How frequency dependency of Q affects spectral ratio estimates
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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 Q is constant (independent of frequency) in the frequency band of the signal. If this assumption is violated, then Q estimates become biased. In particular, when the frequency dependency of Q is a power law Q−1 ∝ωn, then Q is systematically under- or overestimated by a factor of n + 1. The errors are larger for larger values of n, particularly when n is negative. In particular, if n = -1, the frequency content of the signal does not change, and Q is estimated to be infinite, regardless of the true value of Q. 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 Q 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.
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