The Transition to the Elastic Regime in the Vicinity of an Underground Explosion
Abstract
Wave propagation problems were examined in nonlinear materials for which attenuation, described by the inverse quality factor i/q, 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 .000001 to .0001. 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, i/q 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. 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 18, 1990
- Accession Number
- ADA236030
Entities
People
- J. B. Minster
- P. M. Shearer
- S. M. Day
Organizations
- Scripps Institution of Oceanography