R. Stoneley, M.A., 2007. "Elastic Waves at the Surface of Separation of Two Solids", Classics of Elastic Wave Theory, Michael A. Pelissier, Henning Hoeber, Norbert van de Coevering, Ian F. Jones
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In considering how the energy of a seismic disturbance is dissipated one is led to enquire into the possibility of the existence of waves, analogous to Rayleigh waves and Love waves, that are propagated in the interior of the earth along the junction of strata, or chiefly within a certain stratum, so that the energy is dissipated by internal viscosity without the occurrence of any appreciable surface displacement.
Two surfaces of discontinuity of density and elastic properties are commonly believed to exist below that part of the earth’s crust which is accessible to geologists, namely, the junction of the granitic layer with the basic rocks, and the surface of separation of the Wiechert metallic core from the rocky shell. It becomes of interest to examine whether a wave of the Rayleigh type can be propagated along such an interface; an enquiry may also be made into the circumstances in which a wave of the Love type may exist if a stratum of uniform thickness is bounded on both sides by very deep layers of different materials.
It has been pointed out to me by Dr. Harold Jeffreys that the former problem is in some respects a particular case of Prof. Love’s discussion
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Classics of Elastic Wave Theory
In this chapter, we give a brief synopsis of each of the classic papers referred to in this collection. Where relevant, we reproduce the basic equations, recast in modern notation. Supporting works also are referred to. They are listed in the “General References” section.
Table 1 is a quick outline of the key contributions of each paper reprinted in this book.
Robert Hooke, “Potentia Restitutiva, or Spring” (Oxford, 1678)
The article by Robert Hooke, “Potentia Restitutiva, or Spring,” contains the statement of the proportional relation between stress and strain universally referred to as Hooke’s law. Although the English language has evolved somewhat since 1678, the article does not require translation. Hooke describes a variety of experiments, accompanied by illustrations, confirming the stress/strain relation over a wide range of applied loads. He emphasizes the great generality of his results.
Based on his experimental work from 1660 onward, Hooke first published his law in 1676 in the form of an anagram in Latin,
which he later revealed to be “ut tensio sic vis.” Roughly translated, this means “as the force, so is the displacement” (Love, 1911; Boyce and DiPrima, 1976).
In his treatise, Hooke examined the behavior of springs, so his first casting of the equations dealt with the restoring force on a spring, for a given displacement: