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When the refractor is dipping, it turns out that the inverse slope of the refracted arrival is no longer equal to the bedrock velocity (Figure 3.4-11c). An extra parameter — the dip of the refractor, needs to be estimated (Section C.6). This requires reverse profiling as illustrated in Figure 3.4-11d. We have the refracted arrival in the forward direction and the refracted arrival in the reverse direction obtained by interchanging the shots with receivers. The traveltimes for the refracted arrivals of the forward and reverse profiles are expressed as
The inverse slopes are given by
where φ is the refractor dip and θc is the critical angle of refraction given by
Finally, the intercept times are given by the following relations:
Derivation of the relations (3-44a,b) and (3-45a,b) are left to Section C.6.
To estimate the thickness of the near-surface layer, first we compute the refractor dip φ from the slope measurements — These measurements are then inserted into the expression
Then, we compute the bedrock velocity vb using the expression
Finally, we compute the depth to the bedrock at shot/receiver stations
Again, equations (46a,46c) reduces to equation (41a).
Keep in mind that, whether it is the flat refractor (equation 41a) or dipping refractor case (equation 46c), the depth to bedrock estimation at a shot-receiver station requires the knowledge of weathering velocity, bedrock velocity and intercept time. In the case of a flat refractor, these can be measured directly from shot profiles; whereas, in the case of a dipping refractor, they can be computed by way of equations (46a, 46b, 46c).
- First breaks
- Field statics corrections
- Flat refractor
- The plus-minus method
- The generalized reciprocal method
- The least-squares method
- Processing sequence for statics corrections
- Model experiments
- Field data examples
- Topics in moveout and statics corrections