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![]() | Continuous time-varying Q-factor estimation method in the time-frequency domain | ![]() |
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Seismic waves propagating in underground media experience amplitude attenuation and phase distortion. High-frequency components attenuate faster than low-frequency components, so the centroid frequency of the amplitude spectrum experiences a downshift in the propagation process. Quan and Harris (1997) proposed the CFS method according to the above phenomenon.
When considering seismic wave propagation in the viscoelastic medium, the amplitude spectrum of seismic waves with different travel times can be approximately expressed as (Zhang and Ulrych, 2002)
The CFS method assumes that the amplitude spectrum of the source wavelet satisfies the Gaussian distribution and can be expressed as
By replacing the instantaneous centroid frequency and instantaneous variance in equation 14 with the local centroid frequency and local variance, the time-varying Q-estimation equation can be rewritten as
The CFS method assumes that the amplitude spectrum of the source
wavelet is Gaussian spectrum and that the variance of the amplitude
spectrum does not change with the attenuation effect. However, the
amplitude spectrum of the actual seismic wave usually does not satisfy
the Gaussian distribution. The absorption and attenuation effect would
make the variance smaller and the bandwidth narrower, so the CFS
method would produce the systematic error proportional to the travel
time difference
. When the travel time difference of the two
reflected waves is small, the variances of the two waves are
approximately equal. Thus, this paper improves the Q-estimation
accuracy by reducing the travel time difference. Assuming that each
time sampling point corresponds to a stratum interface, the above
equation can be used to calculate the interval Q-factors between every
two adjacent time sampling points. Then, the interval Q-factors can be
used to further estimate the equivalent Q-factors between the
reference and the target layers. The amplitude spectrum of layer
can be expressed as (Zhang and Ulrych, 2002)
The above equation can be expressed by the equivalent Q theory as
The above equation can be simplifi ed to
By substituting the equation of interval Q-factors estimated using the LCFS
method into the above equation, the equivalent Q-factor of layer
(
th
time sampling point) can be expressed as
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![]() | Continuous time-varying Q-factor estimation method in the time-frequency domain | ![]() |
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