Seismic wave propagation in a viscoelastic medium suffers from energy attenuation and velocity dispersion. For prestack seismic data, the earth absorption not only decreases the seismic resolution, but it also distorts the amplitude variation with offset (AVO). Inverse Q filtering is a technique commonly used to remove these absorption effects. However, its application often suffers from instability in the presence of noise. Therefore, we have developed a two-step scheme to remove the absorption effects. We decompose the seismic absorption into two independent components, namely, the offset and time components. The former is mainly responsible for seismic event variation in the offset direction, whereas the latter is mostly responsible for the decreased temporal resolution. On the assumptions of a horizontally stratified medium and a small incidence angle, we derive the mathematical expression of the effective dissipation factors for both components, and we implement absorption compensation in the offset direction by an inversion scheme. We evaluated the sensitivity of this method to noise and its stability with the Q error using synthetic data, and we examined its performance using real data. The two-step scheme makes the prestack compensation more stable and usable.

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