Complex curvelet‐based adaptive subtraction of several noise templates

Abstract

At the EAGE 2008 annual conference (Neelamani et al., 2008), we proposed a complex curvelet transform‐based algorithm to adaptively subtract from seismic data, noises that can be approximated by a single template. In this paper, we extend that approach so that we can subtract noises that need several templates to be approximated. 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 noise template by controlling the amplitude and phase of its complex curvelet coefficient. We fold these insights into an iterative, convergent algorithm to simultaneously adapt all noise templates. The basic step during the iteration is to adapt each 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.