To make a geologic body more outstanding, it is necessary to preserve edges when filtering. For this reason, a filtering method based on anisotropic diffusion is introduced. The key point of this method is that diffus...To make a geologic body more outstanding, it is necessary to preserve edges when filtering. For this reason, a filtering method based on anisotropic diffusion is introduced. The key point of this method is that diffusion filtering will be made along the edge while diffusion is forbidden in the direction perpendicular to the edge, so the filtering has directionality. When doing anisotropic diffusion filtering, parameters like diffusion coefficient and threshold have great impacts on the results, so the anisotropic diffusion model parameters are discussed, the diffusion coefficient equation is introduced, and the diffusion threshold selection criterion is derived and analyzed. In addition, this method was used with the diffusion coefficient equation＇s proper diffusion threshold to highlight the tidal channel geobodies in the XX area, sand body in the YY area, and faults in the ZZ area. The good delineation results prove that the diffusion threshold selection criterion introduced in this paper is reasonable.展开更多
To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical da...To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.展开更多
The rnemmorphic functions of positive order(both finite positive order and infinite order) are discussed.First,the precise order and type function are given by using the characteristic function.Then some singular dire...The rnemmorphic functions of positive order(both finite positive order and infinite order) are discussed.First,the precise order and type function are given by using the characteristic function.Then some singular directions are defined and their existence is proved.展开更多
We introduce a new class of meromorphic functions on the plane, *_ normal functions say, their properties are very similarly as the normal functions in the unit disk and give three necessary conditions in judging it...We introduce a new class of meromorphic functions on the plane, *_ normal functions say, their properties are very similarly as the normal functions in the unit disk and give three necessary conditions in judging it. Further we prove that each Julia exceptional function is *_normal and that there exists a *_normal function which has Julia aline.展开更多
The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical prop...The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.展开更多
基金sponsored by National Natural Science Foundation of china (Grant Nos. 40904034 and 41174115)
文摘To make a geologic body more outstanding, it is necessary to preserve edges when filtering. For this reason, a filtering method based on anisotropic diffusion is introduced. The key point of this method is that diffusion filtering will be made along the edge while diffusion is forbidden in the direction perpendicular to the edge, so the filtering has directionality. When doing anisotropic diffusion filtering, parameters like diffusion coefficient and threshold have great impacts on the results, so the anisotropic diffusion model parameters are discussed, the diffusion coefficient equation is introduced, and the diffusion threshold selection criterion is derived and analyzed. In addition, this method was used with the diffusion coefficient equation＇s proper diffusion threshold to highlight the tidal channel geobodies in the XX area, sand body in the YY area, and faults in the ZZ area. The good delineation results prove that the diffusion threshold selection criterion introduced in this paper is reasonable.
基金supported by the National Program on Key Basic Research Project of China(973 Program)(No.2013CB036002,No.2014CB046901)the National Major Scientific Equipment Developed Special Project(No.51327802)+3 种基金National Natural Science Foundation of China(No.51139004,No.41102183)the Research Fund for the Doctoral Program of Higher Education of China(No.20110131120070)Natural Science Foundation of Shandong Province(No.ZR2011EEQ013)the Graduate Innovation Fund of Shandong University(No.YZC12083)
文摘To minimize the number of solutions in 3D resistivity inversion, an inherent problem in inversion, the amount of data considered have to be large and prior constraints need to be applied. Geological and geophysical data regarding the extent of a geological anomaly are important prior information. We propose the use of shape constraints in 3D electrical resistivity inversion, Three weighted orthogonal vectors （a normal and two tangent vectors） were used to control the resistivity differences at the boundaries of the anomaly. The spatial shape of the anomaly and the constraints on the boundaries of the anomaly are thus established. We incorporated the spatial shape constraints in the objective function of the 3D resistivity inversion and constructed the 3D resistivity inversion equation with spatial shape constraints. Subsequently, we used numerical modeling based on prior spatial shape data to constrain the direction vectors and weights of the 3D resistivity inversion. We established a reasonable range between the direction vectors and weights, and verified the feasibility and effectiveness of using spatial shape prior constraints in reducing excessive structures and the number of solutions. We applied the prior spatially shape-constrained inversion method to locate the aquifer at the Guangzhou subway. The spatial shape constraints were taken from ground penetrating radar data. The inversion results for the location and shape of the aquifer agree well with drilling data, and the number of inversion solutions is significantly reduced.
文摘The rnemmorphic functions of positive order(both finite positive order and infinite order) are discussed.First,the precise order and type function are given by using the characteristic function.Then some singular directions are defined and their existence is proved.
文摘We introduce a new class of meromorphic functions on the plane, *_ normal functions say, their properties are very similarly as the normal functions in the unit disk and give three necessary conditions in judging it. Further we prove that each Julia exceptional function is *_normal and that there exists a *_normal function which has Julia aline.
基金supported by the National Science and Technology Major Projects(No.2011ZX05020-008)Well Logging Advanced Technique and Application Basis Research Project of Petrochina Company(No.2011A-3901)
文摘The radial basis function （RBF） interpolation approach proposed by Freedman is used to solve inverse problems encountered in well-logging and other petrophysical issues. The approach is to predict petrophysical properties in the laboratory on the basis of physical rock datasets, which include the formation factor, viscosity, permeability, and molecular composition. However, this approach does not consider the effect of spatial distribution of the calibration data on the interpolation result. This study proposes a new RBF interpolation approach based on the Freedman＇s RBF interpolation approach, by which the unit basis functions are uniformly populated in the space domain. The inverse results of the two approaches are comparatively analyzed by using our datasets. We determine that although the interpolation effects of the two approaches are equivalent, the new approach is more flexible and beneficial for reducing the number of basis functions when the database is large, resulting in simplification of the interpolation function expression. However, the predicted results of the central data are not sufficiently satisfied when the data clusters are far apart.
