We consider the case of a cylindrical cored specimen of a saturated argillaceous sediment located between two reservoirs filled with an electrolyte. One of the boundaries of the sample is submitted to a sharp pressure (or salinity change). The migration of the resulting pressure (or saline) front through the core specimen is responsible for the apparition of an electrical field, which is called the streaming potential (the diffusion potential for a salinity gradient, respectively). The temporal variation of this electrical field is recorded with Ag/AgCl nonpolarizable electrodes and used to monitor the evolution of the pressure (or saline) front between the two reservoirs. There is a finite interval of time before which the steady state condition holds through the core. In both cases, the electrical potentials exhibit a relaxation with a relaxation time constant depending on the square of the length of the cylindrical core specimen and on its hydraulic (or ionic) diffusivity. The experiments described here provide new methodologies to determine the hydraulic and ionic diffusivities of clay-rich materials. These experiments confirm also the predictions of a transport model developed recently for such materials and illustrate a powerful geophysical method to obtain transport properties, not only in the laboratory, but also in the field using a network of nonpolarizable electrodes to remotely monitor dissipation processes occurring inside the investigated system.