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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 V1,2 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 V2 to be used. However, a wave that travels down-dip not only has to travel further at velocity V2 to reach more distant geophones, but also further at the slow velocity V1 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: Vapp = V2/(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/V2 = 1/Vup + 1/Vdown 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.