Reconstruction of unknown storativity and transmissivity functions in 2D groundwater equations

ABSTRACT

The paper deals with the identification from some pumping tests of unknown storativity and transmissivity functions defining a $2D$ confined aquifer. We introduce an appropriate change of variables that transforms the groundwater equation into a diffusion-reaction one wherein the diffusion term is defined by the fraction transmissivity/storativity and the reaction term yields the right hand side of a second-order nonlinear elliptic partial differential equation satisfied by the unknown storativity function. Using time records of the drawdown taken at some measuring wells within the monitored aquifer, we establish identifiability results on the involved unknown variables. We develop an identification approach that starts by determining the two auxiliary diffusion and reaction variables. Afterwards, the developed approach proposes local and global procedures to reconstruct the unknown storativity function. That leads to deduce the sought transmissivity function from the product of the two identified storativity and diffusion functions. Some numerical experiments on a variant of groundwater equations are presented.

Keywords:

• Nonlinear inverse problem
• partial differential equations: $2D$ Groundwater equations
• identification of storativity and transmissivity
• impulse response techniques and optimisation
• $2D$ confined aquifer

2010 Mathematics Subject Classification:

• 65M32

Disclosure statement

No potential conflict of interest was reported by the authors.