nDetermination of magnitude and epicenter of historical earthquakes in Brazil by inversion techniques using intensity attenuation curves: application to the 1861 and 1950 events

This study aims to determine the epicenter and magnitude of historical earthquakes of 1861 (mb=5) and 1950 (mb=3.9), through the implementation of an inversion algorithm and compare the results with the Boxer program (Gasperini et. al., 1999). An inversion algorithm was implemented with the Nelder-Mead technique (Nelder and Mead, 1965), using the Intensity Attenuation Law applicable to Brazilian earthquakes with magnitudes between 3.5 to 5.5 and intensities III to VI (MM) (Assumpção and Burton, 1985). The earthquakes of 1955 (mb=6.2) and 1998 (mb=5.2), with known instrumental measurements, were used for testing. The inverse problem searches for the magnitude and epicenter of the earthquake that minimizes the objective function (rms deviation of the intensities) by the Nelder-Mead algorithm. The results were satisfactory and provided subsidy to evaluate the applicability of the proposed methodology for the historical earthquakes of 1861 and 1950. The Boxer method was also tested to determine the parameters of the 1955 and 1998 earthquakes. For this, we used the attenuation coefficients derived for Italy, and also those for the Continental Stable Region in Europe (Gomez-Capera et. al., 2014). The same procedures were applied to the historical earthquakes of 1861 and 1950. When the distribution of macroseismic data points (MDP) show a clear trend of higher and lower intensities, such as the 1998 and 1955 earthquakes, the Nelder-Mead inversion gives a better epicenter (closer to the instrumental) than the Boxer method (which assumes the epicenter is within the area enclosed by the MDPs). When the intensity distribution is more scattered or subject to larger uncertainties, such as the 1861 event, the Boxer method gives more reasonable results. For the 3.9 mb earthquake of 1950, with good MDP distribution in a small area, the two methods give similar results.