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 backpropagation might lead to numerical instabilities, especially for field data with strong high-frequency noise. To mitigate this problem, we have developed a robust space-wavenumber compensation operator and applied 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 the 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 also can 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 data set examples demonstrate the feasibility and adaptability of our method.

中文翻译：

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具有鲁棒空间波数域衰减补偿算子的粘声逆时偏移

固有衰减会在地震波传播过程中引起相位色散和振幅损失。不校正地震成像中的这些影响会导致反射体位置不准确、振幅变暗和空间分辨率降低。在逆时偏移 (RTM) 中，可以通过反转耗散项的符号并保持色散项不变来实现衰减补偿，以进行反向波场外推。虽然这个Q-补偿RTM方案可以有效地校正衰减效应，反向传播过程中的幅度放大可能会导致数值不稳定，特别是对于高频噪声强的现场数据。为了缓解这个问题，我们开发了一个强大的空间波数补偿算子并将其应用于粘声 RTM。通过分析纯色散和粘声格林函数，我们得到了均匀介质中衰减补偿算子的解析解。因为它是一个时频算子，将它直接应用于粘声 RTM 需要访问特定时间窗口内的外推波场。为了避免存储波场并提高计算效率，我们使用近似色散关系并将时频算子转换为等效的空间波数算子，这使我们能够在波场外推期间即时实现衰减补偿。算子的混合域特性使我们能够解释依赖波数的补偿。类似的策略也可以作为叠后处理方法应用于偏移图像，这比叠前补偿更有效。两个合成和一个陆域数据集示例证明了我们方法的可行性和适应性。类似的策略也可以作为叠后处理方法应用于偏移图像，这比叠前补偿更有效。两个合成和一个陆域数据集示例证明了我们方法的可行性和适应性。类似的策略也可以作为叠后处理方法应用于偏移图像，这比叠前补偿更有效。两个合成和一个陆域数据集示例证明了我们方法的可行性和适应性。