Complex spherical-wave seismic inversion in anelastic media for the P-wave minimum quality factor

Attenuation always exists when seismic waves propagate in underground anelastic media, especially in hydrocarbon-bearing reservoirs. Quality factor Q or attenuation factor 1/Q can be used to quantify the seismic wave attenuation and has become an important hydrocarbon indicator. The relationship between the plane-wave reflection coefficient (Rplane) in anelastic media and P- and S-wave quality factors has been widely used in the plane-wave seismic inversion to estimate the quality factors. The Rplane provides an adequate approximation for the deeper subsurface. However, for the shallow subsurface and anelastic wavefields excited by point sources, the Rplane is inaccurate and its meaning involves some fundamental difficulties. In view of this, a Q-dependent P-P spherical-wave reflection coefficient (Rsph) in anelastic media is used here. Considering that having too many parameters to be inverted will lead to unstable and inaccurate inversion results, we further derive an approximate anelastic Rsph and anelastic spherical-wave impedance (Zsph), which are frequency dependent and are the functions of P- and S-wave velocities, density, and P-wave minimum quality factor (Qpm). Finally, a complex spherical-wave seismic inversion approach in anelastic media for the P-wave minimum quality factor is developed. Using the Bayesian inversion approach and complex convolution model, we first estimate the multilayer Zsph from the complex seismic traces with different frequencies and incidence angles. Based on the inverted angle- and frequency-dependent Zsph, the P- and S-wave velocities, density, and P-wave minimum quality factor are further estimated using a nonlinear inversion tool. Synthetic examples verify the feasibility and robustness of the complex spherical-wave seismic inversion approach in anelastic media. In the shallow subsurface, the spherical-wave inversion is superior to plane-wave inversion. A field example further demonstrates the accuracy and great potential of our approach in hydrocarbon-bearing reservoir prediction.