We image the rupture process of the 2021 Mw 7.4 Maduo, Tibet earthquake using slowness‐enhanced back‐projection (BP) and joint finite fault inversion, which combines teleseismic broadband body waves, long‐period (166–333 s) seismic waves, and 3D ground displacements from radar satellites. The results reveal a left‐lateral strike‐slip rupture, propagating bilaterally on a 160 km long north‐dipping sub‐vertical fault system that bifurcates near its east end. About 80% of the total seismic moment occurs on the asperities shallower than 10 km, with a peak slip of 5.7 m. To simultaneously match the observed long‐period seismic waves and static displacements, potential deep slip is required, despite a tradeoff with the rigidity of the shallow crust. The deep slip existence, local crustal rigidity, and synthetic long‐period Earth response for Tibet earthquakes thus deserve further investigation. The WNW branch ruptures ∼75 km at ∼2.7 km/s, while the ESE branch ruptures ∼85 km at ∼3 km/s, though super‐shear rupture propagation possibly occurs during the ESE propagation from 12 to 20 s. Synthetic BP tests confirm overall sub‐shear rupture speeds and reveal a previously undocumented limitation caused by the signal interference between two bilateral branches. The stress analysis on the forks of the fault demonstrates that the pre‐compression inclination, rupture speed, and branching angle could explain the branching behavior on the eastern fork.
Enhanced Digital Image Correlation Analysis of Ruptures with Enforced Traction Continuity Conditions Across Interfaces
Accurate measurements of displacements around opening or interfacial shear cracks (shear ruptures) are challenging when digital image correlation (DIC) is used to quantify strain and stress fields around such cracks. This study presents an algorithm to locally adjust the displacements computed by DIC near frictional interfaces of shear ruptures, in order for the local stress fields to satisfy the continuity of tractions across the interface. In the algorithm, the stresses near the interface are extrapolated by local polynomials that are constructed using a constrained inversion. This inversion is such that the traction continuity (TC) conditions are satisfied at the interface while simultaneously matching the displacements produced by the DIC solution at the pixels closest to the center of the subset, where the DIC fields are more accurate. We apply the algorithm to displacement fields of experimental shear ruptures obtained using a local DIC approach and show that the algorithm produces the desired continuous traction field across the interface. The experimental data are also used to examine the sensitivity of the algorithm against different geometrical parameters related to construction of the polynomials in order to avoid artifacts in the stress field
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- Award ID(s):
- 1651235
- NSF-PAR ID:
- 10141612
- Date Published:
- Journal Name:
- Applied sciences
- Volume:
- 9
- Issue:
- 8
- ISSN:
- 2076-3417
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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ABSTRACT The circular-crack model has been widely used in seismology to infer earthquake stress drop. A common assumption is that the background medium is isotropic, although many earthquakes occur in geologically anisotropic settings. In this article, we study the effect of anisotropy on stress drop for a circular crack model and present explicit formalism in both static and kinematic cases. In the static case, we obtain the relationship between stress drop and slip for a circular crack model in an arbitrarily anisotropic medium. Special attention is given to the transversely isotropic (TI) medium. The static formalism is useful in understanding stress drop, but not all quantities are observables. Therefore, we resort to the kinematic case, from which we can infer stress drop using recorded far-field body waves. In the kinematic case, we assume that the crack ruptures circularly and reaches the final displacement determined by the static solutions. The far-field waveforms show that the corner frequency will change with different anisotropic parameters. Finally, we calculate the stress drops for cracks in isotropic and anisotropic media using the far-field waveforms. We find that in an isotropic medium, only shear stress acting on the crack surface contributes to shear slip. However, in a TI medium, if the anisotropy symmetry axis is not perpendicular or parallel to the crack surface, a normal stress (normal to the crack surface) can produce a shear slip. In calculating stress drop for an earthquake in an anisotropic medium using far-field body waves, a large error may be introduced if we ignore the possible anisotropy in the inversion. For a TI medium with about 18% anisotropy, the misfit of inferred stress drop could be up to 41%. Considering the anisotropic information, we can further improve the accuracy of stress-drop inversion.more » « less
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Abstract We study how the asymmetric geometry of thrust faults affects the dynamics of supershear ruptures and their associated trailing Rayleigh ruptures as they interact with the free surface, and investigate the resulting near‐field ground motions. Earthquakes are mimicked by propagating laboratory ruptures along a frictional interface with a 61° dip angle. Using an experimental technique that combines ultrahigh‐speed photography with digital image correlation, we produce sequences of full‐field evolving measurements of particle displacements and velocities. Our full‐field measurement capability allows us to confirm and quantify the asymmetry between the experimental motions of the hanging and footwalls, with larger velocity magnitudes occurring at the hanging wall. Interestingly, because the motion of the hanging wall is generally near‐vertical, while that of the footwall is at dip direction shallower than the dip angle of the fault, the horizontal surface velocity components are found to be larger at the footwall than at the hanging wall. The attenuation in surface velocity with distance from the fault trace is generally larger at the hanging wall than at the footwall and it is more pronounced in the vertical component than in the horizontal one. Measurements of the rotations in surface motions confirm experimentally that the interaction of the rupture with the free surface can be interpreted through a torqueing mechanism that leads to reduction in normal stress near the free surface for thrust earthquakes. Nondimensional analysis shows that the experimental measurements are consistent with larger‐scale numerical simulations as well as field observations from thrust earthquakes.
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Abstract Continuous‐assumed‐strain (CAS) elements were recently introduced (Casquero and Golestanian. Comput Methods Appl Mech Eng. 2022; 399:115354.) to remove the membrane locking present in quadratic ‐continuous NURBS‐based discretizations of linear plane curved Kirchhoff rods. In this work, we generalize CAS elements to remove shear and membrane locking from quadratic NURBS‐based discretizations of linear plane curved Timoshenko rods. CAS elements are an assumed strain treatment that interpolates the shear and membrane strains at the knots using linear Lagrange polynomials. Consequently, the inter‐element continuity of the shear and membrane strains is maintained. The numerical experiments considered in this work show that CAS elements excise the spurious oscillations in shear and membrane forces caused by shear and membrane locking. Furthermore, when using CAS elements with either full or reduced integration, the convergence of displacements, rotations, and stress resultants is independent of the slenderness ratio up to while the convergence is highly dependent on the slenderness ratio when using NURBS elements. We apply the locking treatment of CAS elements to quadratic ‐continuous NURBS and the resulting element type is named discontinuous‐assumed‐strain (DAS) elements. Comparisons among CAS and DAS elements show that once locking is properly removed, continuity across element boundaries results in higher accuracy than continuity across element boundaries. Lastly, CAS elements result in a simple numerical scheme that does not add any significant computational burden in comparison with the locking‐prone NURBS‐based discretization of the Galerkin method.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.3390/9081625
