An Elliptical Model for Deformation Due to Groundwater Fluctuations     

Kristy F. Tiampo  Francois-Alexis Ouegnin  Sreeram Valluri  Sergey Samsonov  José Fernández  Garrett Kapp 《Pure and Applied Geophysics》2012,169(8):1443-1456

Historically, surface subsidence as a result of subsurface groundwater fluctuations have produced important and, at times, catastrophic effects, whether natural or anthropogenic. Over the past 30?years, numerical and analytical techniques for the modeling of this surface deformation, based upon elastic and poroelastic theory, have been remarkably successful in predicting the magnitude of that deformation (Le Mouélic and Adragna in Geophys Res Lett 29:1853, 2002). In this work we have extended the formula for a circular-shaped aquifer (Geertsma in J Petroleum Tech 25:734–744, 1973) to a more realistic elliptical shape. We have improved the accuracy of the approximation by making use of the cross terms of the expansion for the elliptic coordinates in terms of the eccentricity, e, and the mean anomaly angle, M, widely used in astronomy. Results of a number of simulations, in terms of e and M developed from the transcendental Kepler equation, are encouraging, giving realistic values for the elliptical approximation of the vertical deformation due to groundwater change. Finally, we have applied the algorithm to modeling of groundwater in southern California.  相似文献