## 4 Seismic Response Spectra in the USA
### Site-Specific Spectrum According to ASCE/SEI 7-16  
For soils previously determined to be with site class E or F, it is required to obtain the seismic elastic design spectrum by taking into account the dynamic amplifications of the ground for specific sites. Additionally, a dynamic soil analysis must be performed when \(S_{S}\geq 1.0\) for site class E, \(S_{1}\geq 0.2\) for site classes D and E [2]. Similar to MDOC Sismo CFE 2015 code, we must follow a few steps to obtain the dynamic amplifications of the ground and apply them to a series of accelerograms in the rock layer to modify the spectral acceleration values. The process is shown below. Step 1: Obtain the spectrum using an \(MCE_{R}\) in the rock layer and simulate at least five synthetic accelerograms adjusted to the target spectrum, or select five representative accelerograms of real earthquakes. First, the geographic site location is required to obtain the spectral acceleration parameters, \(S_{S}\) and \(S_{1}\), to create the seismic elastic design spectrum for an \(MCE_{R}\), with the soil factors \(F_{a}\) and \(F_{v}\) in rock related to site class B, using the same process for the regional spectrum procedure previously described. A class A site can be used when the average shear wave velocity in the ground is \(\overline{v}_{s}\geq 1524\) m/s [2]. With the \(MCE_{R}\) spectrum in rock available, the graph will be used as a target spectrum and at least five synthetic accelerograms should be performed, similar to step 1 of the site-specific spectrum procedure of the MDOC Sismo CFE 2015 described in Section 3.4. SeismoArtif can be used to simulate the synthetic accelerogram, reviewing whether the response spectra of each simulation are compatible with the target spectrum [5]. Alternatively, at least five real recorded earthquakes can be selected to perform an appropriate scaling process to fit the target spectrum. The selection of the accelerograms must consider the conditions of the site, such as the magnitude, the geological fault type, and the distance between the seismic event and the site location. The Pacific Earthquake Engineering Research Center, or PEER, has a database of accelerogram records on its website, with the option to select real earthquakes using a target spectrum, either defined by the user, PEER, and/or ASCE recommendations [20]. Figure 17 shows an example of a response spectral acceleration graph with a logarithmic scale, taking as a target spectrum the location of El Centro, California, and the scaling results of the selected 10 real earthquakes, including a geometric mean spectrum with a damping ratio of 5%. According to the previous figure, the red line represents the target spectrum, the thick black line represents the geometric mean spectrum of the real earthquakes, and the thin gray lines represent the spectra of the 10 adjusted earthquakes. A good fit between the target spectrum and the mean values can be observed between 0.1 to 10 s.  
Step 2: Obtain the soil layer inputs and perform the transfer function to consider the dynamic site effects. The inputs related to the physical properties of the soil layers and the procedure to obtain the transfer function, \(F(\omega)\), are explained in step 2 previously presented in the site-specific spectrum of the MDOC Sismo CFE 2015 code in Section 3.4. Programs such as DeepSoil [7] or ProShake [8] can be used to create a 1D model of the soil layers to obtain the graph of the transfer function, \(F(\omega)\), by applying linear or non-linear analysis procedures. Step 3: Perform the amplification of the scaled synthetic and/or real accelerograms by applying the ground transfer function \(F(\omega)\). Once the graph of the soil transfer function, \(F(\omega)\), is available from step 2, the accelerograms obtained in step 1 must be scaled. The process is similar to step 3, previously presented in the site-specific spectrum of MDOC Sismo CFE 2015 in Section 3.4.