Electron. J. Diff. Equ., Vol. 2016 (2016), No. 184, pp. 1-22.

Mathematical models of seismics in composite media: elastic and poro-elastic components

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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