Intrinsic attenuation gives rise to phase dispersion and amplitude loss during seismic wave propagation. Not correcting these effects in seismic imaging can result in inaccurate reflector locations, dimmed amplitudes and degraded spatial resolution. In 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 this Q-compensated RTM scheme can effectively correct attenuation effects, amplitude amplification during back-propagation might lead to numerical instabilities, especially for field data with strong high-frequency noise. To mitigate this problem, we develop a robust space-wavenumber compensation operator, and apply it to viscoacoustic RTM. By analyzing the dispersion-only and viscoacoustic Green’s functions, we obtain an analytical solution for the attenuation compensation operator in a homogeneous medium. Because it is a time-frequency operator, to apply it directly in viscoacoustic RTM requires access to the extrapolated wavefields within a certain time 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 fly during wavefield extrapolation. The hybrid-domain property of the operator enables us to account for the wavenumber-dependent compensation. A similar strategy can also be applied to the migrated images as a poststack processing approach, which is more efficient than the prestack compensation. Two synthetic and one land field dataset examples demonstrate the feasibility and adaptability of the proposed method.
A Time-Frequency Approach to Feature Extraction for a Brain-Computer Interface with a Comparative Analysis of Performance Measures
