Stochastic dispersion of short‐period P‐waves due to scattering and multipathing

Abstract

Summary. The delay of high frequencies in the teleseismic short‐period explosion P‐wave due to scattering is observed at a number of high Q sites. Recordings for the arrays NORSAR, YKA, GBA, and EKA have been examined as well as the individual sites RSNT, RSON, RSNY, RSSD, ANTO, CTAO, and KONO. p‐waves from Eastern Kazakh explosions observed at NORSAR, and several high Q stations show a systematic delay of high frequencies (4‐5 Hz) relative to lower frequencies (1–2 Hz) by as much as 0.5 s. This apparent dispersion is random and variable from station to station at a given array and from event to event at any single station. Hence it is referred to as ‘stochastic dispersion’ of the P‐wave. The stochastic dispersion of the 4‐5 Hz energy correlates with the decay of spatial coherency of the teleseismic P‐wave. Attempts to model this stochastic dispersion have shown that simple ray theoretical multipathing due to large‐scale length scatterers is not sufficient to delay high frequencies with respect to low frequencies as observed. Also, high‐frequency scalar scattering theory based on the parabolic wave equation does not correctly model the decline of spatial coherency with increasing frequency. Neither do Gaussian beam synthetics mimic the delays of high frequency seen in the first few seconds of the P‐wave. All of the above methods are high frequency approximations to the propagation of seismic waves and do not include wide‐angle scattering and conversion. Linear elastodynamic finite difference calculations of 1‐D and 2‐D heterogeneous media confirm that high frequencies can be delayed with respect to low frequencies with moderate amounts of heterogeneity in the crust and lithosphere. Simulations of 2‐D media demonstrate that significant small‐scale heterogeneity in the lithosphere could delay high frequencies with respect to lower frequencies if the spectrum of heterogeneity in the lithosphere were characterized by multiple scale lengths. The long wavelength heterogeneities in the lithosphere are still required to produce the broadband focusing‐defocusing that is observed at arrays. As a result of the delay of 4–5 Hz P‐wave energy by an average of 0.5 s as averaged over a 3‐6 s window, it is expected that time domain and frequency domain measures of attenuation will show systematic differences. Spectral domain measures of attenuation such as t* that use average spectral shapes should systematically yield lower attenuation estimates than time‐domain estimates of attenuation based on initial P‐wave rise time. Copyright © 1987, Wiley Blackwell. All rights reserved