M. P. Rudzki, 2007. "On the Shape of Elastic Waves in Rocks: IV. Study on the Theory of Earthquakes", Classics of Elastic Wave Theory, Michael A. Pelissier, Henning Hoeber, Norbert van de Coevering, Ian F. Jones
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This treatise is the continuation of another study that I published under a similar title about a year ago; thus, I shall start with a summary of this older work.
As a consequence of [overburden] pressure or layering—or both—rocks can by no means be regarded as being globally isotropic. On the contrary, the potential of elastic forces in a horizontally layered rock and [vertical] pressure must contain five elastic constants. One has
[are (related to) the strain components]. Moreover, it has turned out that the wave surface decouples into an ellipsoid of rotation and another very complicated surface of rotation. The equation of the meridional section of the ellipsoid is
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: