Fractal-interpolation of seismic traces using vertical scale factor with residual behavior

Abstract

The inaccessibility of the terrain causes an irregular spatial seismic sampling, leading to poor reliability in the images of the subsoil generated by the processing algorithms; an accurate reconstruction of regular data is therefore crucial. This paper presents a fractal reconstruction method based on the self-similarity fractal property of the seismic data, on local and global scales. The method interpolates non-collected samples on the basis of the vertical scale factor value, thus making a solution possible to a system of coupled equations. However, tests with synthetic data show errors, with a tendency related to the scale factor. To reduce the imbalance, this approach takes into account the behavior of the discrepancy between the expected and the estimated values. The method applied to synthetic and real data sampled irregularly indicates that the fine structure of the seismic data can be quickly and accurately reconstructed using the localized fractal approach. The interpolation method can be fruitful in other fields where data need to be reconstructed from data sets not suitably sampled.