In viscoacoustic reverse-time migration (RTM), attenuation compensation can be implemented by reversing the sign of the dissipation term and keeping the dispersion term unchanged for backward wavefield extrapolation. Although the Q-compensated RTM scheme can effectively correct attenuation effects, amplitude amplification in back propagation might lead to an unstable problem, especially for field data with strong high-frequency noises. To mitigate this problem, we develop a stable space-wavenumber compensation method, and apply it to viscoacoustic RTM. Since the compensation operator is a time-frequency function, directly applying it in viscoacoustic RTM needs to access the extrapolated wavefields within a certain window. To avoid storing the wavefields and improve computational efficiency, we use an approximated dispersion relation and convert the time-frequency operator to an equivalent space-wavenumber operator, which allows us to implement attenuation compensation on the y during wavefield extrapolation. A similar strategy can also be applied to the migrated images as a poststack processing approach, which is more efficient than the prestack compensation. Numerical tests for a land field dataset demonstrate the feasibility and adaptability of the proposed method.

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