Seismic microzoning in Novi Sad, Serbia – A case study in a low-seismicity region that is exposed to large and distant earthquakes

Abstract

We use a method based on Uniform Hazard Spectrum (UHS) to compile seismic microzonation maps for the broader area of Novi Sad, a city in Serbia. The maps are intended for use in the performance-based design (PBD) of earthquake-resistant structures. At present, PBD requires the use of two sets of spectral amplitudes, one in which the structure remains linear and the other in which it may respond nonlinearly. These PBD requirements cannot be met by using only one (same) fixed-shape spectrum and scaling by peak ground acceleration alone for varying probabilities of exceedance. The alternative we present in this paper is based on UHS and describes a combined contribution from (a) seismic excitation by local earthquakes, for which region-specific attenuation equations are used, and (b) seismic excitation by large, distant earthquakes, for which different attenuation equations are used. Our maps also take into account the influences of site geology and site soil conditions in a balanced manner.

Appendix A PSV(T) scaling equations for the former Yugoslavia

The empirical scaling equation for pseudo relative velocity (PSV) spectra in the former Yugoslavia (Lee 1995, 2002) is:

$$\begin{gathered} \log_{10} \left( {PSV(T)} \right) = M + Att\left( {\Delta ,M,T} \right) \hfill \\ + \left[ {\hat{b}_{1} (T)M + \hat{b}_{2}^{(1)} (T)S^{(1)} + \hat{b}_{2}^{(2)} (T)S^{(2)} + \hat{b}_{3} (T)v + \hat{b}_{4} (T) + \hat{b}_{5}^{(1)} (T)S_{L}^{(1)} + \hat{b}_{6} (T)M^{2} } \right] \hfill \\ \end{gathered}$$

(3)

Here T is the vibration period, M is the earthquake magnitude, $Att\left( {\Delta ,M,T} \right)$ is the Yugoslav-specific frequency-dependent attenuation function, $S^{(1)}$ = 1 if geological parameter s = 1 and 0 otherwise, and $S^{(2)}$ = 1 if s = 2 and 0 otherwise.$S_{L}^{(1)}$ is the soil conditions variable, with $S_{L}^{(1)}$ = 1 if $S_{L}$ = 1, and $v$ = 0 and $v$ = 1 for prediction of the horizontal and vertical ground motion, respectively.

$Att\left( {\Delta ,M,T} \right)$ is the Yugoslav frequency-dependent attenuation function,

$$Att\left( {\Delta ,M,T} \right) = \left\{ {\begin{array}{*{20}l} {A_{0} (T)\log_{10} \left( \Delta \right)} \hfill & {R \le R_{0} } \hfill \\ {A_{0} (T)\log_{10} \left( {\Delta_{0} } \right) - \frac{{\left( {R - R_{0} } \right)}}{200}} \hfill & {R > R_{0} } \hfill \\ \end{array} } \right.,$$

(4)

with $\Delta$ the representative source-to-site distance, defined as

$$\Delta = S\left( {\ln \frac{{R^{2} + H^{2} + S^{2} }}{{R^{2} + H^{2} + S_{0}^{2} }}} \right)^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}}$$

(5)

with

$$\Delta_{0} = S\left( {\ln \frac{{R_{0}^{2} + H^{2} + S^{2} }}{{R_{0}^{2} + H^{2} + S_{0}^{2} }}} \right)^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} ,$$

(6)

and $S_{0}$ is the source coherence radius. The term $A_{0} (T)\log_{10} \left( \Delta \right)$ refers to the frequency-dependent function used to estimate the attenuation at distances up to transitional distance $R_{0}$ (when $\Delta = \Delta_{0}$). Based on our experience with California data, the attenuation for distance $R > R_{0}$ is set as a linear function of R with a 1/200 slope (Lee and Trifunac 1995). The role of $R_{0}$ is further discussed in Lee and Trifunac (1993).

When plotted against M, PSV(T) can be depicted by a parabola for given values of the geology parameter s, representative source-to-site distance $\Delta , \,$ magnitude M, and local soil condition $S_{L}$. The parabola reaches its maximum at $M = M_{\max } (T)$, with the $M^{2}$ coefficient $b_{6} (T) < 0$, where:

$$M_{\max } (T) = - (1 + b_{1} (T))/2b_{6} (T).$$

(7)

The regression Eq. (3) is considered to apply only in the range $M_{\min } \le M \le M_{\max }$, where

$$M_{\min } (T) = - b_{1} (T)/2b_{6} (T)$$

(8)

is the value at which the parabola has a unit slope. The regression equation can then be written as

$$\log_{10} \left( {PSV(T)} \right) = M_{ < } + A_{0} (T)\log_{10} (\Delta ) + \left[ {\hat{b}_{1} (T)M_{ < > } + \hat{b}_{2}^{(1)} (T)S^{(1)} + \hat{b}_{2}^{(2)} (T)S^{(2)} + \hat{b}_{3} (T)v + \hat{b}_{4} (T) + \hat{b}_{5}^{(1)} (T)S_{L}^{(1)} + \hat{b}_{6} (T)M_{ < > }^{2} } \right]$$

(9)

with $M_{ < } = M_{ < } (T) = \min \left( {M,M_{\max } (T)} \right)$ and $M_{ < > } = M_{ < > } (T) = \max \left( {M_{ < } (T),M_{\min } (T)} \right)$.

For example, in complex or intermediate geological site conditions $s = 1 \, \left( {S^{(1)} = 1, \, S^{(2)} = 0} \right)$ and “rock” local soil $S_{L}$ = 0 $\left( {S_{L}^{(1)} = S_{L}^{(2)} = 0} \right)$, the scaling equation will become:

$$\log_{10} \left( {PSV(T)} \right) = M_{ < } + A_{0} (T)\log_{10} (\Delta ) + \left[ {\hat{b}_{1} (T)M_{ < > } + \hat{b}_{2}^{(1)} (T) + \hat{b}_{3} (T)v + \hat{b}_{4} (T) + \hat{b}_{6} (T)M_{ < > }^{2} } \right],$$

(10)

using the term $\hat{b}_{2}^{(1)} (T)$ corresponding to $s = 1 \, \left( {S^{(1)} = 1, \, S^{(2)} = 0} \right)$ and deleting the term $\hat{b}_{5}^{(1)} (T)$ corresponding to $S_{L}$ = 1 $\left( {S_{L}^{(1)} = 1} \right., \, \left. {S_{L}^{(2)} = 0} \right)$.

For basement rock sites $s = 2 \, \left( {S^{(1)} = 0, \, S^{(2)} = 1} \right)$ and “rock” local soil $S_{L}$ = 0 $\left( {S_{L}^{(1)} = S_{L}^{(2)} = 0} \right)$, the scaling equation can be written as

$$\log_{10} \left( {PSV(T)} \right) = M_{ < } + A_{0} (T)\log_{10} (\Delta ) + \left[ {\hat{b}_{1} (T)M_{ < > } + \hat{b}_{2}^{(2)} (T) + \hat{b}_{3} (T)v + \hat{b}_{4} (T) + \hat{b}_{6} (T)M_{ < > }^{2} } \right],$$

(11)

using the term $\hat{b}_{2}^{(2)} (T)$ corresponding to $s = 2\left( {S^{(1)} = 0, \, S^{(2)} = 1} \right)$.

The numerical values of the coefficients $\hat{b}_{1} (T)$, $\hat{b}_{2}^{(1)} (T)$, $\hat{b}_{2}^{(2)} (T)$, $\hat{b}_{3} (T)$, $\hat{b}_{4} (T)$, $\hat{b}_{5} (T)$, and $\hat{b}_{6}^{(1)} (T)$ employed in Eqs. (3) through (4) can be found in Lee (1995, 2002). To prevent distortions in the estimated amplitudes that would have been caused by the low signal-to-noise ratio in the strong motion records, the regression of Yugoslav PSV amplitudes was limited to periods shorter than $T = 2 \,$ sec.

The numerical values of the coefficient function $\hat{b}_{3} (T)$ that should be used to convert the horizontal UHS of PSV amplitudes (for $\zeta = 0.05$) to the corresponding vertical amplitudes are given in Table 1 at 12 periods between 0.04 s to 2.0 s.

Table 1 Scaling Coefficient Function $\hat{b}_{3} (T)$ versus Period $T$, for $\zeta = 0.05$ in the PSV Regression Model for the Former Yugoslavia (Lee 1995)