## 2 Materials and Methods  
Several earthquake catalogs will be required to develop appropriate magnitude homogenization relationships for the South Korean region. Specific catalogs used in this study include:  
1. International Seismological Centre (ISC), Reviewed ISC Bulletin. This is a global catalog of seismic events recorded from all over the world starting from 1900. The ISC bulletin is updated periodically [25; 26]. Many international seismological agencies submit data to the ISC. These agencies include the United States Geologic Survey National Earthquake Information Center (NEIC) as well as the Commission for the Comprehensive Nuclear-Test-Ban Treaty Organization International Data Center (IDC). The NEIC was formerly known as the National Earthquake Information Service (NEIS), while the IDC was formerly known as the Experimental International Data Center (EIDC). 2. Global Centroid Moment Tensor catalog (GCMT). This is an earthquake moment tensor catalog for global earthquakes [27]. Data starts from 1976. 3. ISC-GEM Global Instrumental Earthquake Catalog. This catalog focuses primarily on large earthquakes in the ISC Bulletin, where the data is more reliable, to improve, extract, and constrain certain earthquake parameters [19; 28; 29; 30]. When available, ISC-GEM uses M\({}_{\text{W}}\) stated by GCMT. Data starts from 1904. 4. Korea Meteorological Administration (KMA). This is a local catalog of seismic events local to the Korean peninsula [31]. Most of the data is recorded as M\({}_{\text{L}}\) due to historical reasons [21]. Data starts from 1978. This online database is in Korean. A search is made within these catalogs to compile a set of earthquakes relevant to the South Korean region. Events from the beginning of 1900 until the end of 2020 were considered. The search region was restricted to within 200 km of the mainland border and the islands of South Korea within 31\({}^{\circ}\) to 41\({}^{\circ}\) N and 122\({}^{\circ}\) to 134\({}^{\circ}\) E. Depth was limited to 40 km as any earthquake deeper could be below the crust and from the mantle. Earthquakes originating in the mantle have different wave propagation behavior and mechanisms than those within the crust, concerns typically not accounted for in seismic hazard analyses. Additionally, when the option was available, a minimum magnitude of 2.5 was selected as it is assumed earthquakes with magnitudes at 2.5 or less would not influence magnitude homogenization model development. It is rare to see an earthquake catalog with listed events at M\({}_{\text{W}}\) below three. Moreover, there will be no distinction between a main shock and foreshocks or aftershocks. Using the compiled earthquake catalog, earthquakes with a listed M\({}_{\text{W}}\) in addition to other magnitude types will be plotted. Data of the same magnitude type from related seismological agencies will be grouped into one representative agency. For example, M\({}_{\text{S}}\) from NEIC will include M\({}_{\text{S}}\) data from NEIC as well as NEIS, and m\({}_{\text{b}}\) data from IDC will include m\({}_{\text{b}}\) data from both IDC and EIDC. Continuing with the previous examples, this suggests a few agencies will have listed events with an M\({}_{\text{W}}\), such as ISC-GEM and GCMT. Data from GCMT is used as the base reference [19; 20] and therefore this study will treat M\({}_{\text{W,GCMT}}\) as the base M\({}_{\text{W}}\). Additionally,although not an international seismological agency, NIED is considered to have accurate constraints of the moment tensors for earthquakes in Japan and the surrounding regions [19; 20]. Therefore, earthquakes listed with a M\({}_{\rm W}\) from NIED will be included in a base list. This base list will contain M\({}_{\rm W}\) data as the dependent variable in regression, with M\({}_{\rm W,GCMT}\) having first priority, M\({}_{\rm W,ISC-GEM}\) having second priority, and M\({}_{\rm W,NIED}\) having third priority.