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In the low frequency limit of the Biot equations the variations of the pore pressure in a fluid saturated elastic medium can be approximately described by a Homogeneous Diffusion Equation (HDE). It can be used, for example, to reconstruct the tensor of hydraulic diffusivity when connecting the microseismicity associated with fluid injection in boreholes, and assuming that these injections cause perturbations of the pore pressure in the rock. In poroelasticity this can be considered as an uncoupled problem. That is, elastic stresses and pore pressure are independent of each other in the governing partial differential equations of the problem. On the other side, those phenomena in which it is necessary to take into account the systematic influence of elastic stresses and pore pressure on each other are known as coupled problems. The intermediate problem, in which pore pressure does not influence the elastic stresses whereas the stresses influence the pressure, is known as the decoupled one. This approximation leads to an Inhomogeneous Diffusion Equation (IDE) that is being commonly used to analyse the pore pressure variations next to dams due to time varying water loads in their reservoirs. When considering flow boundary conditions, the solution of this equation can be obtained as the superposition of a term computed from the HDE with the Dirichlet boundary condition (the term due to the pore pressure diffusion), and the solution of an initial value problem in which the inhomogeneous term related with the stress variations in the IDE is considered (the solution due to the compression in the media). In this work we use a hybrid technique to …