Geological interpretation - 3-D Seismic Interpretation - page 104

to 100 ft in 1 ft increments. The reflection coefficient at the top of the wedge is − 0 . 15
and that at the base is

+ .

185. The material of the wedge is therefore significantly softer
than the material above or below it, and the material above it is slightly softer than that
below it. These values are based on those for a wedge of porous gas-filled sand encased
in Tertiary shales in the UK Central North Sea. Figure 4.1(a) shows the calculated
seismic response for a zero-phase wavelet of bandwidth 6-60 Hz. The polarity of the
display is that a black peak marks a transition downwards to an acoustically softer
material. Where the sand is absent, at the left-hand end, there is a weak white trough
due to the impedance difference between the shales above and below the sand level. At
the right-hand end, the top of the sand is marked by a strong black loop and the base
by a strong white loop. There are small-amplitude wiggles between, above and below
these reflectors, caused by minor oscillations in the wavelet, but it would clearly be
possible to pick the strong loops at top and base sand accurately, and measure the
TWT interval between them to determine sand thickness. As the sand becomes thinner,
however, the separation between the top and base loops reaches a nearly constant value
at a thickness of about 40 ft. The point at which this happens is often called the tuning
thickness. After this, the separation remains nearly constant, and further decrease in sand
thickness causes the amplitude to decrease. This is the result of interference between the
reflections at the top and base of the sand; the reflections from the top and base overlap
and, being of opposite polarity, partly cancel one another. Below 40 ft thickness, the
top and base sand are not visible as separate events. It is very important to take this into
account when estimating reservoir volumes in thin sands; using the isopach between
top and base seismic reflectors will grossly overestimate the volume.
A method to calculate thicknesses for thin sands, below the tuning thickness, was
discussed by Widess (1973) , using a simple model where the reflection coefficients
are the same at the top and base of the bed. As shown in fig. 4.1(b) , the resulting signal
is the sum of the reflections from the top and base of the bed, which are of course of
opposite polarity; it is therefore the difference between two identical wavelets slightly
displaced in time. When the bed is very thin, the character of the reflection is that of
the time derivative of the incident wavelet. Widess showed that the character of the
composite reflection is unchanging for beds whose thickness is less than about λ/ 8,
where λ is the wavelength in the bed material corresponding to the predominant period of
the wavelet. For beds thinner than this, reflection amplitude is given by 4 π Ab /λ , where
A is the amplitude that would be obtained from the top of a very thick bed (i.e. with no
interference effect), and b is the thickness of the bed. Thus the amplitude is proportional
to bed thickness for these thin beds, and this can be used to predict bed thickness from
seismic amplitude if the data are calibrated (e.g. to a well) and if we can assume that
all lateral amplitude change is caused by changes in thickness and not by changes in
impedance of the thin layer or of the material above and below it. As the bed becomes
thinner, the amplitude will eventually decrease so far that it is invisible. The thickness
where this will happen is not easy to predict, because it depends on the level of seismic

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