基于水平集的复杂三维地层模型建模及在地下工程中的应用研究

Study of building 3D complex strata model based on level set methods and application to underground engineering

由于地质体存在断层、尖灭、出露等复杂地质现象,在三维地层建模时,为了表达这些现象,无论是面模型还是体模型或混合模型,都存在空间分割或曲面求交线的问题。由于地质体拓扑关系的复杂性、数据误差以及计算机精度问题,使得这些模型在实际建模过程中常常失效。运用水平集理论可以有效解决这一问题,水平集用隐函数表达曲面(或超曲面),可以实现复杂地质体的表达及并、交、差等拓扑运算。在三维地层建模中,插值生成各种地质界面后,用水平集表达这些地质界面,利用水平理论完成各种复杂的拓扑操作,建立以水平集表达的三维地层模型。在此基础上,插入水平集表达的各种工程活动界面,利用水平集理论进行拓扑操作,可构建各种工程活动后的地层模型。再利用Marching cube算法抽取各种地质界面或工程活动界面,构建可用于实时可视化或用于工程评估(如有限元计算)等的NMTINF-BR地层模型或工程活动后的NMTINF-BR地层模型。

In order to represent three dimension complex stratigraphic objects including faults,disappearances,outcrops and other phenomena,we have to face the difficult problems in the process of spatial partition or calculating intersection lines of curved surfaces in building 3D strata model,either based on surface elements,or based on volume elements,or based on hybrid elements.But these methods in building 3D complex strata models usually failed,because of complex topological relationships of the strata,source data error and computer accuracy etc.It is a good idea to resolve these problems by using level set methods.Level sets are implicit functions of surfaces or hypersurfaces,which can represent complex geological bodies and implement a series of topological operations such as union,intersection,difference etc.In building 3D strata model,after interpolating geological interfaces,these interfaces are transformed into level sets,and the complex topological operations based on level sets are applied to building the 3D strata model.After building the 3D strata model,the interfaces of engineering activities represented by level sets,are inserted into the 3D strata model;and the 3D engineering activities strata model is built by the complex topological operations based on level sets.Then the geological interfaces or the interfaces of engineering activities are extracted by marching cube algorithm to constructing a NMTINF-BR 3D strata model or a NMTINF-BR 3D engineering activities strata model which is suitable for real-time visualization and numerical simulation（such as finite elements）.