# Advanced Unified Earthquake Catalog for North East India
## 1 Introduction  
Earthquakes are inherently complex phenomena, and because of differences in equipment characteristics and station coverage used to record seismic waves at different epicentral distances, most magnitude estimations in space and time are subject to measurement errors. Several earthquake magnitude scales have been used in seismic catalogs to represent the earthquake size, such as M\({}_{\rm L}\) (Local Magnitude), m\({}_{\rm b}\) (Body Wave Magnitude), M\({}_{\rm s}\) (Surface Wave Magnitude), and M\({}_{\rm w}\) (Moment Magnitude). Recent studies (e.g., [1; 2; 3; 4; 5]) show that the M\({}_{\rm w}\) scale has some serious drawbacks in representing earthquake size. Many authors stated that the M\({}_{\rm w}\) scale is not suitable for frequencies applicable for engineering importance (e.g., [6; 3; 7]). The M\({}_{\rm w}\) scale underestimates large earthquakes such as the 11 March 2011--Tohoku-Oki earthquake and the 26 December 2004--Sumatra earthquakes (e.g., [1; 3; 4; 5]) and overestimates the smaller earthquakes (e.g., [1]). Although the M\({}_{\rm w}\) scale is expressed in terms of the moment (Mo), however, it is mainly based on surface waves; therefore, it is not a good representation of the seismic source. As the philosophy of the M\({}_{\rm w}\) scale [8] is based on surface waves and, therefore, it is inappropriate for deeper earthquakes. Furthermore, the M\({}_{\rm w}\) scale is mainly derived and validated based on Southern California tectonics [8]. The M\({}_{\rm w}\) scale given by Ref. [8] is valid for global earthquakes in the magnitude range \(>\)7.5 because the M\({}_{\rm w}\) scale is based on bigger magnitude earthquakes at the global level. As the seismic moment is mainly derived from surface waves (e.g., [9]),the formulation of the M\({}_{\rm w}\) scale ( i.e., '2/3' and '10.7') also originated from surface wave magnitude. Thus, the M\({}_{\rm w}\) scale relates to long-period seismic spectra. Furthermore, the M\({}_{\rm w}\) scale was developed based on constant value for tectonic effect for shallow earthquakes. There was no statistical validation while developing the M\({}_{\rm w}\) scale, only a comparison of the M\({}_{\rm w}\) scale with some Southern Californian earthquakes [8]. Ref. [1] provide a magnitude scale mainly considering global tectonics. As the M\({}_{\rm wg}\) scale is developed by considering p-wave along with consideration of seismic moment M\({}_{0}\), and M\({}_{0}\) is computed from the surface wave trend of the seismic signal ([9; 10]). Thus, the M\({}_{\rm wg}\) scale covers both high and low-frequency spectra of the seismic signal. The M\({}_{\rm wg}\) scale is preferable to the M\({}_{\rm w}\) scale mainly for the following reasons: (1) the M\({}_{\rm w}\) scales underestimate the bigger earthquake and overestimate the smaller and intermediate earthquakes (e.g., [1; 5]); (2) the M\({}_{\rm wg}\) scale is based on directly observed M\({}_{0}\) whereas the M\({}_{\rm w}\) formulation in terms of M\({}_{0}\) was not derived based on observed M\({}_{0}\) but rather based on substitution assuming constant values; (3) In the case of M\({}_{\rm wg}\), the proper representation of global seismicity has been considered for minor, moderate, and large earthquakes, and on the other hand, M\({}_{\rm w}\) is based on the seismicity of Southern California, particularly for minor and intermediate occurrences; (4) M\({}_{\rm w}\) is not a good estimate for high-frequency ground motions, which are critical for estimating the potential shaking damage of earthquakes as M\({}_{\rm w}\) is defined from very long period spectral amplitudes. M\({}_{\rm wg}\), on the other hand, is calculated from low- and high-frequency seismic spectra and thus fills the gap left by M\({}_{\rm w}\). Uncertainties associated with distinct magnitude scales play a significant role during magnitude conversions into a single magnitude scale. Regression relationships are used to transform diverse magnitudes into seismic moment scales to construct a homogeneous earthquake database (M\({}_{\rm wg}\)).