Articles | Volume 3, issue 2
Nonlin. Processes Geophys., 3, 89–101, 1996
https://doi.org/10.5194/npg-3-89-1996
Nonlin. Processes Geophys., 3, 89–101, 1996
https://doi.org/10.5194/npg-3-89-1996

  30 Jun 1996

30 Jun 1996

A new theoretical paradigm to describe hysteresis, discrete memory and nonlinear elastic wave propagation in rock

K. R. McCall1 and R. A. Guyer2 K. R. McCall and R. A. Guyer
  • Los Alamos National Laboratory, Los Alamos, New Mexiko
  • 1Present address Department of Physics, University of Nevada, Reno, Nevada
  • 2Present address Department of Physics and Astronomy, University of Massachusetts, Amherst, Massachusetts

Abstract. The velocity of sound in rock is a strong function of pressure, indicating that wave propagation in rocks is very nonlinear. The quasistatic elastic properties of rocks axe hysteretic, possessing discrete memory. In this paper a new theory is developed, placing all of these properties (nonlinearity, hysteresis, and memory) on equal footing. The starting point of the new theory is closer to a microscopic description of a rock than the starting point of the traditional five-constant theory of nonlinear elasticity. However, this starting point (the number density ρ of generic mechanical elements in an abstract space) is deliberately independent of a specific microscopic model. No prejudice is imposed as to the mechanism causing nonlinear response in the microscopic mechanical elements. The new theory (1) relates suitable stress-strain measurements to the number density ρ and (2) uses the number density ρ to find the behaviour of nonlinear elastic waves. Thus the new theory provides for the synthesis of the full spectrum of elastic behaviours of a rock. Early development of the new theory is sketched in this contribution.

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