Efficient computation of NACT seismograms

We present a modification to the NACT formalism (Li and Romanowicz, 1995) for computing synthetic seismograms and sensitivity kernels in global seismology. In the NACT theory, the perturbed seismogram consists of an along-branch coupling term, which is computed under the well-known PAVA approximation (e.g. Woodhouse and Dziewonski, 1984), and an across-branch coupling term, which is computed under the linear Born approximation. In the classical formalism, the Born part is obtained by a double summation over all pairs of coupling modes, where the numerical cost grows as (number of sources * number of receivers) * (corner frequency)^4. Here, however, by adapting the approach of Capdeville (2005), we are able to separate the computation into two single summations, which are responsible for the “source to scatterer” and the “scatterer to receiver” contributions, respectively. As a result, the numerical cost of the new scheme grows as (number of sources + number of receivers) * (corner frequency)^2. Moreover, by expanding eigen functions on a wavelet basis, a compression factor of at least 3 (larger at lower frequency) is achieved, leading to a factor of ~10 saving in disk storage. Numerical experiments show that the synthetic seismograms computed from the new approach agree well with those from the classical mode coupling method. The new formalism is significantly more efficient when approaching higher frequencies and in cases of large numbers of sources and receivers, while the across-branch mode coupling feature is still preserved, though not explicitly.