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Transient and impulse responses of a one-dimensional linearly attenuating medium — II. A parametric study

Minster, J. B. (1978) Transient and impulse responses of a one-dimensional linearly attenuating medium — II. A parametric study. Geophysical Journal of the Royal Astronomical Society, 52 (3). pp. 503-524. ISSN 0016-8009. doi:10.1111/j.1365-246X.1978.tb04246.x.

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We investigate one-dimensional waves in a standard linear solid for geophysically relevant ranges of the parameters. The critical parameters are shown to be T*= t_u/Q_m where t_u is the travel time and Q_m the quality factor in the absorption band, and τ^(-1)_m, the high-frequency cut-off of the relaxation spectrum. The visual onset time, rise time, peak time, and peak amplitude are studied as functions of T* and τ_m. For very small τ_m, this model is shown to be very similar to previously proposed attenuation models. As τ_m grows past a critical value which depends on T*, the character of the attenuated pulse changes. Seismological implications of this model may be inferred by comparing body wave travel times with a ‘one second’ earth model derived from long-period observations and corrected for attenuation effects assuming a frequency independent Q over the seismic band. From such a comparison we speculate that there may be a gap in the relaxation spectrum of the Earth's mantle for relaxation times shorter than about one second. However, observational constraints from the attenuation of body waves suggest that such a gap might in fact occur at higher frequencies. Such a hypothesis would imply a frequency dependence of Q in the Earth's mantle for short-period body waves.

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Additional Information:Copyright © 1978 The Royal Astronomical Society. Received 1977 August 19; in original form 1977 May 18. Lively and instructive discussions with R. Hart, L. Burdick, G. Mellman, and R. Butler are gratefully acknowledged. D. Anderson and H. Kanamori as well as numerous colleagues offered helpful criticism. V. Cormier provided a useful review of the manuscript. This research was supported by the Advanced Research Projects Agency of the Department of Defense and was monitored by the Air Force Office of Scientific Research under Contract No. AFOSR F49620-77-C-0022. Contribution No. 2914, Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, California 91125.
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Advanced Research Projects Agency (ARPA)UNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-77-C-0022
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Caltech Division of Geological and Planetary Sciences2914
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Official Citation:J. B. Minster Transient and impulse responses of a one-dimensional linearly attenuating medium — II. A parametric study Geophys. J. Int. (1978) 52 (3): 503-524 doi:10.1111/j.1365-246X.1978.tb04246.x
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:51614
Deposited By: George Porter
Deposited On:12 Nov 2014 15:37
Last Modified:10 Nov 2021 19:13

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