Structural interpretation - 3-D Seismic Interpretation - page 96

as might be the case if the gradients between wells are extrapolated beyond them. It is
not usually possible to understand exactly what controls these residual discrepancies,
so the scope for intelligent contouring taking account of geological trends is limited;
this is why the residuals should be quite small before this step is taken.
Quite often, well data give us information at so few points that it would be useful
to bring some extra information into play to interpolate between them. To get velocity
information across the whole of the seismic survey, it is natural to turn to the velocity
fields derived during the processing of the seismic data.

3.3.3 Use of seismic velocities

During the course of seismic processing, a densely sampled velocity field is generated
in order to stack and to migrate the data. It is often assumed that stacking velocities
are root-mean-square (rms) average velocities from the surface down to the reflector
concerned. It was shown by Taner & Koehler (1969) that for a reflector at the base of
n uniform horizontal layers, the reflection time T x corresponding to a source-receiver
distance x is given by

x 2
V rms +

T x = T 0 + C 3 x 4 C 4 x 6 + +··· ,

where the coefficients C are functions of the thicknesses and velocities of the n layers
and V rms is the rms velocity along the zero-offset trajectory defined by

k = 1 v

n

2

k t k

V rms =

.

T 0

Stacking velocities V st are usually calculated by methods that assume a hyperbolic
time-distance relationship, i.e. that fit a relationship of the form

x 2
V st
to the travel-time versus offset data. The stacking velocities are therefore only an ap-
proximation to the rms average velocity from the surface to the reflector concerned.
However, there are other reasons why the velocities that give the strongest stack am-
plitudes and the most sharply focussed reflections are only loosely related to the actual
seismic velocities in the real earth. Al-Chalabi (1994) has provided a useful summary
of them. The most serious effects on stacking velocities are due to statics, structure and
anisotropy.
Statics effects arise when the survey is shot over a near-surface velocity anomaly
(Al-Chalabi, 1979). The geometry is shown in fig. 3.26 for the case of a model involving
a step across which a near-surface delay is generated. When the CMP location is at A,
only the outer traces of the CMP gather experience the delay; the best-fit hyperbola

T x = T 0 +