Noise reduction in seismic data using Fourier correlation coefficient filtering

The correlation coefficient between two frequency (or two wavenumber) components 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. Reflections are assumed to be present in both subsets whereas the noise is found only in one data set. Hence, the reflections are correlative and the noise is noncorrelative. In either case, the filter reduces linearly dipping coherent energy, ground roll, and randomly occurring noise bursts while generally maintaining signal integrity. A primary advantage of this filter is its simplicity. It is implemented much like a simple band-pass filter, thus requiring much less parameterization than alternative noise-reduction methods.