Implementation

There are several issues that must be considered when implementing AMO in this form. The large volume of data that we are dealing with means that the problem must be parallelized. The problem can be parallelized in several different ways. While it is possible to split in the (${\rm cmpx},{\rm cmpy}$) plane, boundary effect are a concern because the operator is applied in the wave-number domain. Because the operator is applied in the frequency domain parallelizing over frequency seems a natural choice. The problem with dividing the problem along the frequency axis is that the intermediate space $\bf s$ can become enormous, even for fairly small datasets, which would require some level of patching along other axes. In addition it requires a troubling transpose. The input data has its inner axis as time, while we want the outer axis to be frequency. For multi-gigabyte this can be quite time consuming. For this reason I chose to parallelize offset. Each process is assigned an output (hx,hy) range. It takes the input that range plus the additional summation range implied by equation (2).

The parallel job is controlled by the library described in Clapp (2005). Each node receives a SEP3D Biondi et al. (1996) volume corresponding to its output space and the summation region implied by (2). The serial code first NMOs, log-stretches, and converts to frequency its data volume. The data volume is transposed and equation (6) is applied. The regularized frequency slices are transposed, inverse Fourier transformed, and has inverse NMO applied to it. Finally the data is recombined to form the regularized volume.