Deconvolution of multicomponent seismic data by means of quaternions: Theory and preliminary results

Multicomponent seismic data are acquired by orthogonal geophones that record a vectorial wavefield. Since the single components are not independent, the processing should be performed jointly for all the components. In this contribution, we use hypercomplex numbers, specifically quaternions, to implement the Wiener deconvolution for multicomponent seismic data. This new approach directly derives from the complex Wiener filter theory, but special care must be taken in the algorithm implementation due to the peculiar properties of quaternion algebra. Synthetic and real data examples show that quaternion deconvolution, either spiking or predictive, generally performs superiorly to the standard (scalar) deconvolution because it properly takes into account the vectorial nature of the wavefields. This provides a better wavelet estimation and thus an improved deconvolution performance, especially when noise affects differently the various components.