Linear matrix operations for multicomponent seismic processing

SUMMARY Multicomponent seismic data contain overlapping information on the polarization states of distinct body‐wave modes, due to the physical process of excitation, propagation and recording. This geometric redundancy should be exploited to provide an accurate separation and estimation of the wavefield attributes in order to understand the medium properly. This may be achieved using linear transforms, originally developed for separating split shear waves in four‐component seismic data. These transforms separate the principal time‐series components of the wavefield from the ray‐path geometry and the orientation of the source and geophone axes for a uniform medium: they are deterministic and can be easily implemented. Here we reformulate the linear transforms by introducing simple geometry and medium‐independent matrix operators. Although for ‘ideal’ experiments the technique may offer nothing new to the estimation of polarization that eigenanalysis cannot offer, nevertheless the formulation avoids the need to consult mathematical libraries and is useful in the interpretation of the wavefield when various inevitable acquisition‐related errors dominate. Some typical problems in processing four‐component data, such as the interpretation of data matrix asymmetry due to misorientations of the acquisition components and non‐orthogonal polarizations for the wave components, may be easily treated and identified using a common framework with this condensed matrix form. In addition, the operation is extended to similar geometric problems in six‐ and nine‐component data. Synthetic and field nine‐component data examples are presented to illustrate the application of the matrix operations.