The migration of multiples can provide complementary information about the subsurface, but crosstalk artifacts caused by the interference between different-order multiples reduce its reliability. To mitigate the crosstalk artifacts, least-squares reverse time migration (LSRTM) of multiples is suggested by some researchers. Multiples are more affected by attenuation than primaries because of the longer travel path. To avoid incorrect waveform matching during the inversion, we propose to include viscosity in the LSRTM implementation. A method of LSRTM of multiples is introduced based on a viscoacoustic wave equation, which is derived from the generalized standard linear solid model. The merit of the proposed method is that it not only compensates for the amplitude loss and phase change, which cannot be achieved by traditional RTM and LSRTM of multiples, but it also provides more information about the subsurface with fewer crosstalk artifacts by using multiples compared with the viscoacoustic LSRTM of primaries. Tests on sensitivity to the errors in the velocity model, the Q model, and the separated multiples reveal that accurate models and input multiples are vital to the image quality. Numerical tests on synthetic models and real data demonstrate the advantages of our approach in improving the quality of the image in terms of amplitude balancing and signal-to-noise ratio.

中文翻译：

---

最小二乘逆向时间迁移在声介质中的倍数

倍数的迁移可以提供有关地下的补充信息，但是由不同阶倍数之间的干扰引起的串扰伪像会降低其可靠性。为了减轻串扰的影响，一些研究人员提出了倍数的最小二乘反向时间迁移（LSRTM）。由于传播路径较长，因此倍数受衰减的影响要大于基数。为了避免在反演期间出现错误的波形匹配，我们建议在LSRTM实现中包括粘度。介绍了一种基于粘声波方程的LSRTM倍数方法，该方程是从广义标准线性固体模型导出的。该方法的优点在于它不仅可以补偿振幅损失和相位变化，传统的RTM和LSRTM的倍数无法实现，但是与基波的粘声LSRTM相比，它可以通过使用倍数来提供更多有关具有较少串扰伪影的地下信息。测试速度模型中误差的敏感性Q模型和分离的倍数表明，准确的模型和输入倍数对图像质量至关重要。对合成模型和真实数据的数值测试证明了我们的方法在幅度平衡和信噪比方面在改善图像质量方面的优势。