Complex Polarization Analysis of Particle Motion

Knowledge of particle motion polarization aids in identifying phases on threecomponent seismograms. The scheme of Montalbetti and Kanasewich (1970) is extended to analytic three-component seismograms, where the imaginary part of the signal is the Hilbert transform of the real part. This scheme has only one free parameter, the length of the time window over which the polarization parameters are estimated, so it can be applied in a routine way to three-component data. The azimuth and dip of the direction of maximum polarization and the degree of elliptical polarization as a function of time for the seismograms are obtained. Polarization analysis of strong motion data from the 1971 San Fernando earthquake aids in the discrimination between wave types, which is important for the understanding of the complicated earthquake-induced shaking observed in basins. Most arrivals are incident on the receivers in the direction of the backazimuth to the epicenter, which suggests that despite the complicated motions, two-dimensional finite difference methods are sufficient to understand the effect on seismic waves of the Los Angeles and San Fernando basins (Vidale and Helmberger, 1986b). INTRODUCTION Although three-component seismograms are commonly used in many branches of seismology, the polarization content is analyzed only crudely and qualitatively. It is well known that P waves, S waves, Rayleigh waves, and Love waves have distinct polarization patterns (c.f. Aki and Richards, 1980; Gal'perin, 1984). One difficulty is that when more than one type of energy arrives in a record at the same time, it is hard to recover polarization data on either arrival, let alone both of them. Another problem is the conversion between P and S waves that takes place at the free surface for P-S V energy, which may lead to phase differences between different components of motion for incident S V waves (Nuttli, 1961) and Rayleigh surface waves (Aki and Richards, 1980). The proposed method identifies the problem of multiple arrivals by indicating a low degree of polarization and can handle elliptical polarization by the use of the analytic signal. If structure is primarily laterally homogeneous, the Love wave appears mostly on the transverse component and the Rayleigh mostly on the vertical and radial components. Two-dimensional polarization analysis of the vertical and radial components can separate linearly polarized body waves from elliptically polarized Rayleigh waves, but will not help much with SH body waves or Love waves. If structure is laterally heterogeneous, however, P-SV and SH energy will no longer cleanly separate onto the vertical and radial, and transverse components of ground motion, and a three-dimensional polarization analysis can aid in the identification and classification of arrivals in the seismogram. Anisotropic materials may also cause polarization anomalies (Kirkwood and Crampin, 1981), and such anomalies are easier to interpret with polarization analysis than by the traditional particle motion diagrams, which require visual interpretation. POLARIZATION ANALYSIS A simple polarization analysis would consist of rotating the motion into the vertical, radial, and transverse components and inspecting them visually. One can 1393