results

In this example, I use a common-offset gather from a sub-sampled version of the Shorncliff 3D land data set from southeastern Alberta Chemingui (1999). I take a single micropatch size and origin, and calculate the number of fitting equations for each scale as a function of micropatch number. Since the time axis is regularly sampled, the number of fitting equations does not change with time (excluding edge effects), and can be ignored. The resulting three-dimensional cube is shown in Figure .

 

subst Figure 2 A time slice from a common-offset gather of the sub sampled Shorncliff data set.

 

parmap Figure 3 The number of fitting equations normalized by the number of filter coefficients, shown as a function of position (x and y) and scale (z). By creating many of these cubes for different parameter combinations, criteria can now be established to estimate optimal parameters.

Most of the results in Figures and are as expected. At the original scale, no fitting equations were possible. The number of fitting equations increase as we coarsen the mesh, but then as the mesh coarsens further, the edge effects start to dominate, until we reach the bottom slice where the micropatch size corresponds to one scaled bin, leaving each micropatch with a maximum of one fitting equation. Note that the number of micropatches and hence the size of the model space stays constant as we vary the scale.