113 The authors Appendix: Static corrections Refraction imaging of the subsurface is based on the analysis of refraction timedistance curves. The arrival time t(x) of the refracted wave is given by the following relationship: t(x) = x.cos(α)/ VR + δ(0) + δ(x) • x: the source – receiver distance, • α: the dip of refractor over the spread length, • VR: the velocity of the refractor, • δ(0): the delay time at the source point, • δ(x): the delay time at the receiver point. To accurately determine the true velocity, dip, and thickness of each subsurface marker, it is essential to obtain time-distance curves in both directions — i.e., up-dip and down-dip shooting. This requires seismic recordings where geophones are aligned with the shot points. The most widely known techniques for this are Hagedoorn’s Plus-Minus method (1959) and the Generalized Reciprocal Method (GRM) introduced by Palmer (1986). The GRM is essentially an extension of the Plus-Minus method, and both rely on the concept of delay time. The Plus-Minus method is extensively used in seismic refraction surveying. Picked travel times are used to construct the t+ and t− curves. The t− curve provides the velocity of the refractor, while the t+ curve offers a time-based image of the refractor’s depth (via delay times). If the velocity of the overlying medium is known, this delay curve can be converted into depth. This velocity is determined from the slope of the direct arrival. The overlying medium is referred to as the weathering zone (WZ). In the HES study area, the refractor velocity has been estimated at 3350 m/s based on t− curve interpretation, while the velocity of the weathering zone is approximately 850 m/s. The arrival times of both direct and refracted waves were picked for all shots. These picked times serve as input data for applying Hagedoorn’s Plus-Minus method. Cross-spread shots with a 60 m offset were also used to compute delay-time curves. These particular shots (Fig. 2d) were selected to ensure that the refracted wave is always the first arrival, regardless of the source–receiver distance. For all shots — whether in-line or cross-line — the picked arrival times were carefully verified. This verification involved flattening the first arrival by applying the picked times as static corrections. Perfect flattening confirms accurate picking. Picked times from in-line shots (Fig. 2b and 2c) and from 60 m cross-spread shots (Fig. 2b and 2d) were used to generate two delay-time maps.
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