Wave propagation and sampling theory - Part II. Sampling theory and complex waves.

Abstract

Morlet et al (1982, this issue) showed the advantages of using complex values for both waves and characteristics of the media. We simulated the theoretical tools we present here, using the Goupillaud-Kunetz algorithm. Now we present sampling methods for complex signals or traces corresponding to received waves, and sampling methods for complex characterization of multilayered or heterogeneous media. Regarding the complex signals, we present a two-dimensional (2-D) method of sampling in the time-frequency domain using a special or 'extended' Gabor expansion on a set of basic wavelets adapted to phase preservation. Such a 2-D expansion permits us to handle in a proper manner instantaneous frequency spectra. We show the differences between 'wavelet resolution' and 'sampling grid resolution.' We also show the importance of phase preservation in high-resolution seismic.-Authors