Geology Reference
In-Depth Information
Seismic
Trace
Wavelet
Least
squares
filter
0
Reflection
Series
Figure 4.9
Schematic illustration of least squares filtering to obtain the wavelet.
straightforward but most software now offers the possi-
bility of extracting the wavelet along the borehole path.
To achieve a reliable extraction the quality of the log
data has to be good and the time
(
Fig. 4.10
) need to satisfy the following relations
(White
1980
; Walden and White,
1984
; White,
1997
):
bT
(3.408 T)/L,
where b
¼
depth conversion has
to be accurate. Matching involves extracting a wavelet
operator (of length L) from a time window of seismic
data (of length T). In signal processing terms L is the
-
¼
analysis bandwidth and is related to L by:
b
constant / L (for correlations tapered with a
Papoulis window, constant
¼
3.408);
bT is referred to as the spectral smoothing factor.
This parameter needs to be
¼
'
lag
window length
'
. Confusingly, L is often referred to as
6;
b/B should between 0.25 and 0.5 (where B
>
the
but it is approximately twice the
length of a three-loop wavelet. The time segment length
should be around 500 ms. If it is any longer the statio-
narity assumption concerning phase may be invalid and
phase rotation with depth could adversely affect the
results. If the segment is shorter, the chances of a statis-
tically valid tie are reduced. If possible it is best to choose
a time segment for which the start and end have muted
reflectivity; wavelet extractions are likely to be distorted
if the time segment truncates close to a large reflection.
In order for matching measures such as the cross-
correlation to be statistically meaningful L and T
'
wavelet length
'
¼
statistical bandwidth estimated from the data).
Effectively these relationships mean that the time
segment to (three-loop) wavelet length ratio should
be around 3 for low-bandwidth data (B ~ 25 Hz) and
around 6 for high-bandwidth data (B ~ 50 Hz).
4.4.1.1 Well tie measures: goodness of fit and accuracy
In the well matching technique goodness of fit is
measured as the proportion of trace energy predicted
(PEP) by the synthetic seismogram:
44
