36 Seismic Imaging Seismic refraction is currently used in civil engineering and hydrogeology for targeted depths of less than 300 m (Mari et al., 1999). The method is particularly suited for the following studies: In civil engineering: • Preliminary studies for construction sites, • Determination of the near surface structures, • Rock mechanics (rippability, Poisson’s ratio), • Search for cavities. In hydrogeology: • Highlighting channels carved in bedrock, • Highlighting fractured areas in bedrock, • Measurement of water table depth. 2.1 Refraction surveying: Plus-Minus and GRM methods Refraction-based velocity estimation of the subsurface is conventionally carried out using well-known methods, such as the Hagedoorn’s Plus-Minus method (1959) or the generalized reciprocal method (GRM) proposed by Palmer (1986), which provides simple models of the subsurface defined by refractors with simple geometry and a relatively constant velocity distribution. The GRM method is widely used in refraction prospecting (Ge et al., 2010). It assumes that first arrivals only originate from critical refraction and lateral continuous refractors with relatively simple velocity distributions. The method becomes less accurate as subsurface variability increases. It is used for shallow investigations and to determine weathering corrections in refraction and reflection surveys. Refraction imaging of the subsurface is based on the analysis of refraction time-distance curves. The arrival time t(x) of the refracted wave is given by the following relationship: t(x) = x.cos(j)/ VR + δ(0) + δ(x) (2.1) • x: source – receiver distance • j: dip of refractor over spread length • VR: refractor velocity • δ(0): delay time at source point • δ(x): delay time at receiver point Equation (2.1) can be rewritten as follows: t(x) - x.cos(j)/ VR = δ(0) + δ(x) (2.2) Equation (2.2) is called the T – X/V curve.
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