Fine Reconstruction of Seismic Data Using Localized Fractals

Abstract

Seismology requires accurate (fine) data reconstruction from sparsely (or irregularly) sampled data sets, but such results are usually not possible with conventional (non-fractal) methods. To produce a highprecision reconstruction of seismic data, a more accurate localized fractal reconstruction approach can be used provided the data is self-similar on local and global spatial scales. In this paper, a novel localized fractal reconstruction approach has been presented. This method is a data-driven algorithm that does not require any geological or geophysical assumptions concerning the data. Here, we report our results of using the approach to reconstruct sparsely sampled seismic data. Our results indicate that the fine structure associated with seismic data can be easily and accurately reconstructed using the localized fractal approach, indicating that seismic data is indeed self-similar on local and global spatial scales. This result holds promise not only for future seismic studies, but also for any field that requires fine reconstruction from sparsely sampled data sets.