interface, at which velocity increases from
Vn
to
Vn
+1. The definition of the
various quantities
Vm,n
is exactly analogous to the definition of
V
1
,
2
citedabove. The presence of intermediate layers may be recognized by
comparinglong- and short-shot data, but at least two points are needed to define
a velocityand three for any confidence to be placed in the estimate. At best,
therefore,only four layers can be easily investigated with a 12-channel system.
Complicated field procedures can be devised to overcome this limitation;
geophones may, for example, be moved one half-interval after a shot has been

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55
fired and the same shot-point can then be reused. Progress is extremely slow
and the problems presented by refractor topography, hidden layers and blind
zones (Section 3.3) still exist. In most circumstances, firing multiple shots into
modified spreads represents an attempt to extract more from the method than is
really obtainable.
3.3 Effect of dip
Depths estimated from refraction surveys are related to geophone and shot point
elevations, which must therefore be measured to obtain a true picture of the
subsurface
refractor.
Furthermore,
the
‘depths’
determined
are
the
perpendicular, not the vertical, distances to interfaces from shot points or
geophones. With this proviso, ‘horizontal’ formulae can be applied without
modification wherever the ground surface and the refractor are parallel. More
usually their slopes will be different. Formulae are then most commonly quoted
in terms of a horizontal ground and dipping refractors, but can equally well be
applied if the ground slopes above, for example, a horizontal water table.
The intercept-time equations require the true value of
V
2 to be used. However, a
wave that travels down-dip not only has to travel further at velocity
V
2 to reach
more distant geophones, but also further at the slow velocity
V
1 in the upper
layer (Figure 3.4). It therefore arrives late, with a low
apparent velocity
. The
reverse is true shooting up-dip, when arrivals at further geophones may actually
precede those at nearer ones. The slope of the line through the refracted arrivals
on a time–distance plot depends on the dip angle,
α
, according to:
V
app =
V
2
/(
1 + sin
α)
If shots are fired from both ends of the spread, different apparent velocities will
be measured because the sign of the dip angle will differ. For dips of less than
about 10
◦
, the true velocity is given by the dip-velocity equation:
2
/V
2 = 1
/V
up + 1
/V
down
3.4 Refractor relief and true velocities
Most refractors, except the water table, are irregular. If there were only a single
local depression in an otherwise flat refractor, refracted arrivals from shots in
opposite directions would plot on straight lines of equal slope, and the
differences between the two arrival times at each geophone would plot on a line
with double this slope. The exception to this rule would seem to be the
geophone immediately above the depression.