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The Leading Edge; November 2009; v. 28; no. 11; p. 1336-1337; DOI: 10.1190/1.3259611
© 2009 Society of Exploration Geophysicists
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TUTORIAL

Multidimensional convolution via a 1D convolution algorithm

Mostafa Naghizadeh and Mauricio D. Sacchi

University of Alberta

Corresponding author: mostafan{at}ualberta.ca

Abstract

The helix transform was introduced to the geophysical community by Claerbout (1998) as a means to perform multidimensional convolution via one-dimensional convolution operators. The helix algorithm proves to be very helpful for multidimensional deconvolution problems like those encountered in noise attenuation and seismic data regularization with prediction error filters (Naghizadeh and Sacchi, 2009). The helix transform can be clearly explained using zero-padding and lexicographic ordering of multidimensional data cubes. The intention of this short presentation is to describe, in very simple terms, how one can perform multidimensional convolution via a 1D convolution algorithm.






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