Self-potential electric and magnetic anomalies are increasingly being observed associated with hydrothermal fields, volcanic activity, and subsurface water flow. Until now a formal theoretical basis for predicting streaming potential of porous materials has not been available. We develop here a model giving both the macroscopic constitutive equations and the material properties entering these equations. The material properties, like the streaming potential coupling coefficient, depend on pore fluid salinity, temperature, water and gas saturations, mean grain diameter, and porosity. Some aspects of the model are directly tested with success against laboratory data. The streaming potential increases with temperature, grain size, and gas saturation and decreases with salinity. At the scale of geological structures the model provides an explanation for the presence of kilometer-scale dipolar self-potential anomalies in geothermal systems and volcanoes. Positive self-potential anomalies are associated with fluid discharge areas, whereas negative self-potential anomalies are associated with fluid recharge areas. Self-potential anomaly maps determined at the surface of active hydrothermal fields appear to be a powerful way of mapping the fluid recharge and discharge areas. In the case of free convection the vorticities of the convection pattern generate a magnetic field. The greater these vorticities, the greater the associated magnetic field. It follows that hydrothermal systems act as natural geobatteries because of the flow of pore fluids in the subsurface of these systems. ¿ 1999 American Geophysical Union