The Location and Sizing of Historical Earthquakes Using the Attenuation of Macroseismic Intensity with Distance

We herein describe new methods for computing the quantitative parameters of earthquakes using macroseismic data and the uncertainties associated with these parameters. The methods allow for the location of epicenters that are offshore or that have no intensities assigned to any points in the epicentral region by maximizing the likelihood function of an attenuation equation with observed intensity data. In the most favorable cases, such an approach also allows the estimation of the source depth and the local attenuation coefficients. We compute the parameter uncertainties in two ways: (1) using formal methods, such as the inversion of the Hessian of the log-likelihood function at its maximum, and (2) by using bootstrap simulations. We tested the performance of our methods by comparison with reliable instrumental hypocenters of onshore earthquakes, and found a reasonable agreement with the epicentral locations (within 10-15 km for more than 70% of cases) but not with the hypocentral depths, for which our results are generally underestimated by a factor of 2 or more and are poorly related to instrumental estimates. This finding indicates that the use of macroseismic depths in seismic hazard and seismotectonic investigations should be treated with caution. We nevertheless found good agreement (within 10 degrees-15 degrees) between the fault-trace orientations that were computed using the macroseismic data and the associated focal mechanisms of earthquakes with M-w >= 5.7. The surprising accuracy of the macroseismic orientations obtained using this method could in some cases allow the true fault to be inferred between the two conjugate planes of a given focal mechanism.