L. Amundsen et R. Mittet, ESTIMATION OF PHASE VELOCITIES AND Q-FACTORS FROM ZERO-OFFSET, VERTICAL SEISMIC PROFILE DATA, Geophysics, 59(4), 1994, pp. 500-517
In seismic processing, we face the problem of characterizing the effec
t of anelastic attenuation on the seismic signal during propagation. T
o solve this problem, approximate physical properties of the porous fl
uid-filled rock are needed. We give a strategy for estimating effectiv
e parameters governing absorption and dispersion of waves in viscoelas
tic media by inverting zero-offset vertical seismic profiling (VSP) da
ta acquired in a medium with plane horizontal layers. The VSP data are
filtered such that all energy except for the direct downgoing wave an
d the primary reflected wave from each interface is zeroed. This proce
dure requires a model with layer thicknesses greater than a minimum li
mit. A stack of thin layers must be replaced by a layer with average p
hysical properties and with thickness exceeding the required minimum.
The model parameter vector is partitioned into two vectors. The first
contains the frequency-dependent complex propagation velocity in each
layer, and is evaluated over the frequency band where the signal-to-no
ise ratio is acceptable. In the second vector, the geophone-to-formati
on coupling factors, which are assumed to be frequency-independent, ar
e gathered. It is straightforward to determine both the frequency-depe
ndent phase velocities and the frequency-dependent quality (Q-) factor
s from the frequency-dependent propagation velocities. We assume that
layer boundaries and layer densities can be obtained from well logs. W
e give the equations for a simplified forward-modeling scheme and the
equations for the solution of the nonlinear inverse problem. The algor
ithm is applied to both synthetic and real data. Inversion of syntheti
c data shows that the phase velocities can be satisfactorily estimated
, and that Q-factors below approximately 50 are well-resolved, even fo
r large errors in the geophone-to-formation coupling factors. The esti
mated phase velocities from the real data behave fairly stable as a fu
nction of frequency. The results for the quality factors are less conc
lusive, but the low Q-factors may be of correct size.