Abstract: A method of geophysical exploration for acquiring and processing multicomponent seismic data obtained with seismic sources generating shear waves having time-varying polarizations and seismic receivers recording at least two modes of propagation of the imparted shear waves is provided. More particularly, a method is described for acquiring multicomponent seismic data with torsional seismic sources and multicomponent seismic receivers, as well as a method for processing such multicomponent seismic data so as to ameliorate the effects of shear wave splitting in displayed seismic data. Additionally, principal time-series signals can be obtained which are representative of formation properties along principal axes of an anisotropic formation essentially free of the effects of shear wave splitting.