Aliasing in ?-? domain and attenuation of aliased linear noise in this domain

One of the common problems in reflective seismic records is the existence of coherent linear and random noises which cause covering of the most important parts of reflective signals; therefore, it is necessary to attenuate them by processing methods.
Several processing techniques have been devised for attenuation of coherent linear noises and linear radon or ?-? transform is a powerful technique for attenuation of these noises.
In this method, by doing slant stack (summing amplitudes in the offset domain along slanted paths), data will transform to ?-? domain and least square method is used for this transform.


p: Ray parameter ?: Zero offset intercept h: Offset
In this domain, reflectors and coherent linear noises map separate points. Then, after elimination of coherent linear noises in this domain, data reconstructs are employed to offset domain by using inverse ?-? transform.
Aliasing in this domain appears as: aliasing in ?, aliasing in P and spatial aliasing. If there is spatial aliasing in data, by using following methods, aliasing affects will be eliminated:
1- High cut filter: By applying this filter alias artifacts will be eliminated.
2- LMO correction: in order to prevent aliasing of the noise trends to be attenuated, LMO may be applied around the ?-? transform.
3- interpolation in h direction: In this method data will be interpolated in h direction and then transform to ?-? domain and linear noise will be eliminated.
By comparing these three methods, it is clear that the result of the interpolation method is the best.
In this study, linear ?-? transform has been tested on several aliased synthetics and real data and acceptable results have been provided. By comparing this method with F-K filter results, it is clear that the results of these two methods are nearly similar but in some seismic data, F-K filter was not a good method for aliased surface wave attenuation and attenuated little energy of reflectors. Therefore, when the reservoir study is the case, ?-? transform is preferred to F-K filter.