基于交叉梯度约束的弹性阻抗同时反演

Elastic impedance simultaneous inversion based on cross-gradient constraint

1.西华师范大学图书馆,四川南充637009;
2.西华师范大学数学与信息学院,四川南充637009;
3.西南石油大学地球科学与技术学院,四川成都610500;
4.西华师范大学最优化理论与应用四川省高校重点实验室,四川南充637009;
5.西华师范大学非线性及应用研究所,四川南充637009

1. China West Normal University Library,Nanchong 637009,China;
2. School of Mathematics and Information,Nanchong 637009,China;
3. School of Geoscience and Technology,Southwest Petroleum University,Chengdu 610500,China;
4. Key Laboratory of Optimization Theory and Application at China West Normal University of Sichuan Province,China West Normal University,Nanchong 637009,China;
5. Institute of Nonlinear Analysis and Applications,China West Normal University,Nanchong 637009,China

目前常用的弹性阻抗反演方法对不同角度数据体独立进行反演,没有考虑不同角度弹性阻抗间的关系。对于信噪比较低的角度数据体,反演结果质量变差。针对这一问题,从不同角度弹性阻抗均描述地下同一地质结构而应具有结构相似性这一观点出发,采用交叉梯度度量不同角度弹性阻抗间的结构相似性。然后,将交叉梯度作为正则化约束项加入到弹性阻抗反演目标泛函中,研究交叉梯度约束下的弹性阻抗反演方法,同时反演多个部分角度叠加数据。模型数据试算与实际数据应用结果显示,交叉梯度约束反演得到的不同角度弹性阻抗间具有地质结构一致性,无论是小角度弹性阻抗,还是中、大角度弹性阻抗,地质体均得到清晰显示,地层横向展布特征自然。因此,交叉梯度约束弹性阻抗反演可提高不同角度数据体反演的稳定性,并提升反演结果的质量。

Common elastic impedance (EI) inversion copes with the datasets of different angles separately without considering the relations among EIs at different angles,which may impair the quality of inversion,particularly at low signal-to-noise ratios.To solve this problem,we adopt cross gradient to measure the structural similarity of EIs at different angles based on the following understandings:multi-angle EIs characterize the same geologic body and should have a similar geologic structure.The cross gradient is added into the objective function of EI inversion as a regularization term to constrain the simultaneous inversion of several partial angle stacks.Model tests and practical application indicate the consistent geologic structure delineated using inverted EIs at different angles.Geologic units could be clearly imaged with laterally credible extension using EIs at small,middle,and large angles.The cross-gradient constraints improve the robustness and quality of multi-angle simultaneous EI inversion

国家自然科学基金项目“格拉姆相关性约束叠前地震反演方法研究”(42204123)、四川省自然科学基金项目“相控地震地质统计学反演驱动的深层超深层储层参数建模方法研究”(2023NSFSC0772)和西华师大研究生教育改革研究项目(2022XM24,2024XM05)共同资助。

10.12431/issn.1000-1441.2025.64.01.008