Regional relations converting the surface and body wave magnitudes to moment magnitude for Northern Algeria using the general orthogonal regression method

The existence of several magnitude scales in the compiled earthquake catalogs of a specific region has made the development of regional relations connecting magnitude scales a necessity, especially for creating a homogeneous seismic catalog in which all magnitudes should be converted to a preferred magnitude scale. To consistently estimate all magnitude ranges and avoid the saturation problem for large earthquakes, the preference is always given to the moment magnitude M-w scale, wherein the most complete and reliable catalog used worldwide is the Global Centroid Moment Tensor (GCMT). However, to our knowledge, no study has yielded regional (in Algeria) relationships for converting different magnitudes to the moment magnitude (M-w,(GCMT)). The main reason is typically due to the lack of data pairs of different magnitude scales with M-w (GCMT). To overcome this issue, in this research paper, the moment magnitudes data used for northern Algeria (the area bounded by 32 degrees to 39 degrees N and 3 degrees W to 10 degrees E) have been taken principally from the GCMT catalog and enhanced with the European-Mediterranean Regional Centroid Moment Tensor catalogs RCMT and ZUR-CMT. Regarding this latter, it has been demonstrated in the literature that for the Mediterranean regions, a minor correction should be addressed before merging its data with the GCMT and RCMT catalogs, which are perfectly correlated. To accomplish this task, the magnitude scales tested against M-w are the surface wave magnitude, M-S,M- and the body wave magnitude m(b) issued from the international seismological sources of ISC and NEIC for the same boundaries. As long as the earthquake magnitudes, in general, are affected by errors of comparable size, the best and most reliable regression method that considers the errors in both dependent and independent variables for linear conversion problems is the General Orthogonal Regression, which is adopted and applied herein to develop the regional relations.