# Apparent and intrinsic Q: the one-dimensional case

## Main Article Content

## Abstract

The propagation of plane waves through statistically layered media is investigated both numerically and with single-scattering theory in the one-dimensional case. Exact apparent or stratigraphic *Q*, *Q _{s}*, is determined from synthetic seismograms with the spectral-ratio method. Maximum velocity (impedance) fluctuations up to 30% (~40%) are studied; the fluctuations are uniformly distributed with zero mean. In all cases the trend of

*Q*as a function of frequency is well described by the analytical

_{s}*Q*, as determined from single-scattering theory under the assumption of an exponential autocorrelation function of the impedance fluctuations. The frequency dependence of the analytical

_{s}*Q*

_{s}^{-1}follows a Debye-peak function, its maximum is

*γ*

^{2}/2 and corresponds to the wavelength 4

*π*

*a*(

*γ*

^{2}= variance of relative impedance fluctuation,

*a*= correlation distance). In further numerical calculations intrinsic or anelastic

*Q*,

*Q*, is introduced, and it is shown that total attenuation

_{a}*Q*

^{ -1}agrees very well with the sum of apparent and anelastic attenuation,

*Q*

_{s}^{-1}+

*Q*

_{a}^{-1}. Finally, a simple, minimum-phase stratigraphic attenuation operator is derived which describes the amplitude decay and the dispersion in a one-dimensional random medium with good accuracy. Stratigraphic attenuation is similar to the anelastic attenuation of a standard linear solid.

**ARK**: https://n2t.net/ark:/88439/y038753

Permalink: https://geophysicsjournal.com/article/119

## Article Details

*Journal of Geophysics*,

*61*(1), 46-54. Retrieved from https://journal.geophysicsjournal.com/JofG/article/view/119

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