# Expanding Moment Magnitude Pools for Earthquake Magnitude Homogenization
## 1 Introduction  
Studies on earthquake risk and recurrence generally derive components from an earthquake catalog. These catalogs are collections of earthquake events containing at a minimum information regarding earthquake occurrence, hypocenter, magnitude, and magnitude type. One of the drawbacks to such a catalog is the diversity of magnitude types recorded, making it very difficult to make comparisons and to derive consistent parameters from the catalog. Seismologists and earthquake engineers generally develop and apply magnitude homogenization relationships to the catalog so that the magnitude data is unified under one specific magnitude type [1; 2; 3; 4].  
A typical magnitude type that modern earthquake risk and recurrence studies utilize is the moment magnitude, \(M_{W}\)[5]. Generally, regressions are made between \(M_{W}\) from a reliable agency against the remaining magnitude types in the target earthquake catalog, usually surface wave magnitude, \(M_{S}\), body wave magnitude, \(m_{b}\), local magnitude \(M_{L}\), and on occasion to \(M_{W}\) from other agencies. The representative \(M_{W}\) from these magnitude homogenization regressions are typically called proxy magnitude, \(M_{W,proxy}\). However, most resultant earthquake catalogs do not explicitly indicate which magnitudes are \(M_{W,proxy}\).  
Catalogs containing many earthquakes with reliably recorded \(M_{W}\)s make magnitude homogenization easier, as the pool of available events for homogenization is wider. However, many catalogs do not have many low \(M_{W}\) events as well as regional seismicity limitations. Additionally, a better understanding of \(M_{W}\) can help in the seismic risk assessment of regional infrastructure [6]. Some studies have tried to expand the pool of \(M_{W}\)for regression through the identification of similar or reliable sources [3; 4; 7] while others suggest the regression results from magnitude homogenization help indicate magnitude type similarity [2; 3; 4; 8], although similarity and reliability were variably defined.  
This study attempts to compare three approaches in extending the earthquake catalog M\({}_{\rm W}\) pool and its effects on magnitude homogenization. One of these three approaches can be considered the control, where the M\({}_{\rm W}\) pool is from a single reliable seismological agency. Another approach is to pool together M\({}_{\rm W}\) records from agencies associated with the control agency in addition to other relatively reliable sources. The third approach is to develop the M\({}_{\rm W}\) pool by utilizing statistical hypothesis testing to determine which agencies' magnitudes are significantly similar to those from control agencies or other related agencies. These three approaches are to be applied to earthquake catalogs of a seismically active region, Indonesia, and a relatively less active region, South Korea. The scope is limited to earthquake records from major global seismological agencies and a local agency to each region. By comparing different regions and focusing on certain sources, the results can help reveal what additional impacts the three approaches have on magnitude homogenization.