Single-station polarization analysis applied to seismic wavefields: A tutorial

The polarization properties of seismic wavefields recorded by triaxial (three-component) stations can been exploited for event detection, seismic direction finding, and wavefield filtering. Analysis tools have been derived by extending conventional electromagnetic polarization theory to transient seismic wavelets. The basis of this class of polarization processing is a (complex) covariance matrix formed over a window of data to characterize single polarized events within random noise. An eigendecomposition of the (complex) covariance matrix provides eigenvalues and eigenvectors to describe the degree and properties of polarization as well as to formulate polarization filters. Different modes of polarized events require different analysis domains. Rectilinearly polarized events can be examined using a real-valued covariance matrix. In contrast, elliptically polarized events (Rayleigh waves) require the analysis of the analytic signal and a complex-valued covariance matrix to describe the elliptical motion. The success of the polarization measures depends on the signal-to-noise ratio. Furthermore, if multiple events interfere, the basic assumptions used for single-station polarization analysis are violated and the method breaks down. The choice of analysis window length controls the resolution and success of the analysis and depends on the dataset being examined. Ideally, the window should be as long as possible but must not include two (or more) separate events. Synthetic datasets, constructed for different modes of events and different noise levels, as well as real data from a seismic reflection and vertical seismic profiling (VSP) survey together with recordings of an earthquake are used to illustrate the benefits and limitations of polarization processing.