Effective AMO implementation in the log-stretch, frequency-wavenumber domain

Cost-cutting avenues

The largest computational savings come from the use of FFTs for AMO, instead of slow Fourier integration necessary in the absence of log-stretch. Standard means of minimizing the CPU time and the amount of memory used to compute the AMO have also been employed. They include computing the AMO shift for only half of the elements of the cube in the complex domain, since the Fourier transform $F$ of a real function is Hermitian:

$$F(s)=F^{*}(-s)$$ (13)

(where $s$ denotes the frequency domain variable and the star symbol denotes the complex conjugate). Another way of reducing computational expenses was through the use of RFFTW and FFTW type Fourier Transforms (Frigo and Johnson, 1998), adaptive to hardware architecture, and taking advantage of the property stated in (13). Also, the code was divided into subroutines in such a way that some quantities were not computed unnecessarily several times when AMO was applied to more than one cube of data. Finally, shared memory parallelization with the OpenMP standard was applied to all the computationally intensive do loops in the code.

Effective AMO implementation in the log-stretch, frequency-wavenumber domain