Mathematical models of seismics in composite media: elastic and poro-elastic components
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 sei...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Texas State University
2016-07-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/184/abstr.html |
| _version_ | 1819230758437388288 |
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| author | Anvarbek Meirmanov Marat Nurtas |
| author_facet | Anvarbek Meirmanov Marat Nurtas |
| author_sort | Anvarbek Meirmanov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-23T11:34:09Z |
| format | Article |
| id | doaj.art-2f56be6732ac46bdbe6e0e311c80b5cc |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-23T11:34:09Z |
| publishDate | 2016-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-2f56be6732ac46bdbe6e0e311c80b5cc2022-12-21T17:48:43ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-07-012016184,122Mathematical models of seismics in composite media: elastic and poro-elastic componentsAnvarbek Meirmanov0Marat Nurtas1 Yachay Tech, Ibarra, Ecuador Kazakh-British Technical Univ., Almaty, Kazakhstan 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.http://ejde.math.txstate.edu/Volumes/2016/184/abstr.htmlAcousticstwo-scale expansion methodfull wave field inversionnumerical simulation |
| spellingShingle | Anvarbek Meirmanov Marat Nurtas Mathematical models of seismics in composite media: elastic and poro-elastic components Electronic Journal of Differential Equations Acoustics two-scale expansion method full wave field inversion numerical simulation |
| title | Mathematical models of seismics in composite media: elastic and poro-elastic components |
| title_full | Mathematical models of seismics in composite media: elastic and poro-elastic components |
| title_fullStr | Mathematical models of seismics in composite media: elastic and poro-elastic components |
| title_full_unstemmed | Mathematical models of seismics in composite media: elastic and poro-elastic components |
| title_short | Mathematical models of seismics in composite media: elastic and poro-elastic components |
| title_sort | mathematical models of seismics in composite media elastic and poro elastic components |
| topic | Acoustics two-scale expansion method full wave field inversion numerical simulation |
| url | http://ejde.math.txstate.edu/Volumes/2016/184/abstr.html |
| work_keys_str_mv | AT anvarbekmeirmanov mathematicalmodelsofseismicsincompositemediaelasticandporoelasticcomponents AT maratnurtas mathematicalmodelsofseismicsincompositemediaelasticandporoelasticcomponents |