<i>Q</i> -estimation and compensation for attenuated seismic data with the scanning- <i>Q</i> nonstationary sparse inversion method

ABSTRACT Influenced by the absorption and attenuation of wave propagation media, seismic waves experience amplitude attenuation, frequency reduction, and phase distortion. This absorption-attenuation is directly linked with viscoelastic properties and can be quantified by the quality factor (Q) or the attenuation factor 1/Q. It notably attenuates the high-frequency components of seismic signals and affects the amplitude consistency between shallow and deep seismic data. In this study, we simultaneously estimate and compensate Q-attenuation using a scanning-Q nonstationary sparse inversion method, in which high-frequency Q-compensated seismic data for each scanned-Q are generated by convolving the inverted reflectivity with a suitable seismic wavelet. The accuracy of the Q-compensated seismic data is directly proportional to the degree of similarity between the scanned-Q and the actual subsurface Q-structure. Therefore, the consistency between shallow and deep seismic data serves as an indicator for determining the optimal Q and corresponding Q-compensated seismic data. To quantify this consistency, we use a relative-error criterion function, which calculates the relative error between the shallow and deep Q-compensated seismic data. Minimizing these relative errors allows us to simultaneously obtain an optimal Q-model and the corresponding high-frequency seismic data. Synthetic and field experiments illustrate that our method can effectively estimate a reliable Q-model, enhance the seismic frequency bandwidth, and improve the shallow-to-deep consistency of the seismic data.