Estimating the Completeness Magnitude mc and the b‐Values in a Snap. Issue 2 (15th February 2023) - Godano, C.; Petrillo, G.
Abstract: A good estimation of the b ‐value is crucial for the earthquake hazard assessment. Its evaluation can be strongly affected by an incorrect estimation of the completeness magnitude m c because a too small m c will reflect into a small b ‐value, whereas a too large m c will imply a larger standard deviation due to the reduction of the magnitude interval. Several methods for the estimation of m c exist, however its evaluation is very delicate and requires some critical decision making in most cases. Here we present a new, very rapid and simple method for m c estimation. It is based on the observation that the Gutenberg‐Richter distribution is an exponential one only for magnitudes larger than m c . As a consequence, the average magnitude m a value should increase linearly with a threshold magnitude m th . The departures from such linear behavior, allows a correct estimation of m c, whereas the linearity of the of m a versus m th allows a correct estimation of the b ‐value. Plain Language Summary: A very simple and rapid method for the estimation of the completeness magnitude and of the b ‐value is here introduced. The method is based on the evaluation of the average magnitude as a function of a threshold one. The method does not require any decision and can be easily implemented in automatic procedures. Key Points: The b and m c parameters are rapidly estimated The two parameters are estimated independently