This paper considers possible approaches to resolving mixtures of propagating signals observed on arrays. In particular, conventional approaches such as beamforming, multiple-signal characteristic (MUSIC), and single-signal F statistics have flaws that will not allow conventional methods to adapt to certain mixtures. In order to solve the mixed signal problem, we derive the partial F statistic for testing for an added signal in a multiple-signal model and a complex version of Akaike’s corrected model selection criterion AICC. In this case a combination of sequential nonlinear partial F statistics used in tandem with AICC leads to determining the correct configuration of signals and their velocities and azimuths. Confidence intervals are given using the frequency domain bootstrap. Finally, we derive unbiased estimated waveforms for each component signal.
The conventional estimators and the new sequential approaches are applied to known and unknown configurations of regional signals from China and to a teleseismic mixture involving two known earthquakes and noise caused by an ocean storm. We also analyze a regional event with propagating noise and show that a deconvolution based on the two velocities and azimuths gives an enhanced view of the depth phase in the estimated signal.