基于Low-rank一步法波场延拓的黏声各向异性介质纯qP波正演模拟

各向异性介质纯qP波正演模拟及逆时偏移近年受到广泛关注，但它虽考虑了地下介质的各向异性特征，却忽略了黏滞性特征，使得最终偏移结果中噪声增加、分辨率降低。常规拟声波方程存在伪横波干扰、受模型参数限制（ε≥δ）、传播不稳定等因素影响，极大地限制了其应用。为此，引入一步法波场延拓方法，推导了黏声介质方程在空间—波数域的表达形式；结合空间—波数域各向异性介质延拓算子，构建一种适用于黏声各向异性介质的空间—波数域纯qP波波场延拓算子；引入Low-rank分解算法，实现基于Low-rank一步法波场延拓的黏声各向异性介质纯qP波正演模拟。数值模拟结果表明：①地震波场能同时表现出各向异性特征和黏滞性特征，更符合实际地下介质情况；②该方法克服了拟声波方程的局限性，消除了伪横波干扰，不受模型参数限制且地震波场能稳定传播；③在适当增大时间步长情形下无数值频散现象，所提算法能同时兼顾计算效率和计算精度，是一种稳定、高效的正演模拟方法，为基于Q补偿的各向异性介质逆时偏移提供了理论依据。

Low-rank one-step wave extrapolation for pure qP-wave forward modeling in viscoacoustic anisotropic media

Forward modelling and reverse time migration (RTM) of pure quasi-P (qP) waves in anisotropic media have attracted a lot of attentions in recent years. However,the results have serious noises and low resolution because of neglecting the viscosity although considering the anisotropy of the media. The application of the conventional quasi-acoustic equation is limited due to the interference from quasi-shear waves,limitation of model parameters and instability of the simulating process. This paper introduces a one-step wave field continuation method,deduces the expression for viscoelastic media in space-wavenumber domain,and constructs a pure qP wave field continuation operator in space-wavenumber domain for viscoacoustic anisotropic media,and finally realizes the forward modeling of pure qP waves in viscoacoustic anisotropic media based on the Low-Rank decomposition algorithm. The modelling results indicate that:a. the seismic wavefield can simulate the anisotropy and viscosity of underground media,so it is consistent with underground conditions; the Low-Ran method is not limited by the weak points of the quasi-acoustic equation which is interfered by quasi-shear waves,restricted by model parameters and with instable simulating process;c. no numerical aliasing appears when the time step is appropriately increased. By improving computational efficiency while ensuring accuracy,the Low-Ran method is stable and effective in calculation.It provides a theoretical basis for reverse time migration for anisotropic media based on Q compensation.