Wave-Equation-Based Q Tomography With Local Peak Frequency Shift Measurements

Viscous effects cause strong energy decay and waveform changes of seismic waves. These distortions can be corrected using Q- compensated reverse time migration ( $Q$ -RTM) algorithms, and high-resolution migration images can be obtained. However, all $Q$ -RTM methods require a relatively accurate $Q$ model. The traditional wave-equation $Q$ tomography can invert the $Q$ model by eliminating the difference in peak frequency between the observed and synthetic early arrivals. However, this approach only can be used to invert the $Q$ value only for large-scale applications or on the surface. Moreover, the reflected wave can also be applied in the extended domain, but its computational efficiency is low compared to that of the early arrivals. To overcome these problems, this work proposes a new wave-equation-based $Q$ inversion methodology to evaluate more accurate underground $Q$ values in local domain. The proposed approach is applicable both to the early arrivals and reflected waves. Accordingly, we first transform the seismic data into the local domain using a sliding Gaussian window to alleviate the crosstalk noise in nearby seismic waves. Then, we use an improved cross correlation algorithm between the amplitude spectra of the observed and synthetic data to calculate the peak frequency shift of each seismic event in local domain. Thus, the inversion accuracy of $Q$ can be improved by using different kinds of waves. The numerical inversion examples demonstrate the ability of our proposed method to produce satisfactory inversion results, especially in high-attenuation and deep areas. The $Q$ -RTM images further illustrate the accuracy of our proposed $Q$ tomography method.