A stable and self-adaptive approach for inverse Q-filter

• Gain-limit is time-variant and self-adaptive to effective bandwidth of seismic data.
• Energy of seismic wavelet in the effective bandwidth can be completely recovered.
• Stabilizing factor changes inverse proportion to square of gain-limit.
• Stabilizing factor is used to control numerical instability and avoid Gibbs effect.
• We can achieve high resolution and high SNR seismic data by the self-adaptive method.

The inverse Q-filter procedure attempts to eliminate the effect of the Earth Q-filter and hence improve the seismic resolution. The numerical instability of inverse Q-filter amplitude compensation reduces the SNR (signal-to-noise ratio) and limits the spatial resolution. Although the gain-limit constrained stable factor method can control the numerical instability and the SNR, but its gain-limit is time-invariant and is not associated with the seismic data; then it usually suppresses high frequencies at later times and reduces the seismic resolution. In this paper, we focus on understanding the impact of the gain-limit, the Q value and the dynamic range of seismic data to the seismic resolution, and propose a self-adaptive method for inverse Q-filter amplitude compensation. The gain-limit in the self-adaptive method is time-variant and self-adaptive to the cut-off frequency of the effective frequency band of seismic data; and the stabilizing factor changes in inverse proportion to the square of the self-adaptive gain-limit; then, the self-adaptive method can restore energy in the effective frequency band and control the numerical instability, and finally achieve high resolution and high SNR seismic data. Synthetic and real data examples demonstrate that the self-adaptive inverse Q-filter compensates for energy loss without boosting high frequency noise, and produces desirable seismic images with high resolution and high SNR.