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

Abstract

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 ([Formula: see text]) 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 [Formula: see text] provides an adequate approximation for the deeper subsurface. However, for the shallow subsurface and anelastic wavefields excited by point sources, the [Formula: see text] is inaccurate and its meaning involves some fundamental difficulties. In view of this, a Q-dependent P-P spherical-wave reflection coefficient ([Formula: see text]) 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 [Formula: see text] and anelastic spherical-wave impedance ([Formula: see text]), which are frequency dependent and are the functions of P- and S-wave velocities, density, and P-wave minimum quality factor ([Formula: see text]). 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 [Formula: see text] from the complex seismic traces with different frequencies and incidence angles. Based on the inverted angle- and frequency-dependent [Formula: see text], 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.