ABSTRACT To unravel the directivity of past large earthquakes along complex fault systems, with o... more ABSTRACT To unravel the directivity of past large earthquakes along complex fault systems, with offsets and branches, we address the mechanics of "backward" branching (Dmowska et al., EOS, 2002). In the 1992 Landers earthquake, such a 4-km long backward branch formed along the southeastern end of the Homestead Valley Fault (HVF), after transfer of slip to it from the Johnson Valley Fault (JVF) via the Kickapoo Fault (KF) (Sowers et al., BSSA, 1994); the main Landers rupture continued to the north along the HVF. Direct bending of a right-lateral rupture path through a strongly obtuse angle, to form a backward branch, is disallowed by the stress field at a dynamic rupture front (Poliakov et al., JGR, 2002). An alternative mechanism must be identified. We propose that rupture arrests at the termination of one fault segment, allowing a Harris-Day (JGR, 1993) jump to an adjoining segment which then ruptures bilaterally; the end propagating oppositely to the arrested rupture forms the backward branch. Using a 2D elastodynamic BIE formulation incorporating slip-weakening rupture (Kame et al., JGR, 2003), we numerically reproduced backward branching for the JVF-KF to HVF geometry. When the rupture stopped at the northern termination of the KF, it jumped to the HVF and then evolved bilaterally, most extensively to the north in continuation of the main rupture, but also along the southeastern HVF, which curves away from the KF to form the backward branch. A 2D rupture model such as we use may often be justified when length scales of phenomena modeled are small compared to the thickness of the seismogenic zone, as in this case here. We showed that stresses radiated to the curved HVF, while the rupture tip was still propagating along the JVF-KF system, would be unlikely to nucleate rupture on the HVF. Rather, the jump was made possible by the much higher stresses radiated when the rupture stopped at the northern termination of the KF. Those stresses succeeded in nucleating on the HVF because the two fault traces are close to parallel there; the less parallel orientation of the curved HVF further to the southeast would not have allowed jumping. Evidence for the termination of the KF and for the lack of its direct connection with the HVF, hence for the necessity of a jump to transfer rupture, is provided by the following: Detailed surface slip mapping (Sowers et al., BSSA, 1994) which showed a gap, relative relocations of aftershocks which projected fault planes to seismogenic depths (Felzer and Beroza, GRL, 1999), and fault zone trapped wave studies (Li et al., JGR, 1994) which showed non-communication between the JVF-KF and HVF. Such a jump followed by bilateral propagation provides a general mechanism of forming rupture segments running backwards by comparison with the general direction of propagation. During the Landers 1992 event two other such cases followed the JVF-KF to HVF transition just discussed, namely one from the northern HVF to the southeastern Emerson Fault, and then another from the northwestern Emerson to southeastern Camp Rock Fault.
This paper is devoted to an acoustic scattering problem in a 2D partially open waveguide, in the ... more This paper is devoted to an acoustic scattering problem in a 2D partially open waveguide, in the sense that the left part of the waveguide is closed, that is with a ‘bounded’ cross-section, while the right part is bounded in the transverse direction by some perfectly matched layers that mimic the situation of an open waveguide, that is with an ‘unbounded’ cross-section. We prove well-posedness of such scattering problem in the Fredholm sense (uniqueness implies existence) and exhibit the asymptotic behaviour of the solution in the longitudinal direction with the help of the Kondratiev approach. Having in mind the numerical computation of the solution, we also propose some transparent boundary conditions in such longitudinal direction, based on Dirichlet-to-Neumann operators. After proving such artificial conditions actually enable us to approximate the exact solution, some numerical experiments illustrate the quality of such approximation.
Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a di... more Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into those of “zigzag type” and those of “armchair type,” generalizing the classical zigzag and armchair edges. We prove that zero-energy/flat-band edge states arise for edges of zigzag type, but never for those of armchair type. We exhibit explicit formulae for flat-band edge states when they exist. We produce strong evidence for the existence of dispersive (nonflat) edge state curves of nonzero energy for most l.
The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electroma... more The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.
ABSTRACT To unravel the directivity of past large earthquakes along complex fault systems, with o... more ABSTRACT To unravel the directivity of past large earthquakes along complex fault systems, with offsets and branches, we address the mechanics of "backward" branching (Dmowska et al., EOS, 2002). In the 1992 Landers earthquake, such a 4-km long backward branch formed along the southeastern end of the Homestead Valley Fault (HVF), after transfer of slip to it from the Johnson Valley Fault (JVF) via the Kickapoo Fault (KF) (Sowers et al., BSSA, 1994); the main Landers rupture continued to the north along the HVF. Direct bending of a right-lateral rupture path through a strongly obtuse angle, to form a backward branch, is disallowed by the stress field at a dynamic rupture front (Poliakov et al., JGR, 2002). An alternative mechanism must be identified. We propose that rupture arrests at the termination of one fault segment, allowing a Harris-Day (JGR, 1993) jump to an adjoining segment which then ruptures bilaterally; the end propagating oppositely to the arrested rupture forms the backward branch. Using a 2D elastodynamic BIE formulation incorporating slip-weakening rupture (Kame et al., JGR, 2003), we numerically reproduced backward branching for the JVF-KF to HVF geometry. When the rupture stopped at the northern termination of the KF, it jumped to the HVF and then evolved bilaterally, most extensively to the north in continuation of the main rupture, but also along the southeastern HVF, which curves away from the KF to form the backward branch. A 2D rupture model such as we use may often be justified when length scales of phenomena modeled are small compared to the thickness of the seismogenic zone, as in this case here. We showed that stresses radiated to the curved HVF, while the rupture tip was still propagating along the JVF-KF system, would be unlikely to nucleate rupture on the HVF. Rather, the jump was made possible by the much higher stresses radiated when the rupture stopped at the northern termination of the KF. Those stresses succeeded in nucleating on the HVF because the two fault traces are close to parallel there; the less parallel orientation of the curved HVF further to the southeast would not have allowed jumping. Evidence for the termination of the KF and for the lack of its direct connection with the HVF, hence for the necessity of a jump to transfer rupture, is provided by the following: Detailed surface slip mapping (Sowers et al., BSSA, 1994) which showed a gap, relative relocations of aftershocks which projected fault planes to seismogenic depths (Felzer and Beroza, GRL, 1999), and fault zone trapped wave studies (Li et al., JGR, 1994) which showed non-communication between the JVF-KF and HVF. Such a jump followed by bilateral propagation provides a general mechanism of forming rupture segments running backwards by comparison with the general direction of propagation. During the Landers 1992 event two other such cases followed the JVF-KF to HVF transition just discussed, namely one from the northern HVF to the southeastern Emerson Fault, and then another from the northwestern Emerson to southeastern Camp Rock Fault.
This paper is devoted to an acoustic scattering problem in a 2D partially open waveguide, in the ... more This paper is devoted to an acoustic scattering problem in a 2D partially open waveguide, in the sense that the left part of the waveguide is closed, that is with a ‘bounded’ cross-section, while the right part is bounded in the transverse direction by some perfectly matched layers that mimic the situation of an open waveguide, that is with an ‘unbounded’ cross-section. We prove well-posedness of such scattering problem in the Fredholm sense (uniqueness implies existence) and exhibit the asymptotic behaviour of the solution in the longitudinal direction with the help of the Kondratiev approach. Having in mind the numerical computation of the solution, we also propose some transparent boundary conditions in such longitudinal direction, based on Dirichlet-to-Neumann operators. After proving such artificial conditions actually enable us to approximate the exact solution, some numerical experiments illustrate the quality of such approximation.
Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a di... more Consider the tight binding model of graphene, sharply terminated along an edge l parallel to a direction of translational symmetry of the underlying period lattice. We classify such edges l into those of “zigzag type” and those of “armchair type,” generalizing the classical zigzag and armchair edges. We prove that zero-energy/flat-band edge states arise for edges of zigzag type, but never for those of armchair type. We exhibit explicit formulae for flat-band edge states when they exist. We produce strong evidence for the existence of dispersive (nonflat) edge state curves of nonzero energy for most l.
The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electroma... more The analysis of Cartesian Perfectly Matched Layers (PMLs) in the context of time-domain electromagnetic wave propagation in a 3D unbounded anisotropic homogeneous medium modelled by a diagonal dielectric tensor is presented. Contrary to the 3D scalar wave equation or 2D Maxwell's equations some diagonal anisotropies lead to the existence of backward waves giving rise to instabilities of the PMLs. Numerical experiments confirm the presented result.
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Papers by Sonia Fliss