Italian seismic amplification factors for peak ground acceleration and peak ground velocity

ABSTRACT Ground motion modification over large areas is generally evaluated by focusing on source effects disregarding local lithostratigraphic site conditions. Hence, amplification maps of peak ground acceleration and peak ground velocity are proposed to improve the forecast of ground motion on a national scale. Topological information about litho-type successions and soil mechanical behaviour were retrieved from the Italian database of seismic microzonation and more than 30 million of seismic site response analyses were performed to quantify the amplification factors (i.e. the ratio between expected ground motion at the site of interest and that at the outcropping engineering bedrock). The maximum value of the amplified peak ground acceleration on the Italian territory results in about twice as much as the value expected at the outcropping of the engineering bedrock. Finally, damage scenario maps based on the amplified ground motion could be produced as a supporting tool for urban planning and emergency system management.


Introduction
Estimation of seismic ground motion over large areas (regional, national), aimed to support urban planning and seismic emergency system evaluation, is a non-trivial task (Barani et al., 2020;Brando et al., 2020;Falcone et al., 2021;Shreyasvi et al., 2019). In fact, the modification of ground motion with respect to what is expected at the outcropping engineering bedrock (i.e. material characterised by shear wave velocity, V S , at least equal to 800 m/s and by flat ground surface) should be quantified based on detailed sub-soil models and numerical simulations of local seismic site response (Falcone et al., 2020b(Falcone et al., , 2018Makra & Chávez-García, 2016;Maufroy et al., 2015;Moczo et al., 2018). The available amount of data, in general, does not allow to define sub-soil models consistent with the site conditions of the whole area of interest (Huber et al., 2015;Moscatelli et al., 2020a); moreover, it is a hard task to carry out numerical simulations of Local Seismic Site Response (LSSR) over large areas. Therefore, numerous works show maps of earthquake intensity based on simplified sub-soil models (i.e. defined according to key-mechanical and geometrical parameters, such as the mean shear wave velocity in the upper 30 m of the soil deposit, V S30 ) as, for example, shown by Falcone et al. (2020a) and Michelini et al. (2019). Forte and co-workers (Forte et al., 2019) provided a seismic classification of Italy based on the V S30 map presented in the same work. Such seismic classification has been proposed also in terms of peak ground acceleration, briefly PGA, both at ideal outcropping rock and considering the sub-soil condition (i.e. the V S30 ), where the amplification factors have been quantified according to the Italian Building Code (ItBC, 2018) depending on the socalled soil category. In a similar way, Falcone et al. (2020a) provided a seismic classification of Italy. Instead, Michelini et al. (2019) presented seismic classification using ShakeMap workflow (the paper of Michelini and co-workers can unveil further insight on such ShakeMap workflow). Despite what is reported in Forte et al. (2019) and Falcone et al. (2020a), in the present paper only amplification factors, AF (that is the ratio of the motion at the site of interest over that at the outcropping engineering bedrock) for PGA and peak ground velocity, PGV, are presented referring to 475 years return period. Moreover, such AF were derived by means of numerical simulations of seismic site response based on site-specific data from the national seismic microzonation database rather than based on ItBC (2018) prescription or ShakeMap workflows. On the other hand, Italian seismic microzonation studies, based on numerical seismic site response analyses and site-specific sub-soil data, are carried out only over the urban area ) not providing homogeneous sub-soil information for the whole Italian territory.
Estimating ground motion is a key parameter for formulating damage scenarios. As a matter of fact, damage scenario maps or the seismic demand on buildings are generally proposed considering the ground motion at the outcropping engineering bedrock (e.g. Dolce et al., 2020;Fontana et al., 2020); ground motion modifications are not included in such kind of forecast, thus leading to a possible underestimation of the structures and infrastructures failures induced by an earthquake (Graziani et al., 2019).
Bearing in mind that damage scenario maps are usually based on PGA and PGV and that point information on subsurface characteristics is unevenly distributed, the AFs for PGA and PGV based on the IGAG_20 workflow suggested by Falcone et al. (2021) are proposed in this study, aiming to support territorial planning and evaluation of the seismic emergency system. Italian territory was classified based on morpho-geological information according to the clustering reported in Mori et al. (2020). Data archived in the Italian DataBase for Seismic Microzonation (DB-SM in DPC, 2018), were collected to define sub-soil one-dimensional (1D) models with reference to 42 morpho-geological clusters. A set of 630 input motions were determined in agreement with the study proposed by the Italian Institute of Geophysics and Volcanology, INGV, for the 475 years return period . About 30 million numerical simulations of LSSR were performed adopting the linear equivalent approach in the frequency domain Kramer, 1996). A set of 126 AF PGA_PGV -V S30 correlations were obtained depending on the cluster and intensity of the input motion. Hence, the maps of AF PGA and AF PGV were obtained based on the Italian V S30 map proposed by Mori et al. (2020).
Finally, the AF PGA_PGV maps were compared with the results based on numerical simulation of LSSR referred to detailed sub-soil 1D models to validate the IGAG_20 methodology.

IGAG_20 methodology
The IGAG_20 methodology, proposed by Falcone et al. (2021) with reference to AF defined in three intervals of periods, was adopted to obtain the AF PGA and AF PGV . The IGAG_20 main steps are described in the following.
i) Morpho-geological clustering of the Italian territory (Iwahashi et al., 2018;Mori et al., 2020)   DB-SM (DPC, 2018), where geological, geotechnical and geophysical data are archived (accessible at www.webms.it). About 2 million of 1D soil columns were identified and adopted for the numerical simulation of the LSSR. Each 1D soil column differs from others in terms of topological information (i.e. stratigraphic succession of lithotypes), in terms of V S -z gradient and in terms of depth to the engineering bedrock (H EB ), that is the depth below which the harmonic mean of shear wave velocity is at least equal to 800 m/s. iii) A set of 630 response spectra (15 spectra multiplied by 42 morpho-geological clusters) in terms of pseudo-acceleration were determined according to the seismic hazard study made available by the INGV , accessible at http://esse1.mi.ingv.it/. iv) About 30 million numerical simulations of the LSSR were performed by means of an original numerical code, build up by the authors, adopting the linear equivalent approach in the frequency domain Kramer, 1996). With reference to each 1D soil column, the AFs were determined according to the following equations: where the subscripts o and i are referred to the motion obtained at the ground surface of the 1D soil column by means of the LSSR analysis and to the input motion (i.e. at the outcropping engineering bedrock), respectively. v) With reference to each of the 42 morpho-geological clusters and three intensity levels of the seismic input, the AF PGA -V S30 and AF PGV -V S30 correlations were estimated in terms of the 16°, 50°, and 84°percentiles from IGAG_20 results adopting the stepwise multiple quantile regression (Liu & Wu, 2009). Therefore, the AF maps were determined by adopting such AF PGA--V S30 and AF PGV -V S30 correlations, the Italian reference seismic hazard maps available at http://esse1.mi.ingv.it/, and the Italian V S30 map, see Figure 1, reported in Mori et al. (2020). The authors are aware that V S30 should not be used as the unique soil parameter to describe seismic amplification (Lee & Trifunac, 2010;Zhu et al., 2020). Nevertheless, national maps of additional parameters such as the fundamental period of the deposit or depth to the seismic bedrock are not provided for large areas (e.g. entire Italy), at most for the regional area (Martelli, 2021; Mascandola et al., 2019). However, the AF-V S30 correlations derived according to the IGAG_20 workflow are specific for each morpho-geological cluster, in turn, characterised by different sub-soil conditions (e.g. V S gradient with depth and depth to the seismic bedrock). In this way, the AF also includes the site-specific conditions even if quantified based on the only V S30 value.Italian map showing the distribution of the harmonic mean of the shear wave velocity in the upper 30 m of the soil, leading to recognize soft soil as in the case of the Po plain or stiff material as in the case of the rocky sub-flat areas of the Apulian block.

AF PGA and AF PGV maps
Following what is discussed in Section 2, the AFs were assigned to a regular 50 × 50-m grid. The AF PGA and AF PGV maps are shown in Figure 2 and Figure 3, respectively, with reference to the only 50°percentile for sake of brevity (16°and 84°percentiles are reported as Figures 5-8). As a matter of fact, the proposed AF PGA and AF PGV maps depend on the morpho-geological cluster and intensity of the input motion expected at the outcropping engineering bedrock with reference to the return period of 475 years. The main relationship between soil deposit properties and seismic performance of the deposit itself, in general, can be presented by means of the following key points (Gazetas, 1982;Kramer, 1996;Rollins et al., 1998Rollins et al., , 2020Seed & Idriss, 1970): (k1) assuming the V S constant with depth, the higher the depth to the engineering bedrock (H EB ) the lower the fundamental frequency of the soil deposit (i.e. the higher the fundamental period), (k2) for a fixed value of the H EB , the higher the deposit V S the higher the fundamental frequency (i.e. the lower the fundamental period), (k3) for a specific deposit, the higher the intensity of the input motion the lower the AF due to the non-linear response of soils. Bearing in mind that AF PGA and AF PGV are related to amplification effects at very low and intermediate periods, respectively, the above-mentioned key points are included in the proposed maps. In fact, in the east side of the Po plain, where H EB > 100 m (the reader should refer to the work of Mascandola et al., 2019) and V S30 < 300 m/s, AF PGV is higher than AF PGA , while in the southern Apulia, where H EB < 30 m (Mori et al., 2020) and V S30 < 300 m/s, AF PGA is higher than AF PGV (i.e. accordingly to key-point k1). In addition, with reference to the southern part of Apulia, where the PGA of input motion is higher than 0.1 g (the reader should refer to the Italian reference seismic hazard available at http://esse1-gis.mi.ingv.it/) and H EB is lower than 30 m, the AF PGA of that part characterised by V S30 < 300 m/s is higher than the AF PGA in that part where V S30 is higher than 300 m/s (in agreement with keypoint 2). Moreover, with reference to the eastern area of the Po plain characterised by V S30 < 300 m/ s, the AF PGV (or AF PGA ) in the northern part, where input PGA is lower than 0.1 g, is higher than the AF PGV (or AF PGA ) in the southern part, where input PGA is higher than 0.1 g (i.e. in agreement to what reported at the key-point k3). Thus, in general, the lithostratigraphic effects related to the vertical heterogeneity of 1D soil column could highly increase the seismic demand on a structure or infrastructure at a site with respect to what expected in case of the outcropping engineering bedrock at the same site. As an example, in the southern Apulia, Salento area, the AF PGA (Figure 2) is the highest compared to the rest of Apulia well in agreement with the observed historical damage pattern referred to the 1743 earthquake (Galli & Naso, 2008;Nappi et al., 2017).
Finally, with reference to about 4,500 sites, for which detailed sub-soil models were available, the AF PGA and AF PGV values obtained by means of IGAG_20 and site-specific LSSR analyses were compared. The error was computed according to the following equation: where AF IGAG_20 and AF LSSR are referred to the AF obtained by means of IGAG_20 methodology and site-specific LSSR, respectively. The IGAG_20 forecast and the results of site-specific LSSR are in satisfactory agreement, as shown by the box plots of the error ε AF sketched in Figure 4, since the median error is lower than 10%. It is worth noting that the AF PGV IGAG_20 forecast is characterised by a better precision and accuracy than AF PGA , see Figure  4, since the recurrent site condition is characterised by V S30 in the range of 200-600 m/s and H EB in the range of 6-30 m, hence, the main amplification phenomena and related uncertainties are referred to low periods as in the case of PGA rather than of PGV.

Conclusions
Italian maps of amplification factors for peak ground acceleration and peak ground velocity are proposed, based on the IGAG_20 methodology (Falcone et al., 2021), to modify the ground motion referred at the outcropping engineering bedrock considering the lithostratigraphic site effects. About 2 million onedimensional soil columns were determined based on the site data archived in the Italian database of seismic microzonation. A set of 630 response spectra related to the return period of 475 years were defined according to the Italian seismic hazard referred to as the outcropping engineering bedrock. A total of about 30 million numerical simulations of the local seismic site response were carried out adopting the linear equivalent approach in the frequency domain. The IGAG_20 forecast was in satisfactory agreement with the results of site-specific analyses based on detailed sub-soil models.
The proposed maps are expected to improve (i) real-time prediction of ground motion after an earthquake (shakemaps), (ii) scenario maps of seismic-induced landslides and rockfalls, (iii) seismic risk maps referred to lifelines and (iv) scenario damage-maps at regional or inter-municipality scale to support planning strategies, estimation of seismic retrofitting costs, and improvement of seismic emergency system.

Software
The raster datasets were created with GRASS GIS V.7.6.1 software, using a bash script written specifically for the purpose. The maps were generated using the ArcGIS V.10.8.1 software.