The Transition to the Elastic Regime in the Vicinity of an Underground Explosion

  1. Steven R. Taylor,
  2. Howard J. Patton and
  3. Paul G. Richards
  1. J. Bernard Minster1,
  2. Steven M. Day2 and
  3. Peter M. Shearer1

Published Online: 18 MAR 2013

DOI: 10.1029/GM065p0229

Explosion Source Phenomenology

Explosion Source Phenomenology

How to Cite

Minster, J. B., Day, S. M. and Shearer, P. M. (1991) The Transition to the Elastic Regime in the Vicinity of an Underground Explosion, in Explosion Source Phenomenology (eds S. R. Taylor, H. J. Patton and P. G. Richards), American Geophysical Union, Washington, D. C.. doi: 10.1029/GM065p0229

Author Information

  1. 1

    Scripps Institution of Oceanography, Institute of Geophysics and Planetary Physics, A-025, La Jolla, California 92093-0025

  2. 2

    San Diego State University, Department of Geological Sciences, San Diego, California 92182-1900

Publication History

  1. Published Online: 18 MAR 2013
  2. Published Print: 1 JAN 1991

ISBN Information

Print ISBN: 9780875900315

Online ISBN: 9781118663820



  • Underground nuclear explosions—Detection—Congresses;
  • Seismology—Congresses


We have examined wave propagation problems in nonlinear materials for which attenuation, described by the inverse quality factor Q−1, is independent of frequency but grows linearly with strain amplitude. This particular relationship is an adequate representation of many laboratory observations for rocks tested in the strain range 10−6 to 10−4. However, our concern is that use of data reduction techniques developed in the context of a linear theory (e.g. spectral ratios, Lorentz peaks) may yield biased answers at these moderately high strains.

The results of our elementary, one-dimensional numerical modeling experiments are mixed, and do not seem to be easily predictable from simple arguments. For example, Q −1 estimates derived from the half-width of a resonance peak appear to be surprisingly accurate well into the nonlinear regime. Similarly, the nonlinear interaction of one-dimensional pulses does not lead to strong departures from linear superposition in the range of nonlinear behavior we have considered. On the other hand, the propagation of a one-dimensional narrow pulse through a medium with frequency-independent, but amplitude-dependent Q is not described accurately by an equivalent “Q-operator”, and observed resonance peak distortions due to nonlinearity are worse than predicted by the calculations.

We rely on fully nonlinear finite difference simulations in which attenuation is independent of frequency but is proportional to the local strain amplitude. We find that, in contrast to linear Q models for which the spectrum of the “Q operator” tends to unity at low frequencies, a nonlinear rheology may lead to significant spectral distortions at all frequencies, and energy losses can be substantial even at wavelengths long compared to the propagation distance. Thus, even though this nonlinear rheology is only relevant in a limited range of scaled distances from a contained explosion, this raises the possibility that the far field source spectrum can be affected to some degree at all frequencies, including those pertinent to teleseismic body waves. In that case, nonlinear amplitude dependent attenuation would have to be taken into account when evaluating the effectiveness of seismic coupling. However, we show that extrapolation of our one-dimensional results to the spherically symmetric case is not straightforward. Nonlinear wave propagation is pulse-shape sensitive, and each individual problem must be tested separately in numerical simulations.