井间地震资料全变差正则化波形反演

Total variation regularization waveform inversion of crosswell seismic data

(中国石油大学(北京)地球物理与信息工程学院CNPC物探重点实验室,北京102249)

Wang Shoudong,CNPC Key Laboratory,College of Geophysics and Information Engineering,China University of Petroleum (Beijing),Beijing 102249,China

针对井间地震资料走时层析成像分辨率低、稳定性差的问题,研究了一种井间地震资料成像新方法——全变差正则化波形反演方法(TVWI)。该方法基于Gauss-Newton波动方程反演,将井间地震资料的速度求取问题归结为波动方程反演问题,通过极小化合成地震记录与观测地震记录的差实现波动方程反演；利用局部线性化逐步迭代的方法实现非线性泛函优化问题的求解；将波动方程反演的目标泛函加入全变差约束项,提高反演过程的稳定性和反演结果的分辨率。设计了一个复杂的速度模型验证了TVWI方法的有效性,结果表明,在给定不同速度初值的情况下,反演结果都具有较高的精度。选取与真实速度相差较大的初始速度模型讨论了TVWI方法对初值选取的依赖性：反演结果对初值选取的依赖性不强,但初值选取不好,会增加迭代次数和计算成本。最后进行了抗噪能力试验,结果表明，TVWI方法具有较强的抗噪能力。

Aiming at the low-resolution and instability of crosswell seismic travel-time tomography,a total variation regularization waveform inversion (TVWI) method for crosswell seismic data was proposed.High resolution velocity distribution between two wells can be obtained by TVWI using crosswell seismic data.TVWI is based on Gauss-Newton wave equation inversion,which converts the velocity calculation of crosswell seismic data into wave equation inversion and achieves the wave equation inversion through minimizing the difference between the calculated seismic data and observed data.The local linearization step by step iteration method is used to optimize the nonlinear objective functional.The total variation constraint item is added to the wave equation inversion objective functional,to improve the stability and the resolution of inversion.A complex velocity model was designed to verify the validity of TVWI method,and the result shows that for the different given initial velocity,all the inversion has relatively high accuracy.The initial velocity model which has large difference to real velocity was selected to discuss the dependence of TVWI method on the picking of initial value.Inversion result shows that it is not depend on the picking of initial value,but if the initial value is not well picked,the iteration times and computation cost will increase.Finally,anti-noise ability 〖JP2〗of TVWI method was tested,and it was proofed to be strong ability.