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It is suggested that the geothermal anomalies of the Rhine graben have been caused by hydrothermal convection. Mathematical modelling yields a good agreement between the calculated and the measured temperature. The age of the anomalies may be at least 80,000 years, depending on discharge and maximum depth of convection. The hydrothermal convection is made possible by the active shearing along the axis of the Rhine graben which causes continuously open fractures allowing water flow. Displacements, due to thermal expansion of rocks within the geothermal anomaly, are calculated using the Bett-Maysel reciprocal theorem of elasticity theory. The resulting vertical displacements of 6-8 m maximum may not be observable in the field, whereas the horizontal displacements are sufficient to create normal faults with several metres vertical throw, they can be seen to accompany the geothermal anomalies. (ERA citation 08:031564)