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In the previous two chapters, the GRM parameters of velocity analysis function and generalized time-depth were defined, and then successfully applied to an extreme model with steeply dipping interfaces. Although plane-layer conditions are not uncommon, irregular layers are more usual and are generally of more interest. The following synthetic models permit the GRM to be examined in a variety of cases where departures from plane uniform layering occur.

In the time-depth graphs to follow (Figures 7, 22, 38, 44, and 50), the upper sets of points (circles)are the values for zero XY, the crosses are the values for a 5-m XY-value, and so on. Also, to avoid overplotting of points for various XY-values, each set of calculations uses a different reciprocal time. This results in a simple vertical displacement of plotted values which can be readily corrected if required (see chapter 9).

Perhaps the model of most interest is the irregular refractor. The model shown in Figure 4 has a plane horizontal ground surface and a highly irregular refractor with dips on the sloping surfaces of approximately 18 degrees. The first arrival times for this model, shown in Figure 5, were obtained by wavefront construction, since this method conveniently accommodates dipping refractors, interfering head waves, and diffraction (Thornburgh, 1939; Rockwell, 1967; Palmer, 1974). The traveltimes are also listed in Appendix A.

In Figure 6, the velocity analysis function is plotted for XY-values ranging from 0 to 30 m. For a 20-m XY spacing, the velocity analysis data fall very close to two straight lines,

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