基于广义坐标变换的起伏地表频率域波动方程正演模拟与逆时偏移

Forward modeling of wave equation and reverse-time migration in frequency domain with rugged topography based on generalized coordinate transformation

高效精确的波动方程正演模拟是地震偏移成像和参数反演的核心,频率域的有限差分方法在正演模拟具备一定优势,包括能够在多震源模拟中计算效率更高,在选择网格间距时更具有灵活性等.然而,这种方法在处理起伏地表问题上较为困难.为了解决起伏地表情况下的频率域波动方程正演模拟与逆时偏移问题,我们提出通过建立广义坐标系,利用传统笛卡尔坐标系到起伏地表坐标系的映射关系,在起伏地表条件下高精度地模拟地震波传播波场.在此基础上,进一步讨论了实现频率域逆时偏移的可行性.并使用均匀模型和Foothills模型的数值测试来验证本文方法基本流程的有效性和计算效率.结果表明,在进行复杂地表场景的频率域地震成像和反演时,本文方法具有作为正演建模求解器的潜力.

Efficient and accurate forward modeling of wave equations is the key of seismic structure imaging and parameter inversion.The finite difference method in frequency domain offers notable advantages for forward modeling,including enhanced computational efficiency in multi-source simulations and greater flexibility in grid spacing selection.However,challenges arise in effectively addressing topographic surface conditions using this method.To tackle the issues associated with frequency domain wave-equation forward modeling and reverse time migration with rugged topography,we propose employing a generalized coordinate system.This approach involves utilizing a mapping from the traditional Cartesian coordinate system to an topographic coordinate system to accurately simulate the propagation of seismic wave fields.Building upon this framework,we further explore the feasibility of implementing frequency domain reverse time migration.We conduct numerical tests using both uniform and Foothills models to validate the effectiveness and computational efficiency of our proposed method.The results demonstrate that this approach offers a promising solution for forward modeling in frequency domain seismic imaging and inversion of complex surface environments.