射线雅可比的直接数值计算方法及应用

射线雅可比是求解输运方程、计算波前几何扩散因子和射线格林函数振幅的关键。该雅可比对于基于射线理论的真振幅偏移成像十分重要，是广义Radon变换（GRT）逆散射偏移真振幅成像条件权函数的组成部分。在强变速介质中，速度场的二阶偏导数变化较大，动力学射线追踪难以得出较准确的射线雅可比，产生伪焦散点，也会遗漏真焦散点。为实现更准确的射线雅可比计算，文中从雅可比的定义出发，通过数值计算射线管的横截面元面积与初始角面元面积的比率实现射线雅可比的计算。射线雅可比的直接数值计算方法具有明确的物理意义，计算的雅可比更准确，能有效识别出真实的焦散点；同时，采用了一种合理的雅可比平滑阈值方法，避免了逆散射保幅偏移成像中焦散引起的奇异问题。盐丘模型的逆散射偏移成像测试结果，验证了该射线雅可比直接数值计算方法的有效性和适用性。

Direct numerical calculation of ray Jacobian and its application

Ray Jacobian plays a fundamental role in solving transport equation,obtaining the geometrical propagating factor of seismic wavefront and the amplitude of the Green’s function.The ray Jacobian is of great importance for true amplitude migration imaging based on the ray theory and is a part of the weight function of the true amplitude imaging condition of generalized Radon transform (GRT) based inverse scattering migration.In the medium with strong velocity variation,the ray Jacobian computed by dynamic ray tracing may be rather problematic for the unstable second spatial derivatives of the velocity field,which results in generating pseudo-caustic points and missing real caustic points.To compute ray Jacobian accurately,we focus on its definition and calculate it through the ratio of the element cross-sectional area of a ray tube to the element initial angular area.Since the direct method has a clear physical meaning,we can get an accurate Jacobian,and real caustic points can be detected effectively.In addition,the singularity in inverse scattering amplitude-preserved migration caused by the caustics can be avoided by adopting a reasonable ray Jacobian smoothing threshold.Application to a salt dome model has proved the method is effective and applicable.