Putting Ancient Ideas into Modern Use - 3D Seismic Edge Detection with Magic Cube Operators

A.A. Al-Shuhail¹ and S. Al-Dossary²

Abstract

Magic squares are popular numerical constructions that existed in the mathematical literature for over a thousand years. Their extensions to higher dimensions have been known also in recreational mathematics for hundreds of years. Recently, the use of magic squares in image processing has proven useful. In this study, we extend this analysis by using magic cubes as edge detection operators and apply them on 3D seismic data.

Our analysis shows that magic cube operators result in a similar or better edge detection performance compared to the conventional Sobel operator. We think that this result stems from the fact that the magic cube operator offers more directions over which the amplitude gradient is calculated. These many distinct directions are formed by rotations and/or reflections of the same magic cube. In contrast, the Sobel operator calculates amplitude gradients only along three axes. We illustrate the effectiveness of magic cube operators in detecting discontinuities using various slices of a real 3D stacked seismic data set.

AAPG Search and Discovery Article #90188 ©GEO-2014, 11th Middle East Geosciences Conference and Exhibition, 10-12 March 2014, Manama, Bahrain