# Site-Specific Spectra for the City of Mexicali, Mexico, Obtained from April 2010 Earthquake Records
## 2 Determination of the Site-Specific Spectra
### Response Spectra  
Response spectrum is a valuable tool to support, in some cases, the seismic design of structures (buildings, bridges, etc.). It represents the maximum response of a structure considered as a system of one degree of freedom to different periods of vibration due to the features of ground motion triggered by an earthquake. From a ground acceleration record, the displacement, velocity, or acceleration response of a system with one degree of freedom can be calculated for a defined damping value and for different values of natural vibration periods as a function of time. The response spectrum is calculated by taking the maximum response values considering the absolute maximums, of each analysis for different natural periods of vibration. The results are charted as a function of the periods of vibration. In recent years, significant efforts have been made to clearly describe the procedure for determining a design spectrum based on response spectra and other considerations. The design spectrum usually has a smoother shape than the response spectrum. One purpose of these efforts is that the structural engineer can properly use the response spectrum and the design spectrum to understand the probable behavior of the building that he is designing. Generally, design regulations [15; 16; 17; 18] propose a series of design spectra that are obtained by considering aspects of regional tectonics, seismology, seismic hazard, and, in a few cases, site-specific considerations. This last fact makes it necessary for the spectra proposed by the building regulations to be reviewed and compared with those obtained considering the aforementioned aspects in addition to the properties of the site of interest. This last procedure allows for the verification of whether site-specific data were considered for the determination of the design spectrum. To have criteria for making decisions associated with seismic actions in building design, it is advisable to have basic information about seismic hazard assessment. Particularly, to define the seismic actions, the design spectra are an essential tool that is frequently used  
Figure 8: The empirical transfer functions were obtained for stations close to the epicenter of the 4 April 2010 earthquake. in building regulations. If these design spectra are obtained from a number of response spectra related to a complete catalog of earthquakes, then the maximum response can be reasonably estimated for a specific site. However, there is not enough information in several regions of Mexico. Soil seismic response in MOC-CFE [18] can be determined using the software called PRODISIS v4.1 [35], where estimation of site effect is mainly tied to Ts and to shear-wave velocity. The stratigraphic profile can be replaced by a single layer with a velocity equal to the mean velocity of the actual profile. Non-linearity is considered by means of a factor called non-linearity factor, which depends, among other parameters, on Ts, mechanical impedance contrast, and a so-called distance factor. Using the signals obtained at the surface, i.e., already affected by the site effect given in Figure 6, the response spectra with 5% damping were obtained for the site and compared with the design spectrum proposed by MOC-CFE [18]. Figure 9 shows this comparison. The smoothed spectrum (orange) corresponds to that proposed by the regulation. It can be seen in Figure 9 that in all cases, there are pulses, and almost all of them are more significant than the design spectrum proposed by MOC-CFE [18]. The shape of these pulses can be attributed to a near-fault ground motion as suggested by some authors [36; 37], as the records used are from stations close to the epicenter, but multi-pulse or single pulse (the closest station, GEO, shows the greater amplitude in a single pulse at 0.05 s), amplitudes are greater than the MOC-CFE design spectra.