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Modified spectral ratio method<br />
To obtain an estimate of frequency dependent Q, the natural logarithm of the amplitude<br />
ratio, ln[ A ( z,<br />
f ) A0 ( z0<br />
, f )], from equation (2) is plotted against the arrival-time difference<br />
T − of two receivers for each frequency. The slope of the regression line isπ f Q .<br />
( ) T 0<br />
SYNTHETIC DATA EXAMPLE<br />
The algorithms of the spectral method and the modified spectral method, which are developed<br />
in this study, were applied to synthetic data sets with a velocity model including five<br />
horizontal layers (Figure 1). A source was located at 20 m from the well head to simulate<br />
‘zero-offset VSP’ geometry. Receivers were located from 1,530 to 1,850 m in the borehole.<br />
Only direct arrivals were created to calculate the Q-factors and three synthetic data sets were<br />
generated with different receiver intervals of 2, 5, and 10 m, respectively. Synthetic<br />
seismograms were created by ray theory and the effects of frequency-dependent Q were<br />
applied by using Strick’s model (1970). A Klauder wavelet with a frequency bandwidth of 8<br />
to 180 Hz was used as a source wavelet. Figure 2 shows the amplitude spectrums of the direct<br />
arrivals in traces when the receiver interval was 10 m. As shown from the figure, the<br />
amplitude decreases with increasing the depth of the receiver and the attenuation occurs more<br />
significantly in higher frequencies.<br />
Q factors extracted from direct arrivals in the synthetic data by using the spectral ratio method<br />
are shown in Figure 3. The frequency range of 30 to 160 Hz is used in the calculation, and Q<br />
factors for the second, the third, the fourth, and the fifth layers are obtained. Only positive<br />
values out of the computed Q’s are represented in the Figure 3 because negative value for Q<br />
factor cannot exist. All results show similar patterns regardless of the receiver interval. Note<br />
that the Q’s computed by the spectral ratio method approach to the true Q only for the fourth<br />
layer which has a low Q factor (Q=50). In the layers with large Q values, the differences of<br />
the amplitude spectrums of traces are very small and it makes the computation of Q-factor<br />
very unstable. However, the computed Q-factors except for those from the fifth layer<br />
(Q=1000) show the similar variation pattern to that of true Q-factors. Very low Q factors<br />
computed for the fifth layer might be due to lack of the data used in the calculation.<br />
20 m<br />
0<br />
Vp=1500m/s<br />
Vs=<br />
0m/s<br />
Q = 62000<br />
=1.93g/<br />
1530<br />
Vp=1580m/s<br />
Vs= 650m/s<br />
Sea bottom<br />
Q = 500<br />
=1.95g/<br />
1000<br />
Depth (m)<br />
1850<br />
Vp=1850m/s Vs= 700m/s<br />
Vp=1550m/s Vs= 700m/s<br />
Q=150 =2.03g/<br />
Q=50 =1.94g/<br />
Vp=1700m/s<br />
Q = 1000<br />
Vs= 980m/s<br />
=1.99g/<br />
1630<br />
1730<br />
1830<br />
2000<br />
Figure 1. A subsurface model used in creating synthetic zero-offset VSP data.<br />
New Energy Resources in the <strong>CCOP</strong> Region - Gas Hydrates and Coalbed Methane 37