Radial Smoothing

In the examples so far, the smoothing applied to filters has been (approximately) isotropic. Clapp et al. show how to control the direction of smoothing. In certain cases, it may make sense to specify some preferred direction of filter smoothing. For instance, CMP gathers tend to have approximately constant dip spectra at constant values of x/t, which correspond to radial lines. Figure radial shows randomly scattered points smoothed with radial-flag filters, in the adjoint and forward directions, and in combination. Not surprisingly, the radial operator needs a divergence correction, to avoid all the energy in the panel collecting at the origin.

 

radial
Figure 5 Radial smoothing. Top left panel shows result of smoothing random scattering of dots with the adjoint. Top right panel shows the result of smoothing the top left panel with the forward operator. Bottom left panel shows result of smoothing random dots with the forward. Bottom right show result of smoothing the bottom left with the adjoint.