Surface-measured wavefront attributes are the key ingredient to multiparameter methods, which are nowadays standard tools in seismic data processing. However, most operators are restricted to application to isotropic media. Whereas application of an isotropic operator will still lead to satisfactory stack results, further processing steps that interpret isotropic stacking parameters in terms of wavefront attributes will lead to erroneous results if anisotropy is present but not accounted for. In this paper, we derive relationships between the stacking parameters and anisotropic wavefront attributes that allow us to apply the common reflection surface type operator to 3-D media with arbitrary anisotropy for the zero-offset and finite-offset configurations including converted waves. The operator itself is expressed in terms of wavefront attributes that are measured in the acquisition surface, that is, no model assumptions are made. Numerical results confirm that the accuracy of the new anisotropic operator is of the same magnitude as that of its isotropic counterpart.