## 3 Seismic Response Spectra in Mexico
### Site-Specific Spectrum According to MDOC Sismo CFE 2015  
According to Table 3, the structures of importance A1 and A+ are related to buildings intended for the power generation industry, whose failure due to seismic events could have major negative consequences. Therefore, the spectral acceleration values require an accurate result, obtained by applying the site-specific spectrum procedure. The steps are extensive compared with the regional spectrum procedure and need different support tools, including specialized software and numerical methods. The steps for the site-specific spectrum procedure are given below. Step 1: Obtain the reference spectrum ER or EPR in the rock layer and perform at least five synthetic accelerograms adjusted to the target spectrum. PRODISIS requires the geographic coordinates to locate the site and obtain the reference spectrum ER or the return period reference spectrum EPR in the rock layer. Figure 3 presents the ER spectrum related to the city of Puebla, showing an optimal return period of \(T_{r}=408\) years and its spectral acceleration graph in blue. Additionally, the EPR spectrum is shown for a provided return period of \(T_{r}=975\) years with a spectral acceleration graph in green. Moreover, PRODISIS has a specific section related to synthetic accelerogram calculations, where simulations are performed by applying an assigned target spectrum, either the reference spectrum ER or the return period reference spectrum EPR, with the values previously obtained. The software performs a numerical process to obtain different accelerogram simulations, compatible with the seismic spectrum input used [4]. At least five synthetic accelerogram simulations should be performed, including a compatibility check, by performing a comparison between the response spectrum of each simulation and the target spectrum used, showing a match between the results. Figure 6 gives examples of 10 synthetic accelerograms using the reference spectrum ER related to the city of Puebla, as shown previously in Figure 3.  
There are other programs such as SeismoArtif, developed by Seismosoft Earthquake Engineering Software Solutions [5], that can be used to perform simulations of synthetic accelerograms using any target spectrum as initial input, substituting for the process performed by PRODISISIS. Any number of synthetic accelerogram results can be used; the only restriction is the need to perform a compatibility check by matching the values between the response spectrum of each simulation with the target spectrum. For each of the synthetic accelerograms in Figure 6, the response spectra are obtained and compared with the reference spectrum ER to ensure the compatibility check. This comparison can be performed within PRODISIS or SeismoArtif, providing graph results as shown in Figure 7, where the thin black lines represent the response spectrum of each synthetic accelerogram, the blue line represents the mean average of the response spectra, and the red line represents the target spectrum used. The simulation process requires the Fourier transform and wavelets methods [4; 5]. Step 2: Use the soil layers data from the site to perform the transfer function and obtain the dynamic amplification of the ground. To perform a dynamic analysis of the soil, data on the physical properties of each layer \(i\) in the site are required, focused on the thickness \(h_{i}\), the volumetric weight \(\rho_{i}\), the shear wave velocity \(v_{si}\), the damping ratio \(\xi_{i}\), and the total depth \(H_{s}\). The goal is to obtain the dynamic amplification of the seismic waves at the site from the rock layer to the surface layer, according to the different frequencies. Figure 8 shows the seismic wave path from the fault to the site of interest, where the surface layer tends to amplify the seismic wave amplitudes [6]. Figure 6: Synthetic accelerograms based on the reference spectrum ER in Puebla, Mexico. Figure 7: Response and reference spectra comparison for the city of Puebla, Mexico.