Propagation and Structural Interpretation of Non-Plane Waves

Abstract

S U M M A R Y As a model for the 2-D horizontal propagation of seismic surface waves, we study the propagation of non-plane acoustic waves in homogeneous and inhomogeneous media. W e find that their phase velocity depends not only on the medium but also on the local geometry of the wavefield, especially on the distribution of amplitudes around the point of observation. The phase velocity of a wave is therefore conceptually and in most cases numerically different from the phase velocity parameter in the wave equation, which is determined by the elastic properties of the medium. The same distinction must be made for seismic surface waves. Although it is a common observation that waves of the same period can propagate with different phase velocities over the same path, the fundamental character of this observation has apparently not been recognized, and the two phase velocities are frequently confused in the seismological literature. We derive a local relationship between the two phase velocities that permits a correct structural interpretation of acoustic waves in inhomogeneous media, and also of non-plane seismic surface waves in laterally homogeneous parts of the medium.

Observations and interpretation of fundamental mode Rayleigh wavefields recorded by the Transportable Array (USArray)

“…At periods^40 s, fronts of constant phase are remarkably coherent across the entire array, and they illustrate the increase in wavelength with period as well as wavefront distortion arising from interaction with seismic structure. Given the substantial lateral variability in amplitude, these apparently simple phase patterns likely contain laterally variable signal inherited from the teleseismic propagation path [Wielandt, 1993] as well as local structure. This highlights the need to describe the incident teleseismic wavefield with more than one plane wave [Wielandt, 1993;Friederich and Wielandt, 1995;Pollitz, 1999;Yang and Forsyth, 2006].…”

Rayleigh wave phase velocities, small‐scale convection, and azimuthal anisotropy beneath southern California

“…These effects will distort the incoming waves, causing deviations of incoming directions from the great circle azimuths and leading the wavefields to be nonplanar. Neglecting the nonplanar character can systematically bias the apparent phase velocities if only waveforms with constructive interference are selected [Wielandt, 1993]. In California, Rayleigh waves at short periods show strong interference due to scattering and multipathing.…”

Guidelines for the good practice of surface wave analysis: a product of the InterPACIFIC project

“…the near-field), most approaches to dispersion analysis are valid only for plane waves and thus can become biased in the near-field (Wielandt 1993).…”