This paper proposes a complex curvelet transform-based algorithm to adaptively subtract from seismic data those noise for which an approximate template is available. The complex curvelet transform decomposes a geophysical dataset in terms of small reflector pieces, with each piece having a different frequency, location, and direction. The properties of complex curvelet transforms enable us to precisely change the amplitude and shift the location of each seismic reflector piece in a template by controlling the amplitude and phase of its complex curvelet coefficient. Based on these insights, we can adapt a predicted noise template to the actual noise on an event-by-event basis by using the phase and amplitude of the data's and template's complex curvelet coefficients. Results illustrate that the proposed complex curvelet-based approach improves upon the conventional least squares subtraction approach and a more recent real curvelet-based approach.


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