Applications of high-resolution time-frequency transforms to attenuation estimation

Abstract

Attenuation estimates quantify the loss of energy of propagating seismic waves due to anelastic processes. It is often carried out in the frequency domain. The most well-known methods for attenuation estimation, such as the spectral ratio and frequency-shift methods, compare spectral shapes of waveforms along a given raypath. They require broad spectra such as those obtained with the Fourier transform and the continuous wavelet transform. These methods are incompatible with high-resolution time-frequency transforms, which drastically localize time-frequency information. On the other hand, these transforms indicate stronger resistance to noise and can be used in combination with the peak frequency method to estimate attenuation. We have applied high-resolution transforms, namely the synchrosqueezing transform, basis pursuit, and complete ensemble empirical-mode decomposition, to a synthetic wedge example and two seismic data set examples, a seismic reflection profile, and a vertical seismic profile (VSP). Results for the synthetic example find that most high-resolution transforms are able to reliably estimate quality factors. Using centroid frequencies, the seismic reflection profile exhibits local increases in centroid frequencies, which likely indicates imprints from apparent attenuation over intrinsic attenuation. Centroid frequencies and effective quality factors for the VSP are consistent for the different spectral estimation techniques. These three examples illustrate the value of high-resolution transforms for frequency and quality factor measurements.