Estimation of Seismic Noise Structure Using Arrays

Abstract

A theoretical study of the use of arrays for the analysis of seismic noise fields has been completed. The frequency‐wavenumber power spectral density [Formula: see text] is defined and techniques for estimating it are given. The estimates require that the auto‐ and crosspower spectral densities be estimated for all elements in the array. Subject to certain asymptotic properties of these auto‐ and crosspower spectral density estimates, expressions for both the mean and variance of the estimates of [Formula: see text] have been obtained. It has been demonstrated that if [Formula: see text] is estimated by the Frequency Domain Beamforming Method, then the estimate has the same stability as the estimates of auto‐ and crosspower spectral density. [Formula: see text] has been estimated from both long‐ and short‐period noise recorded by the Large Aperture Seismic Array in Montana. At frequencies higher than 0.3 Hz, a compressional body‐wave component which correlates with atmospheric disturbances over distant oceans has been detected. In the frequency range of 0.2 and 0.3 Hz both body waves and higher mode Rayleigh waves are observed. At frequencies below 0.15 Hz the organized vertical component of microseisms consists primarily of fundamental mode Rayleigh waves. Appreciable amounts of fundamental mode Love wave energy may also be present on horizontal instruments at these low frequencies.

Two-receiver measurements of phase velocity: cross-validation of ambient-noise and earthquake-based observations

“…The relative contribution of higher modes to the ambient-noise wavefield are estimated quite differently in the literature and seem to be dependent of the region. However, most authors state that fundamental-mode surface waves dominate the ambient-noise records, especially at periods longer than 5 s (Lacoss et al 1969;Pedersen & Krüger 2007;Nishida et al 2008;Yao et al 2011). Some preliminary numerical tests of our method indicate that even in the presence of a secondary, faster signal emitted by each noise source, roughly corresponding to the first higher mode, the fundamental mode phase-velocity signal dominates the phase-velocity measurement procedure and the fundamental mode phase velocity is correctly reconstructed.…”

Inversion of phase velocity of long-period microtremors to the S-wave-velocity structure down to the basement in urbanized areas.

“…One is the frequency domain beam-forming method (BFM) by LACOSS et al (1969), and the other is the maximum likelihood method (MLM) by CAPON (1969). It should be pointed out that the non-uniformly spaced array has practical importance, because the array cannot always be deployed in such a manner that every distance between two adjacent sensors is equal, especially in urbanized areas where there are many artificial structures on the ground surface.…”

“…Besides the application studies of microtremors cited above, their origin and wave type have also been studied by, for example, DOUZE (1964, 1967), LACOSS et al (1969), and CAPON (1969. ASTEN (1978) reviewed this literature and summarized that four types of origin (cultural sources, coastal effects, ocean cyclones, and atmospheric loadings and wind actions) could be identified in the frequency range 0.5Hz to 3.0Hz and that the first two generated mainly Rayleigh waves, the third P waves, and the fourth undefined modes.…”

Array performances for ambient vibrations on a shallow structure and consequences over V s inversion

“…Three approaches are of common use for analysing signals: the frequency wavenumber method (Lacoss et al [1969], Horike [1985]), the high resolution frequency wavenumber method (Capon [1969], Asten and Henstridge [1984]) and the spatial auto-correlation technique (Aki [1957], Ohori et al [2002], Roberts and Asten [2004]). Frequency-wavenumber (f-k) analysis assumes plane waves to travel across the array of sensors laid out at the surface.…”