A high-resolution algorithm for complex spectrum search

The principal aim of this work is to estimate, or to approximate, the complex k-space spectrum of the wave field arriving on a linear array. First, using linear approximation, the location-dependent effect of the wave field magnitudes is modeled as an extra 'loss' factor in the complex spectral variable. This complex spectrum model may provide a better description of the physical process and require less sensor elements than the real spectrum model because of the additional degree of freedom provided by the 'loss' factor. A high-resolution algorithm combining the singular value decomposition method and the eigen-matrix pencil method is then employed to find the complex spectra representing the incoming real spectrum and the location dependent factors of multipath and multimode arrivals. Five key features (noise immunity, robustness, resolution, accuracy, and physical insight) of the proposed algorithm are studied using numerical examples.