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On 8 May 1939, an earthquake (Ms7.1) occurred near the Azores archipelago, with an epicentre located close to the western end of the Gloria fault. Previous studies present different epicentre locations spreading over a large area, and two different types of focal mechanisms. Given these uncertainties, the interpretation of the seismological information in a complex tectonic environment between the Gloria Fault and the Terceira Ridge is a matter of debate. The event caused a small tsunami recorded in the Azores Islands. In this study, we use the tsunami observations and tsunami numerical modelling to select the earthquake fault rupture that best fits the tsunami observations. We consider the different focal mechanism solutions, perform tsunami numerical modelling, and compute synthetic tsunami waveforms at the tide gauge locations. We find that an earthquake caused by a low-angle dipping fault with dominant strike–slip movement generates a tsunami that reproduces well the record at Ponta Delgada tide gauge. Finally, in areas where earthquakes are rare, the study of ancient earthquakes must use all information available, namely tsunami observations and mareograph data. [ABSTRACT FROM AUTHOR]