On the Epicenter Determination of Historical Earthquakes Attested to by Sparse Intensity Data Sets

Abstract Historical earthquakes have to be parameterized for seismic‐hazard analyses, although there may be only a few intensity assignments available for them. We studied epicenter determination for 18 million synthetic samples of 3–11 intensity data points (IDPs). The IDP distributions corresponded to earthquakes that occurred offshore, close to the coast, or onshore. We assumed an ordinal variable, an attenuation relationship, and a point source. The attenuation relationship was utilized to encompass every IDP of a sample using a lower and upper radius that corresponded to the respective intensity. The epicenter must fit all the intensity rings simultaneously. The successes and failures of epicenter determination were monitored for a fixed magnitude and depth. We investigated where the epicenter was found, its uncertainty, and its uniqueness. Small location uncertainties may be obtained for the smallest samples but increasing the sample size led to a larger proportion of small uncertainties provided that intensities were error‐free. A large range of intensities in the sample, a short distance to the true epicenter, and, to a lesser extent, a small azimuthal gap were indicators of a good solution. A location uncertainty of 20 km and smaller is realistic in many cases, but uncertainties of 5 km are extremely seldom occurrences. The proportion of good locations was reduced when the intensities were erroneous. Epicenters were determined for the earthquakes of 26 April 1458 in central Italy, 14 July 1765 in Sweden, and 23 December 1875 in the eastern United States.