My PhD Thesis, PDF 3MB - Stanford University

F ( )
1
2
8 o ( i )
[ ( i ) 2
- 117 -
2
] o
2 ,
with o 2 14 KHz and 0 . 5 . I use a short time window to extract the P
wave (first arrival) and use equation (5.5) to calculate the spectral centroid (the curve for
Qp=40 in Figure 5.4). For the purpose of reducing the effect of the window length and
the contamination of later wave trains, we only use the seismograms with source to
receiver separation greater than 3.5m for this and the later examples. Changing the Qp
value in Figure 5.3a to Qp = 80 and Qp =120, I obtain two other curves in Figure 5.4.
Figure 5.4 shows that different slopes of the centroid frequency curves correspond to
different Qp values. Using equation (5.8) and the data shown in Figure 5.4, I obtain the
estimated g =1.3x10 -6 sec/m (or g = /(vQg) with Qg = 450) for this given borehole
model.
Figure 5.3a A simple borehole model.