of multiple splay fault activation during megathrust earthquakes and the consequent effects on tsunami generation are not well understood. We use a 2‐D dynamic rupture model with complex topo‐bathymetry and six curved splay fault geometries constrained from realistic tectonic loading modeled by a geodynamic seismic cycle model with consistent initial stress and strength conditions. We find that all splay faults rupture coseismically. While the largest splay fault slips due to a complex rupture branching process from the megathrust, all other splay faults are activated either top down or bottom up by dynamic stress transfer induced by trapped seismic waves. We ascribe these differences to local non‐optimal fault orientations and variable along‐dip strength excess. Generally, rupture on splay faults is facilitated by their favorable stress orientations and low strength excess as a result of high pore‐fluid pressures. The ensuing tsunami modeled with non‐linear 1‐D shallow water equations consists of one high‐amplitude crest related to rupture on the longest splay fault and a second broader wave packet resulting from slip on the other faults. This results in two episodes of flooding and a larger run‐up distance than the single long‐wavelength (300 km) tsunami sourced by the megathrust‐only rupture. Since splay fault activation is determined by both variable stress and strength conditions and dynamic activation, considering both tectonic and earthquake processes is relevant for understanding tsunamigenesis.

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  7. Abstract

    We study the effects of pore fluid pressure (Pf) on the pre‐earthquake, near‐fault stress state, and 3‐D earthquake rupture dynamics through six scenarios utilizing a structural model based on the 2004Mw9.1 Sumatra‐Andaman earthquake. As pre‐earthquakePfmagnitude increases, effective normal stress and fault shear strength decrease. As a result, magnitude, slip, peak slip rate, stress drop, and rupture velocity of the scenario earthquakes decrease. Comparison of results with observations of the 2004 earthquake support that pre‐earthquakePfaverages near 97% of lithostatic pressure, leading to pre‐earthquake average shear and effective normal tractions of 4–5 and 22 MPa. The megathrust in these scenarios is weak, in terms of low mean shear traction at static failure and low dynamic friction coefficient during rupture. Apparent co‐seismic principal stress rotations and absolute post‐seismic stresses in these scenarios are consistent with the variety of observed aftershock focal mechanisms. In all scenarios, the mean apparent stress rotations are larger above than below the megathrust. Scenarios with largerPfmagnitudes exhibit lower mean apparent principal stress rotations. We further evaluate pre‐earthquakePfdepth distribution. IfPffollows a sublithostatic gradient, pre‐earthquake effective normal stress increases with depth. IfPffollows the lithostatic gradient exactly, then this normal stress is constant, shifting peak slip and peak slip rate updip. This renders constraints on near‐trench strength and constitutive behavior crucial for mitigating hazard. These scenarios provide opportunity for future calibration with site‐specific measurements to constrain dynamically plausible megathrust strength andPfgradients.

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  8. Abstract

    Dynamic modeling of sequences of earthquakes and aseismic slip (SEAS) provides a self‐consistent, physics‐based framework to connect, interpret, and predict diverse geophysical observations across spatial and temporal scales. Amid growing applications of SEAS models, numerical code verification is essential to ensure reliable simulation results but is often infeasible due to the lack of analytical solutions. Here, we develop two benchmarks for three‐dimensional (3D) SEAS problems to compare and verify numerical codes based on boundary‐element, finite‐element, and finite‐difference methods, in a community initiative. Our benchmarks consider a planar vertical strike‐slip fault obeying a rate‐ and state‐dependent friction law, in a 3D homogeneous, linear elastic whole‐space or half‐space, where spontaneous earthquakes and slow slip arise due to tectonic‐like loading. We use a suite of quasi‐dynamic simulations from 10 modeling groups to assess the agreement during all phases of multiple seismic cycles. We find excellent quantitative agreement among simulated outputs for sufficiently large model domains and small grid spacings. However, discrepancies in rupture fronts of the initial event are influenced by the free surface and various computational factors. The recurrence intervals and nucleation phase of later earthquakes are particularly sensitive to numerical resolution and domain‐size‐dependent loading. Despite such variability, key properties of individual earthquakes, including rupture style, duration, total slip, peak slip rate, and stress drop, are comparable among even marginally resolved simulations. Our benchmark efforts offer a community‐based example to improve numerical simulations and reveal sensitivities of model observables, which are important for advancing SEAS models to better understand earthquake system dynamics.

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  9. Abstract Despite a lack of modern large earthquakes on shallowly dipping normal faults, Holocene M w  > 7 low-angle normal fault (LANF; dip<30°) ruptures are preserved paleoseismically and inferred from historical earthquake and tsunami accounts. Even in well-recorded megathrust earthquakes, the effects of non-linear off-fault plasticity and dynamically reactivated splay faults on shallow deformation and surface displacements, and thus hazard, remain elusive. We develop data-constrained 3D dynamic rupture models of the active Mai’iu LANF that highlight how multiple dynamic shallow deformation mechanisms compete during large LANF earthquakes. We show that shallowly-dipping synthetic splays host more coseismic slip and limit shallow LANF rupture more than steeper antithetic splays. Inelastic hanging-wall yielding localizes into subplanar shear bands indicative of newly initiated splay faults, most prominently above LANFs with thick sedimentary basins. Dynamic splay faulting and sediment failure limit shallow LANF rupture, modulating coseismic subsidence patterns, near-shore slip velocities, and the seismic and tsunami hazards posed by LANF earthquakes. 
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    Free, publicly-accessible full text available December 1, 2024
  10. ABSTRACT Seismic waves can couple with the atmosphere and generate sound waves. The influence of faulting mechanisms on earthquake sound patterns provides opportunities for earthquake source characterization. Sound radiated from earthquakes can be perceived as disturbing, even at low ground-shaking levels, which can negatively impact the social acceptance of geoengineering applications. Motivated by consistent reports of felt and heard disturbances associated with the weeks-long stimulation of a 6-km-deep geothermal system in 2018 below the Otaniemi district of Espoo, Helsinki, we conduct fully coupled 3D numerical simulations of wave propagation in the solid Earth and the atmosphere. We assess the sensitivity of the ground shaking and audible noise distributions to the source geometry of the induced earthquakes based on the properties of the largest local magnitude ML 1.8 event. Utilizing recent computational advances and the open-source software SeisSol, we model seismoacoustic frequencies up to 25 Hz, thereby reaching the lower limit of the human audible sound frequency range. We present synthetic distributions of shaking and audible sounds at the 50–100 m scale across a 12 km × 12 km area and discuss implications for better understanding seismic nuisances in metropolitan regions. In five 3D coupled elastic–acoustic scenario simulations that include data on topography and subsurface structure, we analyze the ground velocity and pressure levels of earthquake-generated seismic and acoustic waves. We show that S waves generate the strongest sound disturbance with sound pressure levels ≤0.04 Pa. We use statistical analysis to compare our noise distributions with commonly used empirical relationships. We find that our 3D synthetic amplitudes are generally smaller than the empirical predictions and that the interaction of the source mechanism-specific radiation pattern and topography can lead to significant nonlinear effects. Our study highlights the complexity and information content of spatially variable audible effects associated with small induced earthquakes on local scales. 
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    Free, publicly-accessible full text available July 7, 2024