Site-specific probabilistic seismic hazard analysis for the western area of Naples, Italy

Abstract

Probabilistic seismic hazard analysis (PSHA) encompasses quantitative estimation of seismic hazard at a site by considering all plausible earthquake scenarios. The outcome of a PSHA is often reported as the mean rate of exceeding a specific ground motion intensity measure at a given site. This study attempts to perform PSHA for the western area of the city Naples (southern Italy) by employing the most advanced methods and new databases; namely, DISS3.2 (Database of Individual Seismogenic Sources) and CPTI15 (Parametric Catalogue of Italian Earthquakes). Seismogenic models include individual seismogenic structures/faults liable to generating major earthquakes with magnitude greater than 5.5, and background areal source model to evaluate the effect of earthquakes with magnitude less than 5.5. The PSHA is built up based on the long-term earthquake recurrence on seismogenic tectonic faults and the spatial distribution of historical earthquakes. Site amplification is considered based on seismic microzonation maps derived for the western area of Naples. The microzonation maps delineate expected levels of ground motion amplification based on reliable geological and geotechnical subsoil models. Hazard maps are derived for a number of return periods for ground-shaking in terms of peak ground acceleration and 5%-damped pseudo-spectral acceleration at a range of periods that are representative of the existing construction within the area. Detailed comparisons of the PSHA results with Italian national hazard maps and the code-based design spectra emphasize the importance of performing site-specific PSHA with explicit consideration of site effects.

Appendix 1

Consider the standard deviation of the residuals of a GMPE that provides the geometric mean associated with the two horizontal components of ground motion, be denoted as $\sigma_{{{ \ln }IM_{g.m.} }}$. To obtain the standard deviation for the arbitrary horizontal ground motion, $\sigma_{{{ \ln }IM_{arb} }}$, we calculate the variance of the finite record numbers N in the database as follows:

$$\begin{aligned} \sigma_{{\ln IM_{g.m.} }}^{2} = \frac{1}{N}\sum\limits_{j = 1}^{N} {\left( {\ln IM_{g.m.,j} - \mu_{{\ln IM_{g.m.} }} } \right)^{2} } = \frac{1}{N}\sum\limits_{j = 1}^{N} {\ln IM_{g.m.,j}^{2} } - \mu_{{\ln IM_{g.m.} }}^{2} \hfill \\ \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{1}{4}\left[ {\frac{1}{N}\sum\limits_{j = 1}^{N} {\ln IM_{x,j}^{2} } + \frac{1}{N}\sum\limits_{j = 1}^{N} {\ln IM_{y,j}^{2} } + \frac{1}{N}\sum\limits_{j = 1}^{N} {2\ln IM_{x,j} \ln IM_{y,j} } } \right] - \mu_{{\ln IM_{g.m.} }}^{2} \hfill \\ \end{aligned}$$

(25)

where IM_g.m.,j is the ground motion intensity for the geometric mean of the two horizontal components of jth recording, j ∈ [1,…,N], $\mu_{{{ \ln }IM_{g.m.} }}$ is the logarithmic mean of the GMPE (see Eq. 14). Knowing that

$$\sigma_{{\ln IM_{arb} }}^{2} = \frac{1}{N}\sum\limits_{j = 1}^{N} {\left( {\ln IM_{arb,j} - \mu_{{\ln IM_{arb} }} } \right)^{2} } = \frac{1}{N}\sum\limits_{j = 1}^{N} {\ln IM_{arb,j}^{2} } - \mu_{{\ln IM_{arb} }}^{2}$$

(26)

Equation (25) can be written as,

$$\begin{aligned} \sigma_{{\ln IM_{g.m.} }}^{2} = & \frac{1}{4}\left[ {2\sigma_{{\ln IM_{arb} }}^{2} + 2\mu_{{\ln IM_{arb} }}^{2} + \frac{1}{N}\sum\limits_{j = 1}^{N} {2\ln IM_{x,j} \ln IM_{y,j} } } \right] - \mu_{{\ln IM_{g.m.} }}^{2} \\ = & \frac{1}{4}\left[ {2\sigma_{{\ln IM_{arb} }}^{2} + 2\mu_{{\ln IM_{arb} }}^{2} + \frac{1}{2N}\left( {\sum\limits_{j = 1}^{N} {\left( {\ln IM_{x,j} + \ln IM_{y,j} } \right)^{2} } - \sum\limits_{j = 1}^{N} {\left( {\ln IM_{x,j} - \ln IM_{y,j} } \right)^{2} } } \right)} \right] - \mu_{{\ln IM_{g.m.} }}^{2} \\ = & \frac{1}{4}\left[ {2\sigma_{{\ln IM_{arb} }}^{2} + 2\mu_{{\ln IM_{arb} }}^{2} + 2\sigma_{{\ln IM_{g.m.} }}^{2} + 2\mu_{{\ln IM_{g.m.} }}^{2} - \frac{1}{2N}\sum\limits_{j = 1}^{N} {\left( {\ln IM_{x,j} - \ln IM_{y,j} } \right)^{2} } } \right] - \mu_{{\ln IM_{g.m.} }}^{2} \\ = & \frac{1}{2}\sigma_{{\ln IM_{arb} }}^{2} + \frac{1}{2}\sigma_{{\ln IM_{g.m.} }}^{2} - \frac{1}{8N}\sum\limits_{j = 1}^{N} {\left( {\ln IM_{x,j} - \ln IM_{y,j} } \right)^{2} } \\ \end{aligned}$$

(27)

Hence, we have,

$$\sigma_{{\ln IM_{arb} }}^{2} = \sigma_{{\ln IM_{g.m.} }}^{2} + \underbrace {{\frac{1}{4N}\sum\limits_{j = 1}^{N} {\left( {\ln IM_{x} - \ln IM_{y} } \right)^{2} } }}_{{\sigma_{C}^{2} }}$$

(28)