Empirical ground-motion relations using moderate earthquakes recorded by Medellín–Aburrá Valley (Colombia) strong-motion networks

Abstract

We tested attenuation relations obtained for different regions of the world to verify their suitability to predict strong-motion data recorded by Medellin and Aburra Valley Accelerographic Networks. We used as comparison criteria, the average of the difference between the observed and the predicted data as a function of epicenter distance and its standard deviation. We also used the approach developed by Sherbaum et al. (Bull Seism Soc Am 94:2164–2185, 2004) that provides a method to evaluate the overall goodness-of-fit of ground-motion prediction equations. The predictive models selected use a generic focal depth. We found that this parameter has an important influence in the ground-motion predictions and must be taken into account as an independent variable. We also found important to characterize the local soil amplification to improve the attenuation relations. We found empirical relations for peak horizontal acceleration PGA and velocity PGV based on the Kamiyama and Yanagisawa (Soils Found 26:16–32, 1986) approach. $$\begin{aligned} \log _{10} (PGA)=0.5886M_L -1.0902\log _{10}(R)-0.0035H+C_{st}\pm 0.\text{29} \end{aligned}$$ $$\begin{aligned} \log _{10} (PGV)=0.7255M_L -1.8812\log _{10}(R)-0.0016H+C_{st}\pm 0.36 \end{aligned}$$ where PGA is measured in cm/s\(^{2}\) and PGV in cm/s, \(M_{L}\) is local magnitude in the range 2.8–6.5, \(R\) is epicentral distance up to 290 km, \(H\) is focal depth in km and \(C_{st}\) is a coefficient that accounts for the site response due to soil conditions of each recording station. The introduction of focal depth and local site conditions as independent variables, minimize the residuals and the dispersion of the predicted data. We conclude that \(H\) and \(C_{st}\) are sensitive parameters, having a strong influence on the strong-motion predictions. Using the same functional form, we also propose an empirical relation for the root mean square acceleration a\(_\mathrm{rms}\): $$\begin{aligned} \log _{10} \left( {a_{rms} } \right)=0.4797M_L -1.1665\log _{10} (R)-0.00201H+C_{st}\pm 0.40 \end{aligned}$$ where a\(_\mathrm{rms}\) is measured in cm/s\(^{2}\), from the S-wave arrival and using a window length equal to the rupture duration. The other variables are the same as those for PGA and PGV. The site correction coefficients \(C_{st}\) found for PGA, PGV and a\(_\mathrm{rms}\) show a similar trend indicating a good correlation with the soil conditions of the recording sites.