四面体网格剖分下速度与反射界面的同时反演

Simultaneous inversion for velocity and reflector geometry using multi-phase travel-times in 3-D tetrahedral cell model

针对含起伏地表、不规则反射界面及速度异常体的复杂模型的走时正、反演问题,本文采用四面体单元进行模型参数化,实现多震相地震射线的追踪计算,且推导了四面体单元下走时关于速度、走时关于反射点深度的偏导数计算公式;结合共轭梯度法求解带约束的阻尼最小二乘反演问题,实现了多震相走时联合及同时反演成像;通过在同时反演中对不同种类Jacobi偏导元素做归一化处理,有效解决了不规则界面存在散射而导致的散射点所在区域射线过密、速度和界面过度更新问题。数值模拟结果表明:采用四面体单元进行模型参数化,复杂模型正演计算结果具有较高精度;同时反演可准确刻画不规则反射界面和速度异常体。因此,本文提出的走时成像方法具有有效性和实用性。

To conduct forward modeling and simultaneous inversion for a complex geological model with an irregular topography,or irregular reflectors,or irregular velocity anomaly,we propose in this paper simultaneous inversion using multi-phase travel-times in 3-D tetrahedral cell model.First we realize a multi-phase arrival tracking with a multistage modified shortest-path method,develop calculation formula of partial derivative of reflection depth about travel-times under a tetrahedral cell model.Then we solve a constrained-damped leastsquares inversion with a conjugated gradient method to simultaneously invert the velocity model and reflector geometry with multi-phase arrival time information.Finally we normalize the different Jacobi elements in the simultaneous inversion to eliminate undulated reflector scattering,which causes overhigh ray density and over-updated velocity issues.Numerical simulation results show that with the tetrahedral cell model parameterization,it is possible to maintain a high computational accuracy for forward modeling in the complex velocity model,and capture the irregular velocity anomaly and reflector geometry in the simultaneous inversion.Therefore,the proposed simultaneous travel-time inversion has a wide application in real problems.