Anvarbek Meirmanov, Marat Nurtas
Abstract:
In the present paper we consider elastic and poroelastic media
having a common interface. We derive the macroscopic mathematical
models for seismic wave propagation through these two different
media as a homogenization of the exact mathematical model at
the microscopic level. They consist of seismic equations for
each component and boundary conditions at the common interface,
which separates different media. To do this we use the two-scale
expansion method in the corresponding integral identities, defining
the weak solution. We illustrate our results with the numerical
implementations of the inverse problem for the simplest model.
Submitted May 28, 2016. Published July 12, 2016.
Math Subject Classifications: 35B27, 46E35, 76R99.
Key Words: Acoustics; two-scale expansion method;
full wave field inversion; numerical simulation.
An addendum was posted on November 28, 2016. It sates that big portion of this article coincides with the article "Seismic in composite media: elastic and poroelastic components" by Anvarbek Meirmanov; Saltanbek Talapedenovich Mukhambetzhanov and Marat Nurtas (Sib. Elekron. Mat. Izv. 13, (2016) 75-88) (Zbl 06607056). See the last page for an explanation from the authors.
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Anvarbek Meirmanov School of Mathematical Sciences and Information Technology Yachay Tech Ibarra, Ecuador email: ameirmanov@yachaytech.edu.ec | |
Marat Nurtas School of mathematics and cibernetics Kazakh-British Technical University Almaty, Kazakhstan email: marat_nurtas@mail.ru |
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