Characteristics of Earthquake Cycles: A Cross-Dimensional Comparison of 0D to 3D Numerical Models

High-resolution computer simulations of earthquake sequences in three or even two dimensions pose great demands on time and energy, making lower-cost simplifications a competitive alternative. We systematically study the advantages and limitations of simplifications that eliminate spatial dimensions in quasi-dynamic earthquake sequence models, from 3D models with a 2D fault plane down to 0D or 1D models with a 0D fault point. We demonstrate that, when 2D or 3D models produce quasi-periodic characteristic earthquakes, their behavior is qualitatively similar to lower-dimension models. Certain coseismic characteristics like stress drop and fracture energy are largely controlled by frictional parameters and are thus largely comparable. However, other observations are quantitatively clearly affected by dimension reduction. We find corresponding increases in recurrence interval, coseismic slip, peak slip velocity, and rupture speed. These changes are to a large extent explained by the elimination of velocity-strengthening patches that transmit tectonic loading onto the velocity-weakening fault patch, thereby reducing the interseismic stress rate and enhancing the slip deficit. This explanation is supported by a concise theoretical framework, which explains some of these findings quantitatively and effectively estimates recurrence interval and slip. Through accounting for an equivalent stressing rate at the nucleation size h* into 2D and 3D models, 0D or 1D models can also effectively simulate these earthquake cycle parameters. Given the computational efficiency of lower-dimensional models that run more than a million times faster, this paper aims to provide qualitative and quantitative guidance on economical model design and interpretation of modeling studies

Tectonics and seismicity in the Northern Apennines driven by slab retreat and lithospheric delamination

Understanding how long-term subduction dynamics relates to the short-term seismicity and crustal tec tonics is a challenging but crucial topic in seismotectonics. We attempt to address this issue by linking long-term geodynamic evolution with short-term seismogenic deformation in the Northern Apennines. This retreating subduction orogen displays tectonic and seismogenic behaviors on various spatiotemporal scales that also characterize other subduction zones in the Mediterranean area. We use visco-elasto-plastic seismo-thermo-mechanical (STM) modeling with a realistic 2D setup based on available geological and geophysical data. The subduction dynamics and seismicity are coupled in the numerical modeling, and driven only by buoyancy forces, i.e., slab pull. Our results suggest that lower crustal rheology and lithospheric mantle temperature modulate the crustal tectonics of the Northern Apennines, as inferred by previous studies. The observed spatial distribution of upper crustal tectonic regimes and surface displacements requires buoyant, highly ductile material in the subduction channel beneath the internal part of the orogen. This allows protrusion of the asthenosphere in the lower crust and lithospheric delamination associated with slab retreat. The resulting surface velocities and principal stress axes generally agree with present-day observations, suggesting that slab delamination and retreat can explain the dynamics of the orogen. Our simulations successfully reproduce the type and overall distribution of seismicity with thrust faulting events in the external part of the orogen and normal faulting in its internal part. Slab temperatures and lithospheric mantle stiffness affect the cumulative seismic moment release and spatial distribution of upper crustal earthquakes. The properties of deep, sub-crustal material are thus shown to influence upper crustal seismicity in an orogen driven by slab retreat, even though the upper crust is largely decoupled from the lithospheric mantle. Our simulations therefore highlight the effect of deep lower crustal rheologies, self-driven subduction dynamics and mantle properties in controlling shallow deformation and seismicity

Numerical modelling of post-seismic rupture propagation after the Sumatra 26.12.2004 earthquake constrained by GRACE gravity data

In the last decades, the development of the surface and satellite geodetic and geophysical observations brought a new insights into the seismic cycle, documenting new features of inter-, co-, and post-seismic processes. In particular since 2002 satellite mission GRACE provides monthly models of the global gravity field with unprecedented accuracy showing temporal variations of the Earth's gravity field, including those caused by mass redistribution associated with earthquake processes. When combined with GPS measurements, these new data have allowed to assess the relative importance of afterslip and viscoelastic relaxation after the Sumatra 26.12.2004 earthquake. Indeed the observed post-seismic crustal displacements were fitted well by a viscoelastic relaxation model assuming Burgers body rheology for the asthenosphere (60-220 km deep) with a transient viscosity as low as 4× 1017 Pas and constant∼1019 Pas steady state viscosity in the 60-660-km depth range. However, even the low-viscosity asthenosphere provides the amplitude of strain which gravity effect does not exceed 50 per cent of the GRACE gravity variations, thus additional localized slip of about 1 m was suggested at downdip extension of the coseismic rupture. Post-seismic slip at coseismic rupture or its downdip extension has been suggested by several authors but the mechanism of the post-seismic fault propagation has never been investigated numerically. Depth and size of localized slip area as well as rate and time decay during the post-seismic stage were either assigned a priory or estimated by fitting real geodesy or gravity data. In this paper we investigate post-seismic rupture propagation by modelling two consequent stages. First, we run a long-term, geodynamic simulation to self-consistently produce the initial stress and temperature distribution. At the second stage, we simulate a seismic cycle using results of the first step as initial conditions. The second short-term simulation involves three substeps, including additional stress accumulation after part of the subduction channel was locked; spontaneous coseismic slip; formation and development of damage zones producing afterslip. During the last substep post-seismic stress leads to gradual∼1 m slip localized at three faults around∼100-km downdip extension of the coseismic rupture. We used the displacement field caused by the slip to calculate pressure and density variations and to simulate gravity field variations. Wavelength of calculated gravity anomaly fits well to that of the real data and its amplitude provides about 60 per cent of the observed GRACE anomaly. Importantly, the surface displacements caused by the estimated afterslip are much smaller than those registered by GPS networks. As a result cumulative effect of Burgers rheology viscoelastic relaxation (which explains measured GPS displacements and about a half of gravity variations) plus post-seismic slip predicted by damage rheology model (which causes much smaller surface displacements but provides another half of the GRACE gravity variations) fits well to both sets of the real data. Hence, the presented numerical modelling based on damage rheology supports the process of post-seismic downdip rupture propagation previously hypothesized from the GRACE gravity dat

Numerical modelling of post-seismic rupture propagation after the Sumatra 26.12.2004 earthquake constrained by GRACE gravity data

International audienceIn the last decades, the development of the surface and satellite geodetic and geophysical observations brought a new insights into the seismic cycle, documenting new features of inter-, co-, and post-seismic processes. In particular since 2002 satellite mission GRACE provides monthly models of the global gravity field with unprecedented accuracy showing temporal variations of the Earth's gravity field, including those caused by mass redistribution associated with earthquake processes. When combined with GPS measurements, these new data have allowed to assess the relative importance of afterslip and viscoelastic relaxation after the Sumatra 26.12.2004 earthquake. Indeed the observed post-seismic crustal displacements were fitted well by a viscoelastic relaxation model assuming Burgers body rheology for the asthenosphere (60–220 km deep) with a transient viscosity as low as 4 × 10^17 Pas and constant ~ 10^19 Pas steady state viscosity in the 60–660-km depth range. However, even the low-viscosity asthenosphere provides the amplitude of strain which gravity effect does not exceed 50 per cent of the GRACE gravity variations, thus additional localized slip of about 1 m was suggested at downdip extension of the coseismic rupture. Post-seismic slip at coseismic rupture or its downdip extension has been suggested by several authors but the mechanism of the post-seismic fault propagation has never been investigated numerically. Depth and size of localized slip area as well as rate and time decay during the post-seismic stage were either assigned a priory or estimated by fitting real geodesy or gravity data. In this paper we investigate post-seismic rupture propagation by modelling two consequent stages. First, we run a long-term, geodynamic simulation to self-consistently produce the initial stress and temperature distribution. At the second stage, we simulate a seismic cycle using results of the first step as initial conditions. The second short-term simulation involves three substeps, including additional stress accumulation after part of the subduction channel was locked; spontaneous coseismic slip; formation and development of damage zones producing afterslip. During the last substep post-seismic stress leads to gradual ~1 m slip localized at three faults around ~100-km downdip extension of the coseismic rupture. We used the displacement field caused by the slip to calculate pressure and density variations and to simulate gravity field variations. Wavelength of calculated gravity anomaly fits well to that of the real data and its amplitude provides about 60 per cent of the observed GRACE anomaly. Importantly, the surface displacements caused by the estimated afterslip are much smaller than those registered by GPS networks. As a result cumulative effect of Burgers rheology viscoelastic relaxation (which explains measured GPS displacements and about a half of gravity variations) plus post-seismic slip predicted by damage rheology model (which causes much smaller surface displacements but provides another half of the GRACE gravity variations) fits well to both sets of the real data. Hence, the presented numerical modelling based on damage rheology supports the process of post-seismic downdip rupture propagation previously hypothesized from the GRACE gravity data

Linked 3-D modelling of megathrust earthquake-tsunami events: from subduction to tsunami run up

How does megathrust earthquake rupture govern tsunami behaviour? Recent modelling advances permit evaluation of the influence of 3-D earthquake dynamics on tsunami genesis, propagation, and coastal inundation. Here, we present and explore a virtual laboratory in which the tsunami source arises from 3-D coseismic seafloor displacements generated by a dynamic earthquake rupture model. This is achieved by linking open-source earthquake and tsunami computational models that follow discontinuous Galerkin schemes and are facilitated by highly optimized parallel algorithms and software. We present three scenarios demonstrating the flexibility and capabilities of linked modelling. In the first two scenarios, we use a dynamic earthquake source including time-dependent spontaneous failure along a 3-D planar fault surrounded by homogeneous rock and depth-dependent, near-lithostatic stresses. We investigate how slip to the trench influences tsunami behaviour by simulating one blind and one surface-breaching rupture. The blind rupture scenario exhibits distinct earthquake characteristics (lower slip, shorter rupture duration, lower stress drop, lower rupture speed), but the tsunami is similar to that from the surface-breaching rupture in run-up and length of impacted coastline. The higher tsunami-generating efficiency of the blind rupture may explain how there are differences in earthquake characteristics between the scenarios, but similarities in tsunami inundation patterns. However, the lower seafloor displacements in the blind rupture result in a smaller displaced volume of water leading to a narrower inundation corridor inland from the coast and a 15 per cent smaller inundation area overall. In the third scenario, the 3-D earthquake model is initialized using a seismo-thermo-mechanical geodynamic model simulating both subduction dynamics and seismic cycles. This ensures that the curved fault geometry, heterogeneous stresses and strength and material structure are consistent with each other and with millions of years of modelled deformation in the subduction channel. These conditions lead to a realistic rupture in terms of velocity and stress drop that is blind, but efficiently generates a tsunami. In all scenarios, comparison with the tsunamis sourced by the time-dependent seafloor displacements, using only the time-independent displacements alters tsunami temporal behaviour, resulting in later tsunami arrival at the coast, but faster coastal inundation. In the scenarios with the surface-breaching and subduction-initialized earthquakes, using the time-independent displacements also overpredicts run-up. In the future, the here presented scenarios may be useful for comparison of alternative dynamic earthquake-tsunami modelling approaches or linking choices, and can be readily developed into more complex applications to study how earthquake source dynamics influence tsunami genesis, propagation and inundation

TGF-beta-induced endothelial to mesenchymal transition is determined by a balance between SNAIL and ID factors

Endothelial-to-mesenchymal transition (EndMT) plays an important role in embryonic development and disease progression. Yet, how different members of the transforming growth factor-beta (TGF-beta) family regulate EndMT is not well understood. In the current study, we report that TGF-beta 2, but not bone morphogenetic protein (BMP)9, triggers EndMT in murine endothelial MS-1 and 2H11 cells. TGF-beta 2 strongly upregulates the transcription factor SNAIL, and the depletion of Snail is sufficient to abrogate TGF-beta 2-triggered mesenchymal-like cell morphology acquisition and EndMT-related molecular changes. Although SLUG is not regulated by TGF-beta 2, knocking out Slug also partly inhibits TGF-beta 2-induced EndMT in 2H11 cells. Interestingly, in addition to SNAIL and SLUG, BMP9 stimulates inhibitor of DNA binding (ID) proteins. The suppression of Id1, Id2, or Id3 expression facilitated BMP9 in inducing EndMT and, in contrast, ectopic expression of ID1, ID2, or ID3 abrogated TGF-beta 2-mediated EndMT. Altogether, our results show that SNAIL is critical and indispensable for TGF-beta 2-mediated EndMT. Although SLUG is also involved in the EndMT process, it plays less of a crucial role in it. In contrast, ID proteins are essential for maintaining endothelial traits and repressing the function of SNAIL and SLUG during the EndMT process. These data suggest that the control over endothelial vs. mesenchymal cell states is determined, at least in part, by a balance between the expression of SNAIL/SLUG and ID proteins.Cancer Signaling networks and Molecular Therapeutic