AI 中文总结
该研究提出各向异性弹性介质中相空间局部角度域弹性全波形反演的理论框架，推导了相关算子，其海森更对角占优，可集成多项功能，为弹性反演等提供统一工作流程。
AI 中文摘要
我们提出一种基于地震散射的局部角度域（LAD）表示的弹性全波形反演（FWI）的相空间公式。该方法不最小化采集域波形残差，而是最小化由位置、传播方向、散射角、方位和时间参数化的相空间域中的成像域不一致性。该公式的提出源于速度和阻抗扰动占据相空间中大致不同区域的观察结果。对于各向异性弹性介质，我们推导了广义目标函数以及对应的伴随状态梯度和海森算子。通过方向和开口波数表示LAD图像，为传播和散射效应提供了统一描述。该方法独立于正演模拟引擎，可通过有限差分、有限元、谱元、射线基或波束基方法实现。在玻恩线性化下，射线/波束公式允许显式海森计算。由于方向和开口角灵敏度接近正交，海森比传统FWI中更对角占优，改善了参数分离，减少了速度-反射率串扰，增强了反演稳定性。通过在物理上有意义的相空间表示中组织地震信息，LAD-FWI支持自适应、分辨率驱动的反演，且可通过比波形残差变化更平滑的属性减少周期跳跃。该框架自然集成了方向聚焦、反射器一致性分析、各向异性参数估计、转换波成像和基于衍射的表征，为弹性FWI、偏移速度分析、阻抗反演和高分辨率地下成像提供了统一工作流程。
英文摘要
We present a phase-space formulation of elastic full-waveform inversion (FWI) based on local-angle-domain (LAD) representations of seismic scattering. Instead of minimizing acquisition-domain waveform misfits, the method minimizes image-domain inconsistencies in a phase-space domain parameterized by position, propagation direction, scattering angle, azimuth, and time. The formulation is motivated by the observation that velocity and impedance perturbations occupy largely distinct regions of phase space. For anisotropic elastic media, we derive a generalized objective function together with the corresponding adjoint-state gradient and Hessian operators. Representing LAD images through directional and opening wavenumbers provides a unified description of propagation and scattering effects. The approach is independent of the forward-modeling engine and can be implemented with finite-difference, finite-element, spectral-element, ray-based, or beam-based methods. Under Born linearization, ray/beam formulations allow explicit Hessian computation. Owing to the near-orthogonality of directional and opening-angle sensitivities, the Hessian is more diagonally dominant than in conventional FWI, improving parameter separation, reducing velocity-reflectivity crosstalk, and enhancing inversion stability. By organizing seismic information in a physically meaningful phase-space representation, LAD-FWI supports adaptive, resolution-driven inversion and may reduce cycle skipping through attributes that vary more smoothly than waveform residuals. The framework naturally integrates directional focusing, reflector-consistency analysis, anisotropic parameter estimation, converted-wave imaging, and diffraction-based characterization, providing a unified workflow for elastic FWI, migration-velocity analysis, impedance inversion, and high-resolution subsurface imaging.
Comments80 pages, 24 figures
