Rytov-approximation-based wave-equation traveltime tomography
Rytov-approximation-based wave-equation traveltime tomography
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基于 Rytov 近似的波动方程走时层析成像
DOI：
10.1190/geo2019-0210.1
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发表时间：
2020-05-01
期刊：
影响因子：
3.3
通讯作者：
Wang, Huazhong
中科院分区：
文献类型：
--
作者：
Feng, Bo;Xu, Wenjun;Wang, Huazhong
大多数有限频率旅行时层析成像方法都是基于Born近似的，这就要求速度不均匀的尺度和速度扰动的大小必须足够小才能满足Born近似。相反，Rytov近似适用于大尺度速度非均质性。通常，基于Rytov近似的有限频率旅行时灵敏度核(Rytov-FFTSK)可以通过将相位延迟敏感核与归一化加权函数相结合来获得，其中灵敏度核的计算需要格林函数的数值解。然而，显式求解格林函数的计算量相当大，尤其是对于3D问题。为了避免显式计算格林函数，我们证明了Rytov-FFTSK可以通过将正向传播的入射波场和反向传播的伴随波场在时间域中互相关来获得。此外，我们发现Rytov-FFTSK对模型空间矢量的作用可以通过计算两个时间域场的内积来计算，例如灵敏度核与矢量的乘积。因此，可以以无矩阵的方式计算海森向量乘积(即，首先计算灵敏度核与模型空间向量的乘积，然后计算转置后的灵敏度核与数据空间向量的乘积)，而无需显式地形成海森矩阵或灵敏度核。我们用高斯-牛顿法求解旅行时反问题，其中高斯-牛顿方程用我们的无矩阵海森向量积方法用共轭梯度近似求解。一个具有完美采集几何结构的实例表明，我们的基于Rytov近似的旅行时反演方法可以产生高质量的反演结果，并且具有非常快的收敛速度。逆冲推覆合成资料试验表明，如果可以进行长炮检距采集，大到中尺度的模式摄动可以通过潜水波恢复。
Most finite-frequency traveltime tomography methods are based on the Born approximation, which requires that the scale of the velocity heterogeneity and the magnitude of the velocity perturbation should be small enough to satisfy the Born approximation. On the contrary, the Rytov approximation works well for large-scale velocity heterogeneity. Typically, the Rytov-approximation-based finite-frequency traveltime sensitivity kernel (Rytov-FFTSK) can be obtained by integrating the phase-delay sensitivity kernels with a normalized weighting function, in which the calculation of sensitivity kernels requires the numerical solution of Green’s function. However, solving the Green’s function explicitly is quite computationally demanding, especially for 3D problems. To avoid explicit calculation of the Green’s function, we show that the Rytov-FFTSK can be obtained by crosscorrelating a forward-propagated incident wavefield and reverse-propagated adjoint wavefield in the time domain. In addition, we find that the action of the Rytov-FFTSK on a model-space vector, e.g., the product of the sensitivity kernel and a vector, can be computed by calculating the inner product of two time-domain fields. Consequently, the Hessian-vector product can be computed in a matrix-free fashion (i.e., first calculate the product of the sensitivity kernel and a model-space vector and then calculate the product of the transposed sensitivity kernel and a data-space vector), without forming the Hessian matrix or the sensitivity kernels explicitly. We solve the traveltime inverse problem with the Gauss-Newton method, in which the Gauss-Newton equation is approximately solved by the conjugate gradient using our matrix-free Hessian-vector product method. An example with a perfect acquisition geometry found that our Rytov-approximation-based traveltime inversion method can produce a high-quality inversion result with a very fast convergence rate. An overthrust synthetic data test demonstrates that large- to intermediate-scale model perturbations can be recovered by diving waves if long-offset acquisition is available.