# Refraction statics corrections

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store

An important question in estimating shot and receiver statics is accuracy of the results as a function of wavelengths of static anomalies. Figure 3.4-1 is a synthetic data set that is identical to that in Figure 3.3-19, except for additional long-wavelength shot and receiver static components. (Compare the graphic displays in Figures 3.3-19 and 3.4-1.) From the solution in Figure 3.4-2, note that the long-wavelength components of the statics were severely underestimated. A significant difference between the stacked sections, in terms of horizon times, is apparent in Figures 3.3-22 and 3.4-2.

The surface-consistent solution discussed in residual statics corrections resolves the short-wavelength static shifts (less than a spread length), which cause traveltime distortions in CMP gathers, and thus yield an improved stack response. However, merely improving the stack response by correcting for short-wavelength statics may not always be sufficient. The unresolved long-wavelength components are assigned to the structure term in equation (25). If the long-wavelength components are large, reflector geometries inferred by the CMP stack can be distorted significantly. Field statics and refraction statics methods are used to correct for the long-wavelength components.

 ${\displaystyle t'_{ij}=s_{j}+r_{i}+G_{k}+M_{k}x_{ij}^{2},}$ (25)

The statics corrections require knowledge of the near-surface model. The near-surface often consists of a low-velocity weathering layer. However, there are exceptions to this simplified model for the near-surface. Areas covered with glacial tills, volcanic stringers, and sand dunes often have a near-surface that may consist of more than one layer with different velocities. Layer boundaries can vary significantly from a flat interface to an arbitrarily irregular shape. The single-layer assumption for the near-surface also is violated when there is a lateral change in rock composition associated with outcrops, pinchouts or a flood plain along a seismic profile. In areas covered with a permafrost layer, which has a significantly higher velocity than the underlying layer, the surface-consistency assumption for the near-surface corrections is not valid. Moreover, the base of the permafrost layer does not form a head wave and therefore is not detectable.

In practice, a single-layer near-surface model often is sufficient for resolving long-wavelength statics anomalies. Complexities in a single-layer near-surface model can be due to one or more of the following:

1. Rapid variations in shot and receiver station elevations,
2. Lateral variations in weathering velocity, and
3. Lateral variations in the geometry of the refractor, which, for refraction statics, is defined as the interface between the weathering layer above and the bedrock below.

Near-surface velocity-depth models often are estimated using refracted arrivals. The refracted energy is associated with the head wave that travels along the interface between the near-surface weathering layer and the underlying bedrock. If refracted arrivals are observable on common-shot gathers, it almost certainly implies that the near-surface has a simple geometry. Nevertheless, no ray-theoretical method can claim to estimate short-wavelength variations in the base of weathering that are much smaller than a cable length. These variations are left to be handled by subsequent residual statics corrections using traveltime distortions associated with reflections on moveout-corrected common-midpoint (CMP) gathers [1].

The head wave is distorted in the presence of irregularities along the base of the weathering layer, and it turns into a diving wave when there is no sharp velocity contrast between the weathering layer and the substratum [2]. Such cases, if at all possible, may be handled by wave-theoretical modeling and inversion [3] or turning-wave tomography (model updating).