C. G. Knott, D.Sc., F.R.S.E., 2007. "Reflexion and Refraction of Elastic Waves, with Seismological Applications", Classics of Elastic Wave Theory, Michael A. Pelissier, Henning Hoeber, Norbert van de Coevering, Ian F. Jones
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At Lord Kelvin’s suggestion I reproduce, with additions and extensions, a paper I published eleven years ago in the ‘Transactions’ of the Seismological Society of Japan. This Society ceased to exist some years ago; a fact which may serve as a further reason for reproducing a paper, in which the problem of the behaviour of an elastic wave incident on the interface of rock and water was for the first time fully worked out. In that paper also, I believe, the sound method of treating the general problem when the two media are elastic solids was first explicitly stated (see below, pp. 71, 92).
For convenience I have divided the present communication into three parts.
Part I. is a reproduction of my seismological paper of 1888 with a few verbal corrections. Footnotes added now are enclosed in square brackets.
Part II. contains detailed numerical calculations for rock-rock interface and for rock-air interface, similar to the calculations for rock-water interface in Part I.
Part III. gives the mathematical investigation and the various sets of formulæ on which these calculations are based.
Figures & Tables
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: