Refraction statics corrections
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.
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.
Figure 3.3-19 CMP-stacked section associated with a synthetic data set. Shot and receiver statics were applied on moveout-corrected gathers in a surface-consistent manner, while the structure term was applied in a subsurface-consistent manner. These terms are plotted above the stacked section. Random noise was added to prestack data with a spatially varying signal-to-noise ratio.
Figure 3.3-22 CMP-stacked section associated with the synthetic data set as in Figure 3.3-19 with residual statics corrections. The derived shot, receiver, and structure terms are plotted at the top. Compare these estimates with the actual values in Figure 3.3-19. The maximum allowable shift is 80 ms. Also compare the resulting stacked section with that shown in Figure 3.3-20.
Figure 3.4-2 CMP-stacked section associated with the synthetic data set as in Figure 3.4-1 after the application of residual statics corrections. Compare the results with those in Figure 3.3-22.
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:
- Rapid variations in shot and receiver station elevations,
- Lateral variations in weathering velocity, and
- 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 .
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 . Such cases, if at all possible, may be handled by wave-theoretical modeling and inversion  or turning-wave tomography (model updating).
- First breaks
- Field statics corrections
- Flat refractor
- Dipping 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
- Taner et al., 1974, Taner, M. T., Koehler, F., and Alhilali, K. A., 1974, Estimation and correction of near-surface time anomalies: Geophysics, 41, 441–463.
- Hill and Wuenschel, 1985, Hill, R. N. and Wuenschel, P. C., 1985, Numerical modeling of refraction arrivals in complex areas: Geophysics, 50, 90–98.
- Hill, 1987, Hill, R. N., 1987, Downward continuation of refracted arrivals to determine shallow strucutre: Geophysics, 52, 1188–1198.