REFRACTION STATIC CORRECTION IN A LAYER OF UNCONSOLIDATED SAND: EFFECT OF A VERTICAL VELOCITY PROFILE

摘要

Al-Shuhail, A.A., 2002. Refraction static correction in a layer of unconsolidated sand: effect of a vertical velocity profile. Journal of Seismic Exploration, 11: 383-396. The computation process of refraction static corrections, introduced by the weathering layer, usually assumes a vertically homogeneous layer. However, studies on bodies of unconsolidated sand (e.g., sand dunes and beach sands) have shown that they might have vertical velocity profiles, as evidenced by the nonlinear T-X curve of the direct wave in these bodies. The purpose of this study is to present a method for calculating refraction static correction in a layer of unconsolidated sand. The Hertz-Mindlin contact theory has been used to derive the theoretical form of the vertical velocity profile in a layer of unconsolidated sand, which depends on three parameters. These parameters can be estimated from the T-X curve of the direct wave in the layer using a nonlinear least-squares technique. Furthermore, the layer thickness can be estimated using the vertical velocity profile in the layer, and the velocity and intercept time of the refraction from the layer's base. For a sand layer of uniform thickness, the refraction static correction is double the vertical traveltime within the layer. The vertical traveltime within the layer is calculated using its thickness and vertical velocity profile. Modeling results show that the error in the refraction static correction introduced by ignoring the effect of the vertical velocity profile, in most practical cases, is less than 4%. Therefore, for velocity profiles calculated using the Hertz-Mindlin theory, the error in calculating the refraction static correction using conventional techniques is negligible.