PP/PS Wavefield separation by independent component analysis

SUMMARY In blind signal separation one seeks to retrieve the original source signals that are observed as a linear mixture on an array of sensors. No a priori information is available about waveforms or polarizations of the desired source signals—hence the term blind. Blind signal separation can be achieved using independent component analysis (ICA), which is a rapidly emerging technology in the field of advanced signal processing. It separates a set of observed signals into the statistically most independent components by appealing to higher‐order statistics. ICA retrieves the original source signals blindly if they are statistically independent without the need of further a priori information. There are many promising applications of ICA in geophysical signal analysis. ICA can be used to separate P and S waves in three‐component seismic reflection data without knowledge of P ‐ and S ‐wave near‐surface velocities or density. Wavefield separation is achieved by exploiting statistical differences between P ‐ and S waves only. The usual problems of amplitude indeterminacy and signal identification that occur in ICA are overcome by examining the inner products of the independent components with the original observations to ensure that the retrieved P and S waves have the appropriate signs and energies. Mode identification is realized by comparing current polarizations with forward predicted ones for each mode while maximizing the coherence with previously determined modes. The ICA wavefield separation technique is exact in a laterally inhomogeneous anisotropic earth with a homogeneous anisotropic near‐surface layer if only upgoing waves are present.