Noise reduction in seismic data using Fourier correlation coefficient filtering

The correlation coefficient between two frequency (or two wave number) componets equals the cosine of their phase‐angle difference. This relation can be exploited to build a filter that separates noise from signal in seismic data in either the F‐X or F-K domain (termed “correlation coefficient filtering”). To implement this filter, seismic data are first divided to form two subsets that are then compared using the cosine function. Signal is defined as the correlative frequencies (or wavelengths) while noncorrelative energy is attributed to noise. Depending on the application, appropriate subsets may consist of (1) groups of adjacent traces or (2) low‐fold stacks created from differing shot gathers. When comparing adjacent traces [i.e., (1)], the correlation coefficient filter combines both phase and dip information and assumes that reflections advance relatively little in time across traces and less than the noise. Correlation coefficient filtering of low‐fold stacks [i.e., (2)] does not depend on dip. Re...