应用线性程函方程和整形正则化的三维初至波旅行时层析

3D first-arrival traveltime tomography with linearized eikonal equation and shaping regularization

初至波旅行时层析成像是近地表速度结构建模的重要方法。传统的三维旅行时层析反演在应用中存在诸多问题:一是射线追踪技术固有的计算效率低、对复杂模型计算不稳定;二是对于大规模三维模型,Tikhonov正则化难以对零空间和欠定分量进行有效约束,造成迭代收敛速度缓慢,难以满足生产需求。基于线性程函方程,结合迎风有限差分算法提出了一种新的敏感核函数计算方法,并在此基础上引入整形正则化方法,通过共轭梯度法实现了初至波旅行时层析反演。三维理论模型实验表明,与传统射线旅行时层析方法相比该方法具有更高的反演精度与迭代收敛速度。

First-arrival traveltime tomography is an important tool for estimating near-surface long-wavenumber seismic velocities. However, conventional algorithms utilized for traveltime tomography usually encounter problems when handling large 3D seismic data. For instance the raytracing has low computational efficiency and instability when strong velocity contrast exists in velocity models, and conventional regularization algorithms lie in their low iterative convergence rate caused by the insufficient control on models estimated by Tikhonov's regularization, which could be detrimental for large 3D scale problems, when only very few iterations are affordable. Therefore, on the basis of linearized eikonal equation, we propose a new algorithm to calculate the Fréchet derivative matrix with the upwind differences scheme without using cumbersome raytracing. Additionally, we incorporate a shaping regularization into conjugate gradient algorithm to iteratively minimize the data misfit. Finally, numerical experiments on 3D models demonstrate that the proposed algorithm has higher accuracy and faster convergence compared with the conventional algorithms. © 2017, Editorial Department OIL GEOPHYSICAL PROSPECTING. All right reserved.