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 thermodynamic behavior of field equations for the generalized f(R) gravity with arbitrary coupling between matter and geometry is studied in the two kinds of spacetime,i.e.,the both spatially homogenous,isotropic ...The thermodynamic behavior of field equations for the generalized f(R) gravity with arbitrary coupling between matter and geometry is studied in the two kinds of spacetime,i.e.,the both spatially homogenous,isotropic FRW universe and static,spherically symmetric black hole spacetime.The field equations of the generalized f(R) gravity with arbitrary coupling between matter and geometry can be cast to the form of the first law of thermodynamics with the reputed entropy production terms dS,which are quite general and can degenerate to the cases of Einstein's general relativity and pure f(R) gravity with non-coupling and nonminimal coupling as special cases.The appearance of the entropy production term dS illustrates that the horizon thermodynamics is non-equilibrium one for the generalized f(R) gravity with arbitrary coupling between matter and geometry.展开更多
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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11175077 and 11147150)the Natural Science Foundation of Liaoning Province(Grant Nos.20102124 and L2011189)
文摘The thermodynamic behavior of field equations for the generalized f(R) gravity with arbitrary coupling between matter and geometry is studied in the two kinds of spacetime,i.e.,the both spatially homogenous,isotropic FRW universe and static,spherically symmetric black hole spacetime.The field equations of the generalized f(R) gravity with arbitrary coupling between matter and geometry can be cast to the form of the first law of thermodynamics with the reputed entropy production terms dS,which are quite general and can degenerate to the cases of Einstein's general relativity and pure f(R) gravity with non-coupling and nonminimal coupling as special cases.The appearance of the entropy production term dS illustrates that the horizon thermodynamics is non-equilibrium one for the generalized f(R) gravity with arbitrary coupling between matter and geometry.
