Local geometric information, i.e. normal and distribution of points, is crucial for LiDAR-based simultaneous localization and mapping (SLAM) because it provides constraints for data association, which further determines the direction of optimization and ultimately affects the accuracy of localization. However, estimating normal and distribution of points are time-consuming tasks even with the assistance of kdtree or volumetric maps. To achieve fast normal estimation, we look into the structure of LiDAR scan and propose a ring-based fast approximate least squares (Ring FALS) method. With the Ring structural information, estimating the normal requires only the range information of the points when a new scan arrives. To efficiently estimate the distribution of points, we extend the ikd-tree to manage the map in voxels and update the distribution of points in each voxel incrementally while maintaining its consistency with the normal estimation. We further fix the distribution after its convergence to balance the time consumption and the correctness of representation. Based on the extracted and maintained local geometric information, we devise a robust and accurate hierarchical data association scheme where point-to-surfel association is prioritized over point-to-plane. Extensive experiments on diverse public datasets demonstrate the advantages of our system compared to other state-of-the-art methods. Our open source implementation is available at https://github.com/tiev-tongji/LOG-LIO.