## 1 Introduction  
Macroseismic intensity (MSI) is a local measure of the degree of earthquake damage and ground motion shaking in an earthquake, as evidenced by observed damages and human responses. MSI is crucial for seismic hazard, seismic design, and seismic loss, and has been widely used in the seismological, engineering, and loss-modeling communities [1; 2; 3; 4; 5]. MSI can also provide guidelines on seismic retrofitting of existing structures after strong ground motion shaking, in order to reduce the seismic risk of the structures in future earthquakes. There are many different MSI scales, and the most used ones are the modified Mercalli intensity (MMI) scale, European macroseismic scale (EMS), Japan Meteorological Agency (JMA) intensity scale, and Chinese macroseismic intensity scale (CMSIS) [1; 2; 3; 4; 5; 6; 7]. Similar to the MMI scale, CMSIS has twelve levels ranging from I to XII, but the referred values of peak ground acceleration (PGA) and peak ground velocity (PGV) are quite different from those values adopted in MMI scale [6; 7]. One main reason for this difference is that MSI has strong regional dependence and a source mechanism of seismic fault, velocity structures of crust and soil layers, and local site conditions in different regions, resulting in different ground motion prediction equations for both MSI and peak ground motion parameters. Thus, regional regression models for MSIs are generated in different countries and regions, e.g., California, eastern North America, Italy, Greece, and Japan. Another main reason is that the investigated MSIs are primarily based on the assessments of structural damage, which have large dispersion and randomness due to the subjective judgements by the investigating seismologists and structural experts. Thus, the MSI given by objective ground motions is another option, and regression models between MSI and ground motion parameters have recently been generated in different regions. These instrumental seismic intensities from regression models can provide rapid seismic intensity reporting after a destructive earthquake, as long as the ground motion records are available from seismic and strong ground motion instruments. The ShakeMap system in California and Italy, as well as the JMA's seismic intensity rapid reporting system in Japan, are all based on instrumental seismic intensities. Among engineering ground motion parameters, PGA and PGV are widely used to establish a relationship with the MSI. Since PGA is fundamental in seismic ground motion parameter zonation and seismic design of structures, the relationship between PGA and the MSI primarily has been analyzed and established [1; 2; 3; 7; 8; 9; 10; 11; 12; 13; 14]. PGV is more indicative of earthquake damage in more flexible structures, and linear regression models are generated based on PGV [1; 2; 3; 7; 8; 9; 10; 11; 12; 13; 14]. [PERSON] et al. [3] found that the MMI values from the relationship with PGV were better than the value based on PGA if the actual seismic intensity were no less than VII. [PERSON] et al. [16] stated that whether MMI was more related to PGA or PGV depended on the structural stiffness. [PERSON] and [PERSON] [13] concluded that MMI had better linear correlation with PGA for brittle structure and PGV for ductile structure. Besides PGA and PGV, other ground motion parameters are also used to establish the relationships. Since the structural response is derived from acceleration response spectrum, acceleration spectrum intensity was used by [PERSON] and [PERSON] [17] and [PERSON] and [PERSON] [11], and they both found that acceleration spectrum intensity had a higher correlation coefficient than PGA and PGV. Velocity spectrum intensity was also used for establishing relationships [18; 19]. [PERSON] and [PERSON] [20] derived equivalent peak acceleration from band passed three component accelerations and obtained a new relationship between JMA intensity scale and the derived acceleration. This relationship has been implemented in the JMA seismic intensity rapid reporting system.