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Head wave represented by rays which leave the

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head wave represented by rays which leave the interface at the critical angle. The head wave travels through the upper layer at velocity V 1 but, because of its inclination, appears to move across the ground at the V 2 velocity with which the wave-front expands below the interface. It will therefore eventually overtake the direct wave, despite the longer travel path. The cross- over or critical distance for which the travel times of the direct and refracted waves are equal is: xc = 2 d [ (V 2 + V 1 )/(V 2 V 1 ) ] This equation forms the basis of a simple method of refraction interpretation. xc is always more than double the interface depth and is large if the depth is large or the difference in velocities is small. The critical time , obtained by dividing the critical distance by the direct-wave velocity, is also sometimes used. The term ‘critical distance’ is also sometimes used for the minimum distance at which refractions return to the surface, i.e. the distance from the shot point at which energy arrives after reflection at the critical angle. This usage is not common amongst field crews since the refractions arrive after the direct wave at this point, and for some distance beyond, and are difficult to observe. If more than one interface is involved (as in Figure 3.1), the ray that is critically refracted at the lowermost interface leaves the ground surface at an angle in given by: sin in = V 1 /Vn Thus, the angle at which energy leaves the ground surface for ultimate critical refraction at a deep interface depends only on the velocities in the uppermost
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47 Figure 3.1 Critical refraction at two interfaces: sin ic = V 1 /V 2. and lowermost layers involved, and not on the velocities in between. Eventhough this is a surprisingly simple result, cross-over interpretation becomes rather complicated for multiple layers and the intercept-time method discussed below (Section 3.2) is generally preferred. 3.1.3 Lengths of refraction spreads A line of geophones laid out for a refraction survey is known as a spread , the term array being reserved for geophones feeding a single recording channel. Arrays are common in reflection work but are almost unknown in refraction surveys where the sharpest possible arrivals are needed. Sufficient information on the direct wave and reasonable coverage of the refractor is obtained if the length of the spread is about three times the crossover distance. A simple but often inaccurate rule of thumb states that the spread length should be eight times the expected refractor depth. 3.1.4 Positioning shots In most refraction surveys, short shots are fired very close to the ends of the spread. Interpretation is simplified if these shots are actually at the end geophone positions so that travel times between shot points are recorded directly. If this system is used, the geophone normally at the short shot location should be moved half-way towards the next in line before the shot is actually fired (and replaced afterwards). Damage to the geophone is avoided and some extra information is obtained on the direct wave. Long shots are placed sufficiently far from the spread for all first arrivals to have come via the
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