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The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves

Received: 12 December 2013    Accepted:     Published: 10 January 2014
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Abstract

The modification of the matrix method of construction of wavefield on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave propagator" is presented. It is shown that for anisotropic layered medium the matrix propagator can be represented by a "wave propagator" in each layer. The matrix propagator P(z,z0=0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The approbation of the modification of the matrix method for isotropic and anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods and published in foreign papers is executed.

DOI 10.11648/j.earth.20140301.11
Published in Earth Sciences (Volume 3, Issue 1, February 2014)
Page(s) 1-8
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Matrix Propagator, Seismic Moment Tensor, Anisotropic Medium

References
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Author Information
  • Carpatian Branch of the Institute of geophysics named after S.I. Subbotin NAS of Ukraine, Lviv, Ukraine

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  • APA Style

    Anastasiia Pavlova. (2014). The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves. Earth Sciences, 3(1), 1-8. https://doi.org/10.11648/j.earth.20140301.11

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    ACS Style

    Anastasiia Pavlova. The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves. Earth Sci. 2014, 3(1), 1-8. doi: 10.11648/j.earth.20140301.11

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    AMA Style

    Anastasiia Pavlova. The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves. Earth Sci. 2014;3(1):1-8. doi: 10.11648/j.earth.20140301.11

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  • @article{10.11648/j.earth.20140301.11,
      author = {Anastasiia Pavlova},
      title = {The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves},
      journal = {Earth Sciences},
      volume = {3},
      number = {1},
      pages = {1-8},
      doi = {10.11648/j.earth.20140301.11},
      url = {https://doi.org/10.11648/j.earth.20140301.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.earth.20140301.11},
      abstract = {The modification of the matrix method of construction of wavefield on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave propagator" is presented. It is shown that for anisotropic layered medium the matrix propagator can be represented by a "wave propagator" in each layer.  The matrix propagator P(z,z0=0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The approbation of the modification of the matrix method for isotropic and anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods and published in foreign papers is executed.},
     year = {2014}
    }
    

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    T1  - The Modification of the Matrix Method for the Modelling of Propagation of the Body Waves
    AU  - Anastasiia Pavlova
    Y1  - 2014/01/10
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    AB  - The modification of the matrix method of construction of wavefield on the free surface of an anisotropic medium is presented. The earthquake source represented by a randomly oriented force or a seismic moment tensor is placed on an arbitrary boundary of a layered anisotropic medium. The theory of the matrix propagator in a homogeneous anisotropic medium by introducing a "wave propagator" is presented. It is shown that for anisotropic layered medium the matrix propagator can be represented by a "wave propagator" in each layer.  The matrix propagator P(z,z0=0) acts on the free surface of the layered medium and generates stress-displacement vector at depth z. The displacement field on the free surface of an anisotropic medium is obtained from the received system of equations considering the radiation condition and that the free surface is stressless. The approbation of the modification of the matrix method for isotropic and anisotropic media with TI symmetry is done. A comparative analysis of our results with the synthetic seismic records obtained by other methods and published in foreign papers is executed.
    VL  - 3
    IS  - 1
    ER  - 

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