How frequency dependency of Q affects spectral ratio estimates

Abstract

Because seismic amplitudes can be affected by purely geometrical factors, attenuation is often estimated not from amplitudes but from the evolution of the amplitude spectra of the waveform. Such estimation methods (e.g., the spectral ratio method and the centroid frequency shift method) assume that the quality factor [Formula: see text] is constant (independent of frequency) in the frequency band of the signal. If this assumption is violated, then [Formula: see text] estimates become biased. In particular, when the frequency dependency of [Formula: see text] is a power law [Formula: see text], then [Formula: see text] is systematically under- or overestimated by a factor of [Formula: see text]. The errors are larger for larger values of [Formula: see text], particularly when [Formula: see text] is negative. In particular, if [Formula: see text], the frequency content of the signal does not change, and [Formula: see text] is estimated to be infinite, regardless of the true value of [Formula: see text]. To avoid these systematic errors, it is necessary to monitor the evolution of frequency content and amplitude with distance. Zero-offset vertical seismic profile data from the North West Shelf of Australia revealed the decay of the signal amplitude with depth that can be explained by a combination of intrinsic constant [Formula: see text] and a frequency-independent factor, which in turn is caused by the geometric spreading plus transmission loss due to variations of acoustic impedance on a scale larger than the dominant wavelength in the signal.