## 3 Results  
Two events recorded by the network were selected for this study. Their epicenters were off the coast of Michoacan in May 2007 (Figure 3). The small event (\(M=4.3\)) occurred on 27 June 2007, and the large earthquake (\(M=5.1\)) occurred on 31 May 2007. To calibrate the model, the large-magnitude earthquake was simulated using the small-magnitude event. Based on the focal mechanism of the large earthquake determined by Harvard CMT [29], and according to the epicenter localization, the second fault plane solution was considered (strike = 239\({}^{\circ}\) and dip = 86\({}^{\circ}\)). Please note that this source mechanism was not a thrust fault associated with the subduction but was a left-lateral displacement mechanism. From the observed ratios, the values \(CN^{3}=15.9\) and \(CN=2.3\) were obtained at low frequencies, which yields an approximate value of \(N^{3}=18\). Then, \(N_{x}=3\), \(N_{w}=3\), and \(N_{t}=2\) are obtained, and a constant stress ratio drops \(C=0.9\). Taking the adjusted value of the flat levels and correcting for parameters such as stress drop, momentum, and wave velocity of S, an estimated area of \(0.42\times 0.42\) km\({}^{2}\) was obtained for the M 4.3 earthquake. For the M 5.1 event, it was taken \(D_{x}=0.42\), \(D_{w}=0.42\), and \(N_{t}=2\) with \(V_{S}=3.5\) km/s for an area of \(N_{x}=3\), \(N_{w}=2\), which gives a dislocation area of \(1.26\times 1.26\) km\({}^{2}\). Based on the analysis of the acceleration and displacement amplitude spectra, the corner frequency was determined (Figure 4) and compared with the corner frequencies estimated by [30],  
\[u(f)=\frac{\Omega_{0}}{1+\left(\frac{f}{f_{c}}\right)^{2}} \tag{10}\]  
where \(u(f)\) is the displacement spectrum, \(\Omega_{0}\) is the spectral level at low frequencies, and \(f_{c}\) is the corner frequency. As can be seen in Figure 5, the resultant stress drop for this earthquake agreed with most of the Mexican coastal earthquakes that show the 100 bar stress drop, even when this event was not a thrust faulting earthquake [31]. Figure 4: Plots of the acceleration spectrum (**left side**) and displacement spectrum (**right side**). Black lines indicate the flat levels as well as the inclination of the \(\omega^{-2}\) model. The corner frequencies, \(fc\), and the stress drop, \(\Delta\sigma\), were estimated from the flat levels of the acceleration spectrum (at high frequencies) and displacement spectrum (at low frequencies). Starting from relations (2) and (3), the parameter \(N\) was estimated from the acceleration and displacement spectral ratios between large and small earthquakes (see Figure 6). Estimation of \(N\) and \(C\) is obtained by simultaneously solving Equations (7) and (8) with flat levels at low and high frequencies (see Figure 6). From the spectral ratio, a value \(CN^{3}=156\) was obtained for low frequencies and \(CN=4\) for high frequencies. In this case, an approximate value of \(N=6\) was given and the value for the different stress drops is \(C=0.72\). Given these values and the initial conditions for the large event, it was assumed that the fault had 6 \(\times\) 6 subfaults with an area of \(2.52\times 2.52\,\mathrm{km}^{2}\). With these values, the estimation and calculation of the other parameters, such as the rupture velocity, the rise time, and the initiation point of the fracture, are possible by variation of these parameters. Corner frequencies, as well as displacement and acceleration spectra, were graphically and theoretically estimated by considering the average value in the modeling. In order to simulate the acceleration recordings of the main shock, other parameters had to be varied, such as the rupture velocity, the rising time, and the rupture initiation point. The method shows a high sensitivity to the rupture velocity and its location in the fault plane. Figure 5: Plot of the relation between the corner frequencies with the seismic moment data for 7 events. The continuous and dotted lines are [PERSON]’s stress drop for 10, 100, and 1000 bars [30], respectively.