In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical
coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions
to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried
inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical
solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long
axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are
expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively,
the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined
elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed
in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application
example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion
affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the
elliptic inclusion is of finite but nonzero values. 相似文献
Using more than three million Landsat satellite images, this research developed the first global impervious surface area (GISA) dataset from 1972 to 2019. Based on 120,777 independent and random reference sites from 270 cities all over the world, the omission error, commission error, and F-score of GISA are 5.16%, 0.82%, and 0.954, respectively. Compared to the existing global datasets, the merits of GISA include: (1) It provided the global ISA maps before the year of 1985, and showed the longest time span (1972–2019) and the highest accuracy (in terms of a large number of randomly selected and third-party validation sample sets); (2) it presented a new global ISA mapping method including a semi-automatic global sample collection, a locally adaptive classification strategy, and a spatio-temporal post-processing procedure; and (3) it extracted ISA from the whole global land area (not from an urban mask) and hence reduced the underestimation. Moreover, on the basis of GISA, the long time series global urban expansion pattern (GUEP) has been calculated for the first time, and the pattern of continents and representative countries were analyzed. The two new datasets (GISA and GUEP) produced in this study can contribute to further understanding on the human’s utilization and reformation to nature during the past half century, and can be freely download from http://irsip.whu.edu.cn/resources/dataweb.php.