An Elliptical Model for Deformation Due to Groundwater Fluctuations
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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.
KeywordsDeformation numerical techniques groundwater hydrology subsidence inversion geodesy
K. F. Tiampo and S. R. Valluri gratefully acknowledge Discovery Grants from National Science Engineering Research Council Canada (NSERC), Human Resources Development Canada (HRDC) and the UWO Work Study Program for support of F. Ouegnin in this research project. The ERS data were supplied under ESA ENVISAT data grant AO ID = 853 (HAZARDMAP). Technical support for this work has been provided by the POLARIS network. Research by J. Fernández has been supported by Spanish MICINN projects: GEOMOD (CGL2005-05500-C02), PEL2G (CGL2008-06426-C01-01/BTE) and GEOSIR (AYA2010-17448). This research has been partially funded in the frame of the Moncloa Campus of International Excellence (UCM-UPM, CSIC). The DInSAR data was processed by the Repeat Orbit Interferometry Package (ROI PAC) developed at Caltech/Jet Propulsion Laboratory. The DEM data was provided by USGS. The images were plotted with the help of GMT software developed and supported by Paul Wessel and Walter H. F. Smith. The authors would like to thank S. Le Mouélic for providing the original IDL code for the circular deformation model and Dr. D. Argus and Dr. M. Motagh for thorough and helpful reviews.
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