广义Rytov近似有限频初至层析

Wave-equation traveltime tomography using the generalized Rytov approximation

在传统的有限频层析理论中,采用Born或Rytov近似推导地震波旅行时对模型参数的一阶Fréchet微商,隐含了弱散射近似假设。对于强速度扰动,有限频层析正问题的线性化近似不再成立。近年来发展的广义Rytov近似理论可以较为精确地预测散射波的相位扰动,因此更适用于有限频旅行时层析。为突破弱散射近似的限制,将广义Rytov近似应用于传统的有限频层析理论,导出了基于广义Rytov近似理论的有限频旅行时敏感度核函数。由数值试验可知,对于前向小角度散射,无论速度扰动强度如何,新的旅行时核函数均可较为准确地预测地震波的旅行时扰动。针对旅行时层析反问题,提出了一种基于隐式矩阵向量乘的高斯—牛顿反演算法,具有准二阶收敛速度且无需显式计算和存储Hessian矩阵。复杂模型数据测试结果表明,提出的广义Rytov近似旅行时层析可以建立高精度的近地表速度模型,且收敛速度较快。

The conventional finite-frequency tomography is usually derived from the Born or Rytov approximation which implies weak-scattering assumption.Therefore,the linearized forward problem in the finite-frequency theory is not satisfied for strong velocity perturbations.In the case of forward scattering and small-angle propagation,the generalized Rytov approximation(GRA)method recently developed can achieve improving phase accuracy of forward-scattered wavefield,making it more suitable for traveltime tomography.In this paper,we combine the conventional finite-frequency theory with GRA and propose a GRA-based traveltime sensitivity kernel,which works well regardless of the magnitude of velocity perturbations.Numerical examples show that the traveltime perturbation of forward-scattered waves can be correctly handled by the GRA-based traveltime sensitivity kernel.Then we propose an implicit matrix-vector product strategy which can calculate the Hessian matrixvector product without explicitly forming the Hessian matrix,making it more attractive for 3-D problems.We solve the traveltime inverse problem with the Gauss-Newton method,where the Hessian matrix-vector product is obtained by the proposed implicit matrix-vector product method.Consequently,the Gauss-Newton method can be realized in a matrix-free fashion,reducing the computer memory and disk occupancy significantly.Numerical tests demonstrated that the proposed GRAbased traveltime tomography can estimate the nearsurface velocity model with high resolution and at a fast convergence rate.