Table 2 Derived regional fitting relationships between the Ms, Mb, MD, ML magnitudes and the Mw magnitude scale.

From: An updated and unified earthquake catalog from 1787 to 2018 for seismic hazard assessment studies in Mexico

Regression model

No. of events

Application Range

Eq.

\({M}_{W}^{\ast }=\left(5.58\pm 0.29\right)-\left(0.68\pm 0.10\right){M}_{S}+\left(0.13\pm 0.01\right){M}_{S}^{2}\)

458

4.0 ≤ Ms ≤ 7.9

(1)

\({M}_{W}^{\ast }=\left(-1.36\pm 0.13\right)+\left(1.35\pm 0.15\right){M}_{b}\)

712

4.0 ≤ Mb ≤ 7.1

(2)

\({M}_{W}^{\ast }=\left(-0.31\pm 0.26\right)-\left(1.06\pm 0.21\right)\left({M}_{D}\,or\,{M}_{L}\right)\)

57

4.0 ≤ MD/ML ≤ 6.6

(3)