Structural interpretation - 3-D Seismic Interpretation - page 66

as Backus averaging (Backus, 1962 ) . The difference from the simple approach outlined
previously depends on the velocity and density variation between the different layers.
For shale-sand alternation, the difference is usually small; for shale-dolomite, it can
be quite large, perhaps reaching as much as 20%.
It often happens that poor well ties cannot be definitely traced to a specific cause in
the seismic or the log data. As pointed out by Ziolkowski et al . ( 1998) , there is a funda-
mental problem: seismic traces are not in reality the simple convolution of a physically
meaningful wavelet with the reflection coefficient series, as has been assumed above. In
reality, the seismic data we collect are the response of a layered earth to a point source,
including internal multiples and free-surface effects; conventional processing combines
these records to produce stacked sections and attempts to remove multiples, diffractions,
P-S conversions, and so on. It is not surprising if we then find that sometimes the wavelet
that gives the best fit between the stacked seismic trace and the well synthetic varies
from one well to another. Sometimes it may not be possible to have much confidence in
the well tie, even after careful editing of the log data and consideration of all the other
possible complications. At this point, it is useful to have a different line of evidence to
help understand the cause of discrepancies between the well synthetic and the surface
seismic, and this is where the VSP can help.

3.1.2 The VSP

Essentially, the technique is to record a surface source using downhole geophones;
a general account has been given by, for example, Oristaglio ( 1985 ) . The simplest
geometry is the case of a vertical well with a seismic source at the wellhead ( fig. 3.4(a) ,
where the source is shown slightly separated from the wellhead for clarity). Recordings
would be made of the source by a geophone at a series of downhole locations, e.g. at
intervals of 50 ft over a vertical distance of 4000 ft to give records at 80 levels. The record
for any particular level will contain both upgoing and downgoing waves; the former
are reflections from horizons below the geophone, and the latter are the direct arrivals,
as sketched in fig. 3.4(a) . Both upgoing and downgoing arrivals will be contaminated
by multiples due to reflections both above and below the geophone, but the upgoing
waves that immediately follow the downgoing direct arrival have a useful property:
they are free from multiple energy, because any multiple bounces in the ray-path would
delay it and make it arrive significantly later than the direct ray. Also, the waveform
of the direct arrival at a geophone tells us what the wavelet is at that particular depth.
(The seismic wavelet changes slowly with depth owing to a progressive loss of the
high frequencies.) This measured wavelet must also be the wavelet present in the
reflections that immediately follow the direct arrival, because the travel path through
the earth is nearly identical. Therefore, if we can separate the upgoing and downgoing
arrivals, then the downgoing wavefield tells us the wavelet and allows us to calculate a
filter operator to convert it to zero-phase. Applying the same operator to the upgoing