Wave-Equation-Based Q Tomography With Local Peak Frequency Shift Measurements (2022)

Viscous effects cause strong energy decay and waveform changes of seismic waves. These distortions can be corrected using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q-</i> compensated reverse time migration ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -RTM) algorithms, and high-resolution migration images can be obtained. However, all <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -RTM methods require a relatively accurate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> model. The traditional wave-equation <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> tomography can invert the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> inversion methodology to evaluate more accurate underground <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> 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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> -RTM images further illustrate the accuracy of our proposed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$ </tex-math></inline-formula> tomography method.