Single Station Triaxial Seismic Event Detection, Direction Finding and Polarization Analysis

Abstract

The bearing and elevation (azimuth and inclination) of a seismic event can be estimated directly from measurements at a single triaxial station. There are instances in which the angular resolution secured by triaxial polarization analysis is better than that obtained by beamforming with an extended scalar array. In these situations, one depends totally on understanding the inter-relationships between the triaxial records that make up a seismic wavetrain. There are many approaches to seismic direction finding (SDF). Monte-Carlo techniques of triaxial seismic direction finding seek to maximise signal power by examining the seismic wavefield in many rotated co-ordinate frames. There are variants on this approach, which entail null seeking in an inverse space. Instead of searching all possible directions for the one which best fits the polarization model of a single arrival, it is possible to carry out an eigen-decomposition of the (complex or real) covariance matrix formed from the three-component data. The eigenvector corresponding to the principal eigenvalue yields the polarization direction automatically, with significant savings in computational effort. Numerical experiments undertaken for different levels of random noise superimposed on a pure mode signal show that there are no significant advantages in using the Monte-Carlo techniques over eigendecompsoition. Confidence measures of event detection may be obtained by examining eigenvalue ratios when using the eigendecompsoition method. A time-domain formulation (covariance or coherency matrix) is preferable to a frequency-domain formulation (cross-spectral matrix) when there are multiple transient events present. The analysis window should be as long as possible (at least half the dominant period of the signal) without causing separate events to interfere. In practise, the direction-of-arrival estimates deteriorate with increasing levels of random noise, and are generally unacceptable for a SNR of less than 1. Special care is needed to avoid direction errors associated with systematic noise, such as sensor gain misalignment between channels, coupling variations between receiver components, velocity inhomogeneity and anisotropy, the free-surface effect, and multiple event interference.