分数阶拉普拉斯算子黏滞声波方程的最小二乘逆时偏移

衰减补偿型逆时偏移方法能沿波的传播路径对地震波所经历的振幅衰减和相位畸变进行补偿，可提高成像精度和分辨率，但该方法需模拟呈指数增长的地震波场，存在数值不稳定问题。为此，在最小二乘反演理论框架下，基于分数阶拉普拉斯算子黏滞声波方程，推导其对应的Born正演模拟算子和伴随方程，利用反演思路逐步补偿地震波的吸收衰减，解决了传统衰减补偿型逆时偏移方法的不稳定问题。该最小二乘逆时偏移方法采用新颖的常分数阶拉普拉斯算子黏滞声波方程描述地震波的衰减和频散，与实际广泛使用的常Q模型匹配精度高；在反演算法方面，使用限域拟牛顿（L-BFGS）方法计算反射率模型的更新量。Marmousi模型数据和实际数据的偏移算例证实，所提黏滞声波最小二乘逆时偏移方法能稳定地补偿介质的黏滞性，获得高分辨率的地下反射率模型。

Least-squares reverse-time migration based on a fractional Laplacian viscoacoustic wave equation

The attenuation-compensated reverse-time migration (Q-RTM) compensates for amplitude loss and phase distortion along the entire wave propagatiing path,so it can enhance seismic imaging accuracy and resolution.However,since Q-RTM requires to solve an amplitude-boosted wave equation to simulate exponentially increased amplitude,it is not stable.A novel least-squares Q-RTM (LSQRTM) is proposed to stably invert a subsurface reflectivity model.The LSQRTM is based on viscoacoustic Born forward modeling and its adjoint operator that are derived from a new fractional Laplacian viscoacoustic wave equation.The wavefield simulated by the fractional Laplacian viscoacoustic wave equation can well match realistic attenuation and dispersion predicted by a constant-Q model.The L-BFGS algorithm is used in least-squares inversion to calculate the descent direction to update the reflectivity model.Used for Marmousi model and real data,the LSQRTM can stably compensate for the viscosity of the medium and provide a reflectivity model with high resolution.