Published:January 01, 2007
Zoeppritz, Karl, was born on October 22, 1881, in Mergelstetten, Württemberg, Germany, and died on July 20, 1908, in Göttingen, Germany. He studied geology in Munich and Freiburg, Germany, but also was interested in physics and geophysics. In 1905, Zoeppritz obtained a Ph.D. in geology at Freiburg University, studying the alpine geology of Switzerland. He transferred to Karlsruhe, where he obtained a degree in secondary schoolteaching (Oberlehrerexamen).
In 1906, Zoeppritz moved to Göttingen, where he became assistant to Emil Wiechert at the Geophysical Institute. Zoeppritz analyzed earthquake data, soon collaborating with Wiechert. To understand the interior of the earth and possible discontinuities within it, they studied traveltime curves and constructed velocity-depth functions. Wiechert had calculated theoretical traveltime curves for different kinds of first- and second-order discontinuities, and Zoeppritz applied that theory to the full set of reflection and refraction coefficients for plane-wave amplitudes at a first-order discontinuity (Zoeppritz, 1919).
Another part of Zoeppritz’s work, in collaboration with Ludwig Geiger, derived the P-wave velocity within the earth (Zoeppritz and Geiger, 1909).
When Zoeppritz died in 1908 after contracting an infection at age 26, Wiechert, Geiger, and Beno Gutenberg subsequently successfully finished his calculations. Zoeppritz’s wife, Elisabeth Ganz, helped to prepare his manuscripts for printing. Thus, some of Zoeppritz’s work was published shortly after he died. However, the last of his papers, concerned with reflection and transmission coefficients, was not published until 1919, 11 years after his death.
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: