# Site-Specific Spectra for the City of Mexicali, Mexico, Obtained from April 2010 Earthquake Records
## 2 Determination of the Site-Specific Spectra
### Site Effect  
Frequently, site effects have an important influence on the damage distribution during large earthquakes. Subsoil impedance contrasts can substantially amplify the shaking level and increase the duration of strong ground motion. As the city is over-sedimentary and has very homogenous soil, we explore a hypothetical response of the entire valley. One way to estimate the site effect of an area is by modeling the seismic response of soil deposits. Using their stratigraphic characteristics and the mechanical and dynamic properties of the materials that compose them, we can estimate the transfer function that represents the medium's response to an earthquake. Ground motion modeling can be obtained through a theoretical propagation of a green function through this layered media. The physical characterization of the soil is obtained from soil mechanics studies. Data from a geotechnical study conducted in the city of Mexicali were used. The propagation velocities of the shear waves (\(V_{s}\)) of the different strata were estimated using expressions that allow us to determine \(V_{s}\) using only the number of hits obtained from standard soil penetration tests. Two of them [27,28] were compared for this study (Figure 5). \[V_{s}=80.6\times N^{0.331} \tag{1}\]  
\[V_{s}=88.4\times N^{0.333} \tag{2}\]  
where \(N\) is the number of hits in the standard penetration test. Velocities obtained from both expressions give similar results, so our velocity profile was the average of both. A 6-layer model with variable thicknesses and shear wave velocities ranging from 90 to 180 m/s and a semi-space assigned a shear wave velocity (V\({}_{s}\)) of 400 m/s. Low-velocity layers can be seen from about seven to twenty meters. We recognize that a single geotechnical survey conducted at one site is insufficient to represent a geographic region, but given the very homogeneous physical characteristics of the soil in the Mexicali Valley, we consider the sampled site to be a reasonable sample of regional soils. Figure 4: Attenuation of peak acceleration with distance at seismic stations used for both rock and sediment stations. Dashed lines are plotted only to reflect the decay tendency of each group of stations. The average shear wave velocity, as well as the dominant period of the site, were estimated using the following expressions:  
\[V_{s}=\frac{\sum_{i=1}^{n}\text{h}_{i}}{\sum_{i=1}^{n}\left(\frac{\text{h}_{i}}{ \text{V}_{\text{s}_{i}}}\right)} \tag{3}\]  
\[\text{T}_{\text{S}}=\frac{4\text{h}}{\text{V}_{\text{s}}} \tag{4}\]  
where \(\text{h}_{i}\) and \(\text{V}_{\text{s}_{i}}\) are the thickness and shear wave velocity at each layer of the stratigraphic profile. The estimated average velocity up to 30 m depth was 155.84 m/s (\(\text{V}_{\text{S}30}\)). According to the NERPH code, this value would correspond to a type E soil (intermediate to soft consistency). The estimated site period was \(\text{T}_{\text{s}}=0.77\) s, typical of soils with an intermediate to soft consistency. In addition to this result, three measurements of ambient seismic noise were made at the same site where the geotechnical study was carried out. Spectral ratios of horizontal components relative to the vertical recorded simultaneously were calculated to obtain the dominant period or natural frequency of vibration of the site using the [PERSON], 1989, technique [29]. We obtained three ambient vibration records with durations of three minutes each. In every record, we selected a window that showed the fewest transient signals, and the noise appeared more stationary. We calculate the spectral relationship between horizontal and vertical movement from the selected window. These relationships produced HVSR graphs where a peak could be identified from which a dominant period value was determined (Figure 6). Impedance contrasts between soft the soil layer and its basement can significantly amplify the shaking level and increase the duration of strong ground motion.