Summary
The propagation of pressure waves in a two-layered liquid medium (assumed to be compressible) resting on a rigid bottom has been considered. The source of disturbance has been taken to be three-dimensional with spherical symmetry. Similar problems of layered but semi-infinite liquids have been discussed by Pekeris, Press and Ewing (cf Ewing, Jardetzky and Press3)). The problem of generation of Love waves which is akin to these problems is discussed by Sezawa7).
The method of Covert2) using Green’s functions has been suitably adopted here to solve the problem. This elegant method, which is applicable to any number of layered liquids and SH wave generation in layered solids, is believed not to have been used in such problems so far.
Recently Ghosh4) has adopted this method to a two-dimensional model of a semi-infinite layered liquid with slightly slant interface to explain the singing phenomenon in off-shore seismic prospecting. The dispersion equation has been obtained and analysed on the lines of Buchwald1).
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References
Buchwald, V. T., Quart. J. Mech. & Appl. Math.11 (1958) 498.
Covert, E. E., J. Math. Phys.37 (1958) 58.
Ewing, M., W. Jardetzky and F. Press, Elastic Waves in layered media, McGraw-Hill, 1957, pp. 126–156.
Ghosh, M. L., Jeof. Pura Appl.49 (1961) 61.
Magnus, W. and F. Oberhettinger, Functions of mathematical physics, Chelsea, 1954.
Morse, P. and H. Feshbach, Methods of theoretical physics I, McGraw-Hill, 1953, p. 943.
Sezawa, K., Bull. Earthquake Res. Inst.33 (1935) 1.
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Bose, S.K. On pressure waves in a layered liquid. Appl. sci. Res. 12, 282–292 (1963). https://doi.org/10.1007/BF03184978
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DOI: https://doi.org/10.1007/BF03184978