A note on the dynamic and static displacements from a point source in multilayered media

By Lupei Zhu, L. Rivera. 2002

686 citations recorded by the source corpus.

SUMMARY A simple and unified approach is presented to solve both the elasto-dynamic and elastostatic problems of point sources in a multi-layered half-space by using the Thompson-Haskell propagator matrix technique. It is shown that the apparent incompatibility between the two is associated with the degeneracy of the dynamic problem when ω = 0 and both can be handled uniformly using the Jordan canonical forms of matrices. We re-derive the propagator matrices for both the dynamic and static cases. We then show that the dynamic propagator matrix and the solution converge to their static counterparts as ω → 0. Satisfactory static deformation can be obtained numerically using the dynamic solution at near-zero frequency.

Subfields: Computer Vision and Pattern Recognition, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b936844e52c05493ef52a0d763d77528abbaabb4

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In Computer Vision and Pattern Recognition

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Strain Green's Tensors, Reciprocity, and Their Applications to Seismic Source and Structure Studies (2006, methodology): “Kim B. Olsen’s finite-difference code (Olsen 1994) and Lupei Zhu’s frequencywavenumber code (Zhu and Rivera, 2002) were used in some of our numerical calculations.”
Seismic imaging: From classical to adjoint tomography (2012, background): “For receiver function studies of local arrays where incident teleseismic wavefield can be well approximated by plane waves (Liu and Chen, 2011), forward wavefield for a 1D background medium can be easily computed by semi-analytical methods for layered media (Aki and Richards, 2002; Zhu and Rivera, 2”
Joint inversion of strong motion, teleseismic, geodetic, and tsunami datasets for the rupture process of the 2011 Tohoku earthquake (2011, methodology): “dataset, Green’s functions were calculated using the method of Zhu and Rivera [2002]. We used 343 GEONET stations and calculated two-component static displacements by comparing averages before and immediately after the mainshock”
Frechet Kernels for Imaging Regional Earth Structure Based on Three-Dimensional Reference Models (2005, neutral): “Zhu, L., and A. Rivera (2002).”
Retrieval of Moho‐reflected shear wave arrivals from ambient seismic noise (2010, positive): “These synthetics were generated with a frequency–wavenumber (w−k) synthetic seismogram package (Zhu & Rivera 2002) assuming the source station is replaced by a vertical point force.”
Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations (2009, methodology): “8×104, zr =0 and compared to a semi-analytical frequency-wavenumber (FK) solution [13,34,37] using the FK code [36].”
New constraints on mechanisms of remotely triggered seismicity at Long Valley Caldera (2005, methodology): “The first three corrections are calculated with synthetics calculated by using Thompson-Haskell propagator matrices and a standard southern California model [Zhu and Rivera, 2002; Dreger and Helmberger, 1993].”