An exact solution for the one‐dimensional elastic wave equation in layered media

1992 ◽  
Vol 92 (6) ◽  
pp. 3364-3370 ◽  
Author(s):  
Roberto A. Tenenbaum ◽  
Moysés Zindeluk
2021 ◽  
Vol 4 (6) ◽  
pp. 1-10
Author(s):  
Biagio Cassano ◽  
◽  
Lucrezia Cossetti ◽  
Luca Fanelli ◽  
◽  
...  

<abstract><p>In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lamé operators with non self-adjoint perturbations, we provide quantitative bounds on the location of the point spectrum in terms of suitable norms of the damping coefficient.</p></abstract>


Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. U51-U61
Author(s):  
Xufei Gong ◽  
Qizhen Du ◽  
Qiang Zhao ◽  
Pengyuan Sun ◽  
Jianlei Zhang ◽  
...  

Wave-equation datuming (WED) techniques have demonstrated superiority when waves occur on the acquisition surface nonvertically, and traditional static corrections based on the time shift become inaccurate. Meanwhile, as for multicomponent data, those scalar techniques can hardly maintain the vector characteristics for the following multicomponent data processing flows. Considering this, we have developed an elastic-wave datuming approach to handle the static corrections for multicomponent data. Different from those existing scalar WED techniques, the multicomponent data are first decomposed into multicomponent P- and S-wave data. Then, the decomposed data are transformed into the [Formula: see text]-[Formula: see text] domain, and they are extrapolated from the acquisition surface to the datum using the one-way elastic-wave continuation. Finally, the datumed multicomponent data are reconstructed at the output datum by adding up the datumed P- and S-wave data. This elastic WED can guarantee that the same wave modes on different components are equally datumed, and the data remain multicomponent so that they are still applicable to multicomponent-joint processing techniques. Finally, several test examples involved in this paper have proved our method’s effectiveness in multicomponent data datuming application.


2008 ◽  
Vol 2008 ◽  
pp. 1-31 ◽  
Author(s):  
Jürgen Geiser

Motivated by seismological problems, we have studied a fourth-order split scheme for the elastic wave equation. We split in the spatial directions and obtain locally one-dimensional systems to be solved. We have analyzed the new scheme and obtained results showing consistency and stability. We have used the split scheme to solve problems in two and three dimensions. We have also looked at the influence of singular forcing terms on the convergence properties of the scheme.


2021 ◽  
Vol 130 (2) ◽  
pp. 025104
Author(s):  
Misael Ruiz-Veloz ◽  
Geminiano Martínez-Ponce ◽  
Rafael I. Fernández-Ayala ◽  
Rigoberto Castro-Beltrán ◽  
Luis Polo-Parada ◽  
...  

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