# 3-D refraction statics corrections

Series | Investigations in Geophysics |
---|---|

Author | Öz Yilmaz |

DOI | http://dx.doi.org/10.1190/1.9781560801580 |

ISBN | ISBN 978-1-56080-094-1 |

Store | SEG Online Store |

Figures 7.2-6a and 7.2-7a show the shot and receiver statics, respectively. Field statics were computed in the manner described in refraction statics corrections. Specifically, shots and receivers were lowered from the topographic surface to a shallow refractor using the weathering velocity, then moved up to a flat datum using the refractor velocity. The information required to apply the field statics corrections — the weathering velocity, refractor (bedrock) velocity, and depth to bedrock, were derived from the uphole surveys which were carried out in the field at close spatial intervals.

If field statics corrections are judged to be inadequate, then a near-surface model should be estimated from inversion of refracted arrivals (refraction statics corrections). This obviously is possible only if first-break picking for deriving a set of refracted arrival times can be achieved with confidence.

The surface-consistent refraction statics model discussed in refraction statics corrections does not restrict shot and receiver stations to a survey line — they can be situated anywhere, as in a 3-D survey (Figure 7.2-1). Hence, equation (3-52), which is rewritten below, can be used to model the intercept time anomalies at all shot and receiver stations over the entire 3-D survey area as

**Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle t^\prime_{ij} = T_j + T_i + 2s_bh_{ij}.}****(**)

Here, **Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle t^\prime_{ij}}**
are the modeled first-break picks associated with a shallow refractor, *T _{j}* are the intercept time anomalies at shot stations,

*T*are the intercept time anomalies at receiver stations,

_{i}*s*is the bedrock slowness, and 2

_{b}*h*the shot-receiver separation.

_{ij}As in the case of 2-D data (refraction statics corrections), the intercept time anomalies at shot and receiver stations, and the bedrock slowness (inverse of the bedrock velocity) are estimated from the model equation (**1**). The procedure is based on a formulation (refraction statics corrections), where the near-surface model parameters are estimated such that the difference between the modeled times *t′* and the actual times *t* picked from first breaks is minimum in the least-squares sense.

## See also

- Azimuth dependence of moveout velocities
- 3-D dip-moveout correction
- Inversion to zero offset
- Aspects of 3-D DMO correction — a summary
- Velocity analysis
- 3-D residual statics corrections
- 3-D migration
- Trace interpolation