Joint Maximum Likelihood Estimators for Gutenberg-Richter Parameters λ₀ and β Using Subcatalogs

Two new estimators of parameters λ0 and β of the Gutenberg-Richter seismicity relation are presented for the case in which several complete portions of an earthquake catalog are used in the estimation process. These estimators are the ones that maximize the joint likelihood of both parameters, considering Poisson arrivals. Therefore, as shown in this paper, they are more robust than estimators previously presented in the literature. The numerical effort to compute the new estimators is greater than with previously published formulas because the new method requires solution of an implicit algebraic equation, for which we provide an iteration strategy of fast convergence. In our opinion, the extra effort is warranted in view of the usual scarcity of data and in view of the extra precision that the new method brings.