Estimating the Magnitude of Completeness of Earthquake Catalogs Using a Simple Random Variable Transformation
Matteo Taroni
Abstract
Abstract The estimation of the magnitude of completeness for a seismic catalog is the starting point for most of the seismological statistical analyses. It is important, in particular, for the estimation of the Gutenberg–Richter (GR) law parameters. This law corresponds to an exponential distribution of the magnitudes. The recent studies have shown that the proper method to estimate the completeness is to check the exponentiality of the data. Here, we try to improve this method using a simple random variable transformation, which makes the method more robust in the case of catalogs with magnitudes coming from exponential distributions with different parameters, that is, catalogs with different b-values of the GR law.
Topics & Concepts
Completeness (order theory)Magnitude (astronomy)Transformation (genetics)Random variableMathematicsSimple (philosophy)Variable (mathematics)Exponential functionApplied mathematicsStatisticsExponential distributionStatistical physicsCalculus (dental)Mathematical analysisPhysicsDentistryBiochemistryGeneEpistemologyChemistryMedicineAstronomyPhilosophyearthquake and tectonic studiesEarthquake Detection and AnalysisSeismology and Earthquake Studies