Estimating attenuation and the relative information content of amplitude and phase spectra

Abstract

Seismic attenuation affects both the amplitude and phase of seismic waves. Algorithms to estimate attenuation are split among those that use amplitude information (e.g., spectral-ratio method), those that use phase information (e.g., rise-time method), and those that use a combination of both (e.g., time-domain algorithms). In this study, I explore the relative information provided by amplitude and phase spectra. To do this, I show how the difference in phase spectra between waveforms recorded at two depth levels can be used to estimate attenuation. This phase-difference method is analogous to the method of spectral ratios, but uses phase information rather than amplitude information. Under the simplifying assumption that the noise in both log-amplitude and phase spectra can be modeled as uncorrelated Gaussian random variables with equal variance, the posterior variances in the attenuation estimates from the spectral-ratio and phase-difference methods can be compared directly. It turns out that over typical seismic bandwidths and typical levels of attenuation, the relative uncertainty in estimates of attenuation from phase spectra is approximately twice the relative uncertainty in estimates of attenuation from log-amplitude spectra. Including phase and amplitude information simultaneously (as opposed to just amplitude information) reduces the relative uncertainty by only about 10% over seismic bandwidths. This reduction in uncertainty is not large, but may be significant depending on the sensitivity of the application.