Abstract
With a motivation to gain physical insight of reflection as well as transmission phenomena in frozen (river/ocean) situation for example in Antarctica and other coldest place on Earth, the present article undertakes the analysis of reflection and transmission of a plane wave at the interfaces of layered structured comprised of a water layer of finite thickness sandwiched between an upper half-space constituted of ice and a lower isotropic elastic half-space, which may be useful in geophysical exploration in such conditions. A closed form expression of reflection/transmission coefficients of reflected and transmitted waves has been derived in terms of angles of incidence, propagation vector, displacement vector and elastic constants of the media. Expressions corresponding to the energy partition of various reflected and transmitted waves have also been established analytically. It has been remarkably shown that the law of conservation of energy holds good in the entire reflection and transmission phenomena for different angles of incidence. A numerical examples were performed so to graphically portray the analytical findings. Further the deduced results are validated with the pre-established classical results.
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Acknowledgements
The author Ms. Pooja Singh conveys her sincere thanks to Indian Institute of Technology (Indian School of Mines) Dhanbad, India for providing Junior Research Fellowship and facilitating us with its best research facility. Authors express their sincere thanks to Science and Engineering Research Board, Department of Science and Technology, New Delhi for providing financial support through Project no. EMR/2017/000263. They are also thankful to reviewers for their useful suggestions and valuable comments in the improvement of the manuscript.
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Singh, P., Chattopadhyay, A., Srivastava, A. et al. Reflection and Transmission of P-Waves in an Intermediate Layer Lying Between Two Semi-infinite Media. Pure Appl. Geophys. 175, 4305–4319 (2018). https://doi.org/10.1007/s00024-018-1896-8
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DOI: https://doi.org/10.1007/s00024-018-1896-8