Seismic wave attenuation caused by subsurface viscoelasticity reduces the quality of migration and the reliability of interpretation. A variety of Q-compensated migration methods have been developed based on the second-order viscoacoustic quasidifferential equations. However, these second-order wave-equation-based methods are difficult to handle with density perturbation and surface topography. In addition, the staggered grid scheme, which has an advantage over the collocated grid scheme because of its reduced numerical dispersion and enhanced stability, works in first-order wave-equation-based methods. We have developed a Q least-squares reverse time migration method based on the first-order viscoacoustic quasidifferential equations by deriving Q-compensated forward-propagated operators, Q-compensated adjoint operators, and Q-attenuated Born modeling operators. In addition, our method using curvilinear grids is available even when the attenuating medium has surface topography and can conduct Q-compensated migration with density perturbation. The results of numerical tests on two synthetic and one field data set indicate that our method improves the imaging quality with iterations and produces better imaging results with clearer structures, higher signal-to-noise ratio, higher resolution, and more balanced amplitude by correcting the energy loss and phase distortion caused by Q attenuation. It also suppresses the scattering and diffracted noise caused by the surface topography.

中文翻译：

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基于一阶粘声拟微分方程的Q最小二乘逆时偏移

地下粘弹性引起的地震波衰减降低了偏移质量和解释的可靠性。已经基于二阶粘声准微分方程开发了多种Q补偿偏移方法。然而，这些基于二阶波方程的方法很难处理密度扰动和表面形貌。此外，交错网格方案与并置网格方案相比具有优势，因为它减少了数值离散和增强了稳定性，适用于基于一阶波方程的方法。我们已经开发了Q最小二乘基于由导出第一阶viscoacoustic拟微分等式逆时偏移方法Q- 补偿前向传播算子、Q -补偿伴随算子和Q -衰减 Born 建模算子。此外，我们使用曲线网格的方法即使在衰减介质具有表面形貌并且可以通过密度扰动进行Q补偿迁移时也是可用的。对两个合成数据集和一个场数据集的数值测试结果表明，我们的方法通过迭代提高了成像质量，并通过校正图像产生了结构更清晰、信噪比更高、分辨率更高、振幅更平衡的更好的成像结果。Q引起的能量损失和相位失真衰减。它还抑制了由表面形貌引起的散射和衍射噪声。