Performance of Different Regression Procedures on the Magnitude Conversion Problem

Through an extensive set of simulations we investigate the performance different linear regression procedures commonly used to convert magnitudes from type into another one, an operation that also has strong influence on the slope the frequency-magnitude (the b-value of the Gutenberg–Richter) distribution. It already been demonstrated that a general orthogonal regression provides the most results. However, questions arise when the ratio between the variances of magnitudes to be related (the knowledge of which is required to apply the general regression) cannot be computed. therefore systematically investigate the biases introduced by the classical standard -squares regressions and the orthogonal regressions (or similar procedures) a function of the true slope between magnitudes, of the ratio g between magnitude , and of the absolute variances of magnitudes. We compute such biases simulations very close to the real cases inferred from the German and Chinese networks. observe that for 0.7 gtrue 1.8 the orthogonal regression under the g 1 performs better than standard regressions. For values outside this interval procedure is capable of correct estimates. Therefore it is recommended to the absolute errors and their ratio from empirical data and apply the general regression. This requires that a seismological data center publish average of event magnitudes and also their related standard deviations. Regrettably, is not yet a common practice, thus impeding the derivation of optimal magnitude relations.