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The limited size of the spatial aperture of a seismic gather causes multiple‐ and primary‐reflection energy to spread out and cross‐hatch the image of the parabolic Radon transform. This spatial truncation effect devastatingly impairs the separation of primary and multiple reflections in a Radon demultiple process. It is difficult to suppress the spatial truncation effect completely, but it is at least possible to model or to identify implicitly such an effect and then to design automatically a mute function, i.e. a 2D mask filter in the Radon transform domain. This is referred to as the adaptive surgical mute scheme. By using this scheme, it is possible to extract the multiple‐reflection energy cleanly from the Radon transform image, so that the multiple reflections can be more effectively attenuated. It is also possible to preserve the diffused primary‐reflection energy after the surgical mute, so that the final multiple‐attenuated seismic …