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Local depression in an otherwise flat refractor

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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.
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56 Figure 3.4 Refraction at a dipping interface. The refracted energy from S 1 arrives later at B than at A not only because of the greater distance travelled along the refractor but also because of the extra distance d1 travelled in the low velocity layer. Energy from S 2 arrives earlier at P than would be predicted from the time of arrival at Q, by the time taken to travel d2 at velocity V1 . The lines AC and PR are parallel to the refractor . However, both waves would arrive late at this point (Figure 3.5) and, for small dips, the delays would be very similar. The difference between the arrival times would thus be almost the same as if no depression existed, plotting on the straight line generated by the horizontal parts of the interface. The argument can be extended to a refractor with a series of depressions and highs. Provided that the dip angles are low, the difference points will plot along a straight line with slope corresponding to half the refractor velocity. Where a refractor has a constant dip, the slope of the difference line will equal to the dip velocity equation. Figure 3.5 Effect on travel times of a bedrock depression. The arrivals at G 3 of energy from S 1 and S 2 are delayed by approximately the same amounts ‘a’
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57 and ‘b’). Note that, as in all the diagrams in this chapter, vertical exaggeration has been used to clarify travel paths. The lower version gives a more realistic picture of the likely relationships between geophone spacing and refractor depths and gradients . the sum of the slopes of the individual lines, giving a graphical expression The approach described above generally works far better than the very qualitative ‘proof’ (and the rather contrived positioning of the geophones in Figure 3.5) might suggest. Changes in slopes of difference lines correspond to real changes in refractor velocity, so that zones of weak bedrock can be identified. The importance of long shots is obvious, since the part of the spread over which the first arrivals from the short shots at both ends have come via the refractor is likely to be rather short and may not even exist. It is even sometimes possible, especially when centre shots have been used, for the differencing technique to be applied to an intermediate refractor. Differences are easily obtained directly from the plot using dividers, or a pencil and a straight- edged piece of paper. They are plotted using an arbitrary time zero line placed where it will cause the least confusion with other data (see Figure 3.8). 3.5 Reciprocal time interpretation
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local depression in an otherwise flat refractor refracted...

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