General orthogonal regression (GOR) is a superior regression procedure for conversion of different magnitude types into preferred ones. It yields a linear relation between dependent () and independent variable () based on observed data (, ). Recent investigations have shown that the conventional GOR procedure for obtaining by substituting in the GOR relation is incorrect, because the error in introduces some bias in . One way to reduce this bias in the estimate is to use (instead of ) given by a standard linear regression (SLR) relation between and .
However, this approach does not have ease of application and does not permit statistical verification. Therefore, we propose a modified procedure in which the derived GOR relationship is used to develop a SLR relation directly between and to estimate for a given , thereby eliminating the need to estimate and substitute .
We verify the supremacy of the proposed GOR procedure over the conventional procedure ( replaced by ) and the SLR procedure by using observed and synthetic datasets. We observe that the proposed GOR procedure provides an improved estimate of compared with both the conventional GOR and SLR. The proposed GOR provides lower errors in slope and intercept compared with SLR and yields improved correlation coefficient () and standard error values as compared with the other two approaches. The newly developed GOR procedure with provides the highest accuracy in estimates as compared with the SLR and conventional GOR approaches. Our analysis also concludes that incorrect application of regression procedure can introduce a bias in the Gutenberg–Richter parameter in the 5%–42% range. Therefore, we recommend the use of the proposed GOR to develop regression relations for earthquake magnitude conversions.