Application of Empirical Green's Functions in Earthquake Source, Wave Propagation and Strong Ground Motion Studies

Abstract

Over the last couple of decades, empirical Green’s functions [EGFs] have been increasingly used in earthquake source studies, crustal attenuation studies, strong ground-motion prediction, finite rupture modeling, and site-response studies. Theoretically, Green's functions are the impulse response of the medium, and EGFs are recordings used to provide this impulse response. In this chapter, we review the theoretical and observational basis for identifying and using small earthquakes as empirical Green's functions—and their application. We generally refer to analyses that use EGFs as “the EGF method”. The seismic record of an earthquake contains information on the earthquake source, the path the seismic waves propagated through, the site response of the geology beneath the recording site, and the response of the instrument that recorded the ground motion. In seismology, we are interested in isolating either source, path, or site information, depending on the study focus. The instrument response is usually known and easy to remove from recordings, but the same is not true for the other factors. Seismic waves propagate in the earth in a complex way. They are reflected and refracted at interfaces between rocks with different properties, attenuated throughout the path between the earthquake source and the station by scattering and anelastic effects, subjected to energy focusing and defocussing due to lateral changes in the refractive properties of the rock, and amplified and highly attenuated near the recording station as waves pass through unconsolidated near-surface material. These propagation complexities are not well captured by crustal models, which provide the basis for calculating Green's functions, especially for high frequencies (> 1 Hz). At higher frequencies, wave propagation is very sensitive to small crustal heterogeneities, which are generally not well known; at low frequencies (< 1 Hz), wave propagation can be modeled fairly accurately. EGFs can be used instead of mathematical calculations to more accurately represent seismic wave propagation in the geologically heterogeneous crust. The EGF method is the best available method because it empirically corrects for unknown path and site effects, for which a short wavelength resolution is needed. However, true EGFs contain the source rupture process of the small earthquakes in the recorded seismograms. No earthquake has a true impulsive source. Therefore, one must be careful using EGFs. There has not been uniformity in defining EGF’s. Recordings of earthquakes with magnitudes less than 1.0 to 7.0 have been used as EGFs. Here, we apply a strict