The influence of the frequency-dependent spherical-wave effect on the near-surface attenuation estimation

The knowledge of Q is desirable for improving seismic resolution, facilitating amplitude analysis and seismic interpretation. The most commonly used methods for Q estimation are the frequency-spectrum-based methods. Generally, these methods are based on the plane wave theory assuming that the transmission/reflection loss is frequency independent. This assumption is reasonable in the far-field situation and makes the transmission/reflection coefficient irrelevant with the Q estimation result. However, in the near-surface context, this assumption is invalid because the seismic wave propagates in the form of spherical wave in the real seismic surveys and the spherical-wave transmission/reflection coefficient is frequency dependent. As a result, deviation will exist. In this paper, the influence of the spherical-wave effect on the Q estimation in the near-surface context was proved in both synthetic data and field data for the first time, and it was found that the deviation due to the spherical-wave effect is of order comparable to the intrinsic attenuation. The compensation method based on the forward modeling is then proposed to correct this deviation, and the effectiveness of the proposed method is proved by the reasonable estimated results of both synthetic data and field data example. These results raise caution for the interpretation of the extracted Q in the near-surface context if they do not account for the spherical-wave effect and point to the necessity of incorporating a frequency-dependent term in the frequency-spectrum-based method when applied to the Q estimation in the near surface.