A semi-empirical analysis of hypocenter mislocations

Daily experience in locating man-made seismic events shows that small travel-time residuals and small standard errors do not necessarily guarantee accurate hypocenter solutions. Experience also shows that, in many cases, hypocenter error estimates which are based on the assumption that the time residuals are randomly distributed may yield unrealistic results. Simulated cases have been used to analyze mislocations. The analysis of more than 15,000 simulated cases reveals in many instances that the RMS value (SDt) of the time residuals obtained for the true hypocenter is practically independent of the RMS value, σ₀, obtained for the optimal location determination. Furthermore, it seems that the difference, (SDt)-σ₀, is a function of outside parameters, mainly the reliability of the measurements. As these are probably not random variables and should not be considered systematic, a numerical procedure is developed to assess the location errors. In the proposed approach, each measurement is assigned a time error parameter, E_i, which comprises the expected resolution, E_s, the expected error due to uncertainties in the propagation path model, E_m, and an error estimate, V_i, given by the analyst with respect to the quality of the measured ith seismogram. Thus, the location error field is defined as the assembly of all locations which yield time residuals smaller or equal to the pre-defined time errors, E_i, for all measurements. The numerical approach which is developed is applied to simulated cases as well as to real data from rockbursts in South Africa and to earthquake data from the Afro-Eurasian junction.