Detection of seismic reflections from seismic attributes through fractal analysis

Abstract

The concept of fractals is used here for the identification of seismic reflectors with special emphasis on thin-bed delineation, which is generally overlooked during standard data processing. A new fractal analysis scheme is applied to both synthetic and real field seismic data. The fractal dimensions of the three seismic attributes - amplitude, phase, and instantaneous frequency - have been analysed and evaluated. A change in fractal dimension is found to occur whenever there is a reflection. However, the resolution in the delineation of reflectors varies, depending on the attribute under consideration and the method of fractal dimension estimation used. Fractal analysis is performed on both noise-free and noisy synthetic data to establish the noise tolerance limit for both the 'divider method' and the 'Hurst method'. It is then tested with different peak frequencies of the source wavelet to establish the criteria for using the divider method and the Hurst method. The divider method is found to be suitable for high peak frequency source wavelets (> 25 Hz), while the Hurst method is best suited for low peak frequency source wavelets (< 25 Hz). Finally, when applied to the digitally processed and migrated field seismic data, it could even delineate reflectors which otherwise went undetected on the migrated time section.