Q estimation and generalization of the Battaglia–Aki method

SUMMARY: The intrinsic attenuation of a seismic wave is a key property of rocks. Knowledge of Q (quality factor), which measures the attenuation, provides information not only about the type of rock, but above all about the pore fluids. In addition, the attenuation is needed for inverse Q filtering and is useful for localizing seismic sources. The methods for determining Q are based on the amplitude and frequency content of the signal, for example, the spectral ratio and frequency shift methods. In this paper, we consider a nearly frequency-independent Q factor so that the attenuation factor is proportional to frequency, so that high frequencies are attenuated. We use the frequency shifts (from the source to the receiver) to estimate the Q-factor for media with arbitrary geometric interfaces. The amplitude can be affected by factors other than attenuation, namely, geometric spreading and transmission coefficient. The shifts depend on the type of spectrum, which differs for seismic, microseismic and seismological (earthquake) sources. The inversion for Q assumes that the source spectrum is known, as well as the seismic velocities and the location of the interfaces and the source. On the other hand, if Q is known, sources can be located based on a generalization of the Battaglia–Aki method to heterogeneous media and using the centroid of the spectrum and the traveltimes at the receivers instead of the amplitude of the signal in the time domain. Alternatively, we provide formulas for the maximum of the signal spectrum that can also be used (peak frequency shift). Modelling and inversion is performed with 2-D and 3-D ray tracing algorithms based on Fibonacci search and minimizations with the Praxis algorithm and simulated annealing. We generate synthetic test seismograms with a direct 2-D full-wave algorithm based on the pseudo-spectral Fourier method, compare the results with those of ray tracing and use the minimization algorithm in combination with ray tracing to determine the source location.