Initially, it should be mentioned that this report is a highly edited redraft, modification and partial retranslation of a paper by Frenkel (1944) which was written in Russian and translated by Cheng (1972). As the title of the original paper dealt with seismoelectric theory, some of the original text has been deleted, some moved to Appendix A, and additional text and formulae have been added. The writer of this apologizes to the original author and translator for this (possible) misuse of their academic research, but it, compared with other similar works, explains in a fairly uncomplicated manner the implementation of Darcy's law into the elastodynamic equations, producing, at least in principle, the equations of motion for compressional (P) and shear (S) waves propagating in a poroviscoelastic medium. Other papers and texts on this topic will have to be consulted for more numerically specific aspects of this problem. However, a reasonable understanding of the contents of this report should make such undertakings much easier. All equations have been re-derived and typographic errors corrected, and points that may require further investigation are annotated in footnotes. Appendix B has been added, in which all of the parameters used in the text are defined, as the notation of the original translation has been modified to conform to recent works dealing with this topic. Finally, it should be noted that as the original paper was severely modified, this is a preliminary report and is subject to changes to improve its readability or to introduce additional relevant content.
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