Quality assessment for site characterization at seismic stations

Abstract

Many applications related to ground-motion studies and engineering seismology benefit from the opportunity to easily download large dataset of earthquake recordings with different magnitudes. In such applications, it is important to have a reliable seismic characterization of the stations to introduce appropriate correction factors for including site amplification. Generally, seismic networks in Europe describe the site properties of a station through geophysical or geological reports, but often ad-hoc field surveys are missing and the characterization is done using indirect proxy. It is then necessary to evaluate the quality of a seismic characterization, accounting for the available site information, the measurements procedure and the reliability of the applied methods to obtain the site parameters.In this paper, we propose a strategy to evaluate the quality of site characterization, to be included in the station metadata. The idea is that a station with a good site characterization should have a larger ranking with respect to one with poor or incomplete information. The proposed quality metric includes the computation of three indices, which take into account the reliability of the available site indicators, their number and importance, together with their consistency defined through scatter plots for each single pair of indicators. For this purpose, we consider the seven indicators identified as most relevant in a companion paper (Cultrera et al. 2021): fundamental resonance frequency, shear-wave velocity profile, time-averaged shear-wave velocity over the first 30 m, depth of both seismological and engineering bedrock, surface geology and soil class.

1 Introduction

In recent years, the number of stations of permanent seismic networks worldwide has largely increased. As a consequence, the amount of recordings of earthquakes and their applications using real-time data have also risen, together with the improvement of the online databases of seismic networks.

The dissemination of large seismic datasets highlights the complexity of ground-motion prediction (e.g. Akkar et al. 2010; Archuleta et al. 2006; Chiou et al. 2008; Roca et al. 2011; Bozorgnia et al. 2014; Cauzzi et al. 2016; Gee et al. 2011; Luzi et al. 2016; Theodulidis et al. 2004; Traversa et al. 2020), and its strict connection to the properties of the site where the recording instrument was settled. Site response may have a large impact on surface ground motions, and its knowledge is required in many seismological studies such as: calibration of strong-motion records (Douglas 2003; Akkar and Bommer 2007; Regnier et al. 2013 among many others), realistic estimates of shaking at seismic stations (Abrahamson 2006; Convertito et al. 2010; Thompson et al. 2012), site-specific hazard assessment (Rodriguez-Marek et al. 2014; Bindi et al. 2017), estimation of ground-motion attenuation models (Bindi et al. 2011; Campbell and Bozorgnia 2014; Lanzano et al. 2020), and identification of soil classification for building code applications or for microzoning studies (Priolo et al. 2019).

So far, the installation of new instruments and new technologies has been favored for increasing the number of observation sites (Campillo et al. 2019) also with portable arrays (Hetényi et al. 2018), most often neglecting the issue of the quality of site condition metadata, which is however critical for data analysis. It is then necessary to define standards and quality indicators, for site characterization information at seismic stations to reach high-level metadata. These topics are becoming a key issue within the European Union and worldwide. They have been recently addressed with the SERA European Project (“Seismology and Earthquake Engineering Research Infrastructure Alliance for Europe – SERA” Project, no. 730900 funded by the Horison2020 INFRAIA-01–2016-2017 Programme), with a networking activity dedicated to propose standards for site characterization at seismic stations in Europe. More specifically, the Task 7.2 of the Network Activity 5 in Work Package 7 (http://www.sera-eu.org/en/activities/networking/) was focused on three goals: (1) definition of the most recommended indicators to get a reliable seismic site characterization; (2) proposition of a compact summary report for each indicator evaluated as most relevant; (3) proposition of a quantitative strategy towards an “objective” assessment of the quality of a site characterization.

The first two issues are described in a companion paper (Cultrera et al. 2021) that proposed a list of seven indicators considered as the most recommended for a reliable site characterization, and representing a feasible combination of physical relevance and convenience of getting and using them. Additionally, the companion paper proposed the scheme of a summary report for each site characterization indicator, containing the most significant background information on data acquisition and processing. The summary reports are planned to be useful tools to assess the quality of a site characterization at the seismic station location.

The present paper faces the issue (3), with the proposition of an overall quality strategy to enable a ranking of the seismic characterization analysis carried out at different sites. In general, the reliability of a single indicator’s value is mainly linked to the methodology to retrieve it. Different methods can result in different values for the same indicator, because each method has its own resolution and limits. These aspects are addressed by some important good-practice guidelines and reference manuscripts that are helpful for assessing the reliability of important indicators commonly adopted in site response analysis, such as the fundamental resonance frequency f₀ (SESAME 2004; Molnar 2018), the shear-wave velocity profile (V_S) from methods based on surface waves (Socco and Strobbia 2004; Bard et al. 2010; Hunter and Crow 2012; Foti et al. 2018), or V_S profile from cross-hole and down-hole methods (ASTM D4428M-00 2000; ASTM D7400M-08 2008). Some benchmarks were performed to test the reliability among different methods, especially to validate the performance of non-invasive and invasive methods for the measurements of shear-wave velocity profiles (Asten and Boore 2005; Stephenson et al. 2005; Cornou et al. 2009; Moss et al. 2008; Cox et al. 2014; Garofalo et al. 2016; Darko et al. 2020). These benchmarks have outlined the feasibility of non-invasive and invasive methods in supplying comparable results together with an estimate on inter-analysts variability.

The lack of standardized procedures in evaluating the quality of a site characterization analysis prevents a homogenous grading of strong-motion sites and a clear picture of the information available at seismic stations, both at European and at world-wide scales. As a consequence, there is not a homogeneous quality information for site characterization among strong-motion web sites. When geophysical measurements are not collected, terrain-based site condition proxies can be used integrating surface geology, topographic slope and terrain class (Wills and Clahan 2006; Wald and Allen 2007; Yong et al. 2012; Yong 2016; Kwok et al. 2018), or geotechnical or geomorphic categories, such as done in the NGA-West2 PEER ground motion database (http://ngawest2.berkeley.edu/; Ancheta et al. 2014). Also the strong-motion Italian database ITACA (http://itaca.mi.ingv.it; D’Amico et al. 2020), in absence of direct geophysical measurements of V_S30 (time-averaged shear-wave velocity over the first 30 m) at a seismic station, derives the soil class from near-surface geological information or from slope proxies (Felicetta et al. 2017). The European Geotechnical Database (http://egd-epos.civil.auth.gr/; Pitilakis et al. 2018) includes quality indices only for two indicators (f₀ and V_S30) on the basis of the method that was used for their estimation and whether a reference is provided; for example in case of V_S30 an higher grading is assigned to borehole surveys compared to inferred methods based on geology.

In this paper we propose a general strategy for the quality assessment, accounting for the number and relevance of the seven most recommended indicators, and for their consistency based on multi-parametric regressions. We finally applied our strategy to some sites of permanent accelerometric stations that have been characterized in the framework of the Italian Civil Protection Department-INGV agreement (2016–2021). The results allow to rank the seismic stations according to their site characterization.

2 Methodology

We evaluated the overall quality of a seismic characterization at a given site accounting for the seven indicators selected in Cultrera et al. (2021): the fundamental resonance frequency (f₀), the shear-wave velocity profile (V_S) as function of depth, the time-averaged shear-wave velocity over the first 30 m (V_S30), the seismological bedrock depth (H_{seis_bed}, which is defined as the depth of the geological unit controlling the fundamental resonance frequency), the engineering bedrock depth (H_{eng_bed}, the depth at which V_S reaches first in the profile the value of a specific value; for example H₈₀₀ refers to V_S = 800 m/s), the surface geology and the soil class. The seven indicators considered as most representative are not completely independent from each other; e.g. the soil class is usually linked to the V_S30, and the latter can be derived from the V_S profile. However, another task of the same SERA Project (Bergamo et al. 2019; 2021) adopted a regression analysis and a neural network approach, to find the correlation between direct and indirect proxies and the true amplification computed at Swiss and Japan stations. Among the 7 indicators indicated by the Cultrera et al. (2021), Bergamo et al. (2021) did not consider geological information in their analysis. They found that the actual amplification in the range 1.7–6.7 Hz exhibits a good correlation with a combination of velocity profile (described through specific frequency-dependent “quarter-wavelength” quantities: average velocity and impedance contrast), V_S30, bedrock depth and f₀.

In our methodology, the quality of a site characterization is expressed by the computation of a final overall quality index (Final_QI), which is a number ranging between 0 and 1 and accounting for the single indicator quality, its relevance for site characterization, and the consistency between all the significant indicators. Specifically, Final_QI is derived from the computation of three simple quality indices (QI1, QI2 and QI3). QI1 quantifies the reliability of each individual indicator, QI2 combines the QI1 values from the individual indicators available at a given site, and QI3 is aimed at evaluating the consistency between couples of indicators. The principles of such quality metrics have been presented and discussed during a dedicated workshop in Italy (Cultrera et al. 2019) gathering European and worldwide scientists.

2.1 Quality index 1 (QI1)

We propose a simple, common expression involving the different aspects of the quality evaluation of a single indicator (QI1 hereinafter), based on (1) the suitability of the method for acquisition and analysis, (2) the type of input data (direct measurements or derived from proxies) and quality of the processing, and (3) the completeness of the site report.

The quality index QI1 varies from 0 to 1 and is defined by the following expression:

$$ {\text{QI}}1 = \left[ {\left( {a_{MS} + b_{ID} \cdot c_{MI} } \right) \cdot d_{RC} } \right]/3 $$

(1)

where factors a_MS, b_ID, c_MI and d_RC are detailed below and summarized in Table 1, together with some indication on how to evaluate them. The factors are given only discrete values in order to limit subjective choices. The value 3 in the denominator is equal to $a_{MSmax} + b_{IDmax} \cdot c_{MImax}$ where the suffix max indicates the maximum values of the factors.

Table 1 Values of the factors in Eq. 1 for the computation of QI1. The suffixes in the factors name MS, ID, MI and RC stand for method suitability, input data, method implementation and report completeness

2.1.1 Factors in QI1

In Eq. 1, factor a_MS is related to the “theoretical” reliability of the methods used for data acquisition and analysis for deriving the value of the target indicator (the suffix MS stands for “method suitability”). It is equal to 1 when assessed on the basis of peer-reviewed papers or well-established guidelines, otherwise it is given a 0 value (Table 1). As an example, in the case of f₀, a_MS = 1 when the applied methodology follows published peer-reviewed papers or consolidated guidelines (e.g. Nakamura et al. 1989; Field and Jacobs 1995; SESAME 2004; Picozzi et al. 2005; Haghshenas et al. 2008; Molnar et al. 2018 among many others).

Factor b_ID deals with the type of data or information used for evaluating the target indicator (the suffix ID stands for “input data”). As one of the main objectives is to emphasize the importance of direct measurements rather than inferred estimates, it is assigned a value of 2 in case of dedicated, in-situ field experiments, and a 0 value whenever inferred, i.e. obtained from proxies or empirical relationships (Table 1). Almost all funding agencies favor the installation of seismic instruments neglecting the issue of the metadata quality, which is however critical for data analysis. That is why the factor b_ID is given a binary value 2 for actual measurements, and 0 for simply inferred values. For example in case of f₀, spectral ratios from single-station (either noise or earthquake recordings) measurements are considered a direct evaluation (b_ID = 2), whereas the evaluation of f₀ from 1D site response modelling only (i.e., when 1D models are not constrained by specific field measurements) is considered inferred (b_ID = 0). If the target indicator is the V_S profile, invasive measurements (such as downhole, crosshole, PS-logging whatever the investigation depth) or not-invasive extensive field measurements (e.g. based on the inversion of surface-wave dispersion properties) are considered as a direct evaluation (b_ID = 2). For the same consideration, b_ID is 2 if V_S30 is resolved by in-situ measurements. For the sake of simplicity, we also suggest b_ID = 2 when V_S30-V_SZ relationships are used (e.g. Boore et al. 2011; Dai et al. 2013), with the reliability of the estimated V_S30 being translated in factor c_MI as described later. If the target indicator is the near-surface geology, a geological field survey at the station site or a detailed cartography (scale finer or equal to 1:10.000) is considered a direct evaluation (b_ID = 2). When the surface geology is derived exclusively from large scale cartography (i.e. 1:100.000) then b_ID is assigned equal to 0.

Factor c_MI indicates the reliability of the indicator value in relation to the quality of data acquisition, processing and interpretation (the suffix MI stands for the “method implementation” of the selected approach; Table 1). Typically, the quality of the in-situ measurements may be assessed on the basis of the compliance with standard and robust procedures, including the performance and suitability of the used equipment, while the quality of the processing should account for the observance of commonly accepted guidelines, including the proper interpretation of the final results. Depending on the degree of correctness, the factor c_MI can be equal to 0 (incorrect), 0.5 (partially correct) and 1 (correct). From Eq. 1, the c_MI value is obviously irrelevant when the factor b_ID of Eq. 1 is equal to zero (absence of any direct measurements). Published review papers or guidelines can be used to judge the precision of the analysis. For example, the f₀ from single-station noise measurements can be verified through the SESAME (2004) or others criteria (Picozzi et al. 2005), taking into account the sensor cut-off frequency used in the field, the time-window length and number of cycles selected in the analysis step with respect to f₀, the amplitude and narrowness of the spectral peak etc. In case of V_S30 indicator, the factor c_MI is set equal to 1 when the relationships between V_S30 and different time-averaged velocity V_SZ at given depth z are applied (Boore et al. 2011; Régnier et al. 2014; Wang and Wang 2015), assuming that such relationships are calibrated for the studied area. In the estimation of shear-wave velocities at larger depth, the uncertainties of these region-specific relationships obviously increase when the maximum depth of the data is very limited (e.g. for z = 5, 10, 20 m). Because of the large uncertainties, we recommend to set c_MI = 0.5 when z is less than 15 m (Boore et al. 2011; Kwak et al. 2017). Note that the evaluation of factor c_MI can take advantage from the summary reports as described in Cultrera et al. (2021), where the basic information of data processing is collected in a compact form.

Factor d_RC is related with the quality of the available documentation reporting the data acquisition and processing (the suffix RC stands for “report completeness”): the maximum value of 1 is for a complete report (see companion paper for the necessary information), the intermediate value 0.5 is when partial information is present, whereas the absence of a report leads to a d_RC value of 0 (Table 1). The presence of a report is very important in Eq. 1, because QI1 is equal to zero in case of absence of any report, even though there might exist actual measurements followed by a correct interpretation.

The functional form of the generic Eq. 1 includes one addition and two multiplications, which were deliberately introduced with the following rationale:

• Multiplication by a factor that may be equal to 0 indicates that whatever the value of the other term of the multiplication, the absence or poor reliability will affect the whole QI1 term. The product “b_ID · c_MI” may thus be zero in case of absence of site-specific direct measurements (b_ID), or in case of very inadequate acquisition or processing (c_MI). Similarly, the quality of the documentation (d_RC) will drastically impact the QI1 whatever the relevancy of the methodology (a_MS), the type of data (b_ID) and of the method implementation (c_MI). The absence or poor quality site documentation greatly hampers the ability of external users to evaluate the indicator’s quality.

• Addition in Eq. 1 makes the factor a_MS relatively independent from b_ID and c_MI. For instance, when V_S30 is inferred from local slope or geology, a_MS may be equal to 1 because the methodology has been published and is commonly accepted, while b_ID is zero because the derivation is not based on direct measurements but from statistical correlations with very large scatter.

It is worthy of note that in the QI1 evaluation a careful examination of the available site information in the proximity of the selected station is needed. Among the factors of Table 1 contributing to the QI1 definition, the one which is more difficult to judge is probably the factor c_MI. Specifically, factor c_MI takes into account criteria on reliability of the used methods (including their resolution and commonly admitted rules-of-thumb), and appropriate usage of empirical relationship available in literature when indicators are inferred (examples of empirical relationships are V_S30-surface topography, Wald and Allen 2007; V_S30-V_S10, Boore et al. 2011; V_S30-phase velocity at 40 m wavelength; Martin and Diehl 2004). The QI1 assignment should be as much as possible independent from subjective choices, but the factor c_MI could be biased by personal judgment. In order to reduce such bias for each of the seven site indicators, we believe an expert judgment is necessary in the QI1 assessment; the quality evaluation should be in the responsibility of the analysis team and/or of the network operators involved in site characterization.

2.1.2 QI1 examples

To better explain the effect on the different factor’s choices, we simulate the QI1 computation of f₀ as target indicator and for virtual sites with the following characteristics (Table 2):

Table 2 Example of QI1 computation at ten sites. The examples from #1 to #7 are referring to f₀ as target indicator, the examples from #8 to #10 are referring to V_S30 as a target indicator (see text)

Site #1—f₀ evaluated from horizontal-to-vertical (H/V) spectral ratios on ambient noise data (b_ID = 2) evaluated following the SESAME (2004) guidelines (a_MS = 1). The processing is done with the Geopsy code (Wathelet et al. 2020) and a clear H/V peak occurs in the frequency range within the applicability limits of the method (c_MI = 1). A complete report exists describing the field activity and data analysis (d_RC = 1). All the factors of Table 1 take their maximum value as the resulting QI1 (QI1 = 1).

Site #2—f₀ evaluated as a proxy from V_S profile (b_ID = 0) following the simplified approaches described in Dobry et al. (1976) or Wang et al. (2018) (a_MS = 1). There are uncertainties on the layered velocity profile used to derive the f₀ value (c_MI = 0.5): in this case the value of factor c_MI is irrelevant for the computation of QI1 because b_ID = 0 (see Eq. 1). A detailed report exists describing the analysis (d_RC = 1). The resulting QI1 is equal to 0.33.

Site #3—as for site #1 but without any report (d_RC = 0). QI1 is equal to its minimum value (QI1 = 0).

Site #4—as for site #1 but the processing or interpretation of the final results is evaluated incorrectly (c_MI = 0); this happens for example when f₀ doesn’t indicate the fundamental peak but a secondary peak at higher frequency, or in case of the time-window length too short to allow a robust estimation of f₀. QI1 is equal to 0.33.

Site #5—as for site #1 but there is partial confidence in the processing or interpretation of the final results (c_MI = 0.5). QI1 is equal to 0.67.

Site #6—All the factors reach the maximum value, except d_RC because the site report is considered not complete (d_RC = 0.5). QI1 is equal to 0.5.

Site #7—Factors a_MS and b_ID have the maximum values, but the processing or interpretation are not correct (c_MI = 0) and the site report is incomplete (d_RC = 0.5). QI1 is equal to 0.167.

In the next three examples (from #8 to #10 in Table 2), we assume that the target indicator is the V_S30 derived from a measured shear-wave velocity profile (a_MS = 1 and b_ID = 2). It is important to highlight that the maximum depth of investigation can be confined in real situations to a very shallow depth (i.e. < 30 m):

Site #8—V_S30 was calculated using a downhole (DH) test near the seismic station. In this example the DH test is with a maximum depth of 20 m, this is why a relationship between V_S20 and V_S30 was used (for example Boore et al. 2011, factor a_MS = 1). In this case, the DH is a direct measurement (b_ID = 2) although limited in depth, and the applicability of relationship V_S20–V_S30 is reliable (c_MI = 1) because the station is located in the region where the relationship was validated. A complete report exists describing the field activity and data analysis (d_RC = 1). All the factors of Table 1 take their maximum value and QI1 is 1.

Site #9—Similar to site #8, but the maximum depth of the available DH survey reaches only 5 m, and a relationship between V_S5 and V_S30, developed for the area of analysis, was used (a_MS = 1). Although the DH is very limited in depth, we consider it as direct measurement (b_ID = 2) but, because the relationship may lead to large uncertainty, the factor c_MI is set equal to 0.5. The resulting QI1 is 0.667.

Site #10—Similar to site #9, except that the station is located in a region where the V_S5–V_S30 relationship was never calibrated: a_MS (published methods), b_ID (direct measurements), d_RC (presence of a full report) have their maximum values but c_MI is set equal to 0. QI1 is equal to 0.33.

Table 2 summarizes the factors and the resulting QI1 computed for the 10 sites. QI1 can have six possible values (0, 0.167, 0.33, 0.5, 0.667 and 1) that ​​are connected to the reliability of each single indicator and can be interpreted in terms of quality as: unreliable (0), very poor (0.167), poor (0.33), acceptable (0.5), good (0.67) and very good (1).

The absence of a report (d_RC = 0) implies QI1 equals to zero (e.g. site #3). Another significant factor is b_ID: without direct measurements (b_ID = 0; e.g. site #2) QI1 cannot exceed the value of 0.33. The same QI1 value of 0.33 is reached in case of direct measurements (b_ID = 2) but with the method implementation having some problem (c_MI = 0; e.g. site #4). Although the definition of QI1 in Eq. 1 is aimed at penalizing the lack of a report and the use of proxies or empirical relationships, the absence of a direct measurements (i.e. b_ID = 0) does not give necessarily a QI1 equal to zero, as shown from the above examples. Strong-motion databases, like the Italian one, lack of in-situ measurements at the recording station, but they usually adopt peer-reviewed methods (a_MS = 1) which are properly implemented (c_MI = 1) and fully described in a report (d_RC = 1).

Other examples of how to select the proper value for factor a_MS, b_ID and c_MI are reported in the "Appendix" materials ( "Appendix" Tables 7, 8 and 9) and in Bergamo et al. 2019 (see their Tables 1, 2, 3, 4, 5). This auxiliary material provides indications on how to assign the factors that appear in Eq. 1, but is not exhaustive of all situations that may be encountered by analyzing real sites.

2.2 Quality index 2 (QI2)

Once the QI1 is computed for each indicator through Eq. 1, QI2 is evaluated as a weighted sum of the QI1 of all indicators at the target site:

$$ {\text{QI}}2 = \left[ {\mathop \sum \limits_{i = 1,n} w_{i} \cdot QI1_{i} } \right] / \mathop \sum \limits_{i = 1,n} w_{i} $$

(2)

where w_i is the weight relative to the i-th indicator and n indicates their total number. In this paper n is equal to 7, i.e. the number of indicators considered as most appropriate following the companion paper (Cultrera et al. 2021). If some of the indicators are not available at the target site, its corresponding QI1_i is equal to zero in Eq. 2. In detail, QI2 varies from 0 to 1, and it cares for the importance of the indicators on the evaluation of the site characterization through the weights w_i. Because QI1 can assume six discrete values, the choice of weights in the definition of QI2 should ensure a wider and gradual distribution of the QI2 values, depending on the number and importance of available indicators at each site. The weights must take into account the relevance of the selected indicators in the site characterization and, after testing various options for the selection of w_i values (Di Giulio et al. 2019), we propose three simple weight classes (Table 3) according to the indication provided by the survey described in the companion paper:

Table 3 Weights of the relevant indicators for computation of QI2 (Eq. 2). The last column indicates the number of the answer (in percentage) to the online questionnaire indicating the indicator as mandatory (see Fig. 3 of the companion paper Cultrera et al. 2021)

• A maximum weight of 1 for f₀ and velocity profile V_S. These two indicators were the most recommended indicators (72% and 89% respectively; see Table 3) to be used for site metadata, and they are directly linked to the dynamic soil properties and to soil amplification.

• An intermediate weight of 0.5 for the indicators V_S30, engineering and seismological bedrock depth, surface geology. In this group, surface geology has a qualitative relation with site effect estimation, and V_S30 or bedrock depth can be derived from velocity profile V_S and f₀. This group of indicators were considered as mandatory by the participants to the online questionnaire in a percentage ranging between 55 and 63% (Table 3).

• A minimum weight of 0.25 for the “soil class” indicator. Although this indicator had the same percentage of ‘mandatory’ attribution of the previous group (Table 3), we assigned the lowest value because it is an indirect proxy for site conditions, derived mostly from the other indicators already considered in the weighted average (such as V_S30, engineering bedrock depth and geology).

Unlike the QI1 evaluation, QI2 can be computed automatically applying Eq. 2 and it does not require any other analysis from the operator. To illustrate the QI2 index, we computed Eq. 2 at virtual sites characterized by different combinations of the recommended indicators (Fig. 1). For the sake of simplicity, we considered three possible values of QI1: 1, 0.5 and 0. These values ​​were mutually assumed by the seven indicators. The null value of QI1 in Eq. 2 implies the absence of an indicator or the lack of a report. We then decreased gradually the number of the available indicators from 7 to 1, and sorted the results in decreasing order (Fig. 1). The ranking is from the maximum value of 1 (all the seven indicators are available with QI1 = 1) to the lowest value (only V_S30 or geology are available with a QI1 equals to 0.5). The QI2 trend (Fig. 1) is clearly related to the number of the indicators, and to their relevance for site characterization analysis according to the weights of Table 3. The red circles with letters in Fig. 1 indicate five virtual sites: at site A (QI2 = 1) the seven indicators are all available with a QI1 of 1; at site B (QI2 = 0.38) the available indicators are four (f₀, surface geology, V_S30 and soil class) and f₀ is with QI1 = 1 whereas the others have QI1 = 0.5; at site C (QI2 = 0.35) the available indicators are two (V_S30 and V_S profile with QI1 = 1); at site D (QI2 = 0.09) the indicators are two but with lower weight (surface geology and soil class with a QI1 = 0.5); at site E (QI2 = 0.06) the only indicator is V_S30 with a QI1 = 0.5. Other combinations of the indicators may return the same QI2 value of the above examples, as shown in the auxiliary material ( "Appendix" Table 10).

Fig. 1

QI2 values for various sets of indicators. The red circles with letters indicate five virtual sites (see text). The full computation of the histograms is reported in the auxiliary material (see table 10 in “Appendix”)

It is worth noting that QI2 compensates the possible overestimation of the QI1 of some indicator. This is the case of the site #9 in Table 2, for which the QI1 of the V_S30 indicator may appear likely overestimated (QI1 = 0.67) because of the use of the V_S5–V_S30 relationship. However, because of the very limited depth of 5 m of the DH measurements, there are chances that QI1 values for the other indicators (H₈₀₀, H_{seis_bed} and soil class) would be low, and as consequence QI2 is also expected to be low. Only in case of a bedrock site, with few meters (< 5 m) of weathered outcrop over stiff rock, H₈₀₀ and H_{seis_bed} can be intercepted within the first 5 m, and the associated QI2 value gets consistently a relatively high value.

2.3 Quality index 3 (QI3)

QI3 is aimed at evaluating the consistency of various pairs of indicators that are related to each other. It is expressed by the following equation:

$$ {\text{QI}}3 = \left[ {\mathop \sum \limits_{k = 1,m} cs_{k} } \right] / m $$

(3)

where cs_k is the consistency factor for a pair of indicators identified by k, and m is the number of available couples of indicators at the specific site. The consistency factor cs_k can be either 0 (no consistency) or 1 (consistency), and the QI3 is ranging from 0 to 1. QI3 has a physical meaning because it represents the proportion of the selected pairs of indicators that are consistent with one another.

In our proposal, out of the 7 recommended indicators, we fixed the number of possible pairs to 5 (m equals to 5). This is because 5 is the number of pairs of indicators which have been measured for a large enough dataset to allow reliable relationships through scatter plots. The five pairs are: f₀ & V_S30 (k = 1), f₀ & seismic bedrock depth (k = 2), f₀ & engineering bedrock depth (k = 3), V_S30 & engineering bedrock depth (k = 4) and V_S30 & geology (k = 5). The value of cs_k at a specific site is set equal to 0 if one or both indicators of the pair k are not present.

Empirical relationships between various indicators can be found in the form of scatter plots in scientific literature for evaluating the consistency between indicators. Several papers propose empirical relationships between pairs of indicators to investigate the ability of different indicators in characterizing site response, or their use for a suitable definition of the amplification factors within seismic codes (Boore et al. 2014; Kamai et al. 2016; Stambouli et al. 2017). As an example, in the following we list a selection of papers showing correlations for the five pairs considered in Eq. 3:

• (1) f₀—V_S30 (e.g. Luzi et al. 2011; Gofhrani and Atkinson 2014; Régnier et al 2014; Hassani and Atkinson 2016; Derras et al. 2017; Stambouli et al. 2017; Zhu et al. 2020);

• (2) f₀—seismic bedrock depth (e.g. Ibs-Von Seht and Wohlenberg 1999; Parolai et al. 2002; Hinzen et al. 2004; Gosar and Lenart 2009; Luzi et al. 2011);

• (3) f₀—engineering bedrock depth (H₈₀₀) (e.g. Derras et al. 2017);

• (4) V_S30—engineering bedrock depth (H₈₀₀) (e.g. Derras et al. 2017; Piltz and Cotton 2019; Zhu et al. 2020; Bergamo et al. 2021);

• (5) V_S30—surface geology (e.g. Wills et al. 2000 and 2015; Wald and Allen 2007; Lemoine et al. 2012; Stewart et al. 2014; Yong et al. 2016; Derras et al. 2017; Foti et al. 2018; Ahdi et al. 2017; Mital et al. 2021).

Such empirical relationships generally refer to a specific database, and several checks are needed to ensure the applicability to the site under study. First, it is important to check the homogeneity of the analysis at the base of such relationships, and if the definition of the indicators is exactly the same (e.g. “peak” or “fundamental” frequency, derived from H/V spectral ratios of 5% damped pseudo spectral acceleration, or from Fourier Amplitude Spectra, etc.). Second, the relationships might be variable from region to region. Therefore, the consistency evaluations should, as much as possible, take into account the available studies for the areas including or neighboring the target station.

In order to avoid being stuck to a given region or database, we propose in the present paper a reference set of scatter plots (for the selected five pairs of indicators) to compare with the measured value at a specific site and evaluate cs_k in Eq. 3. When the indicators are within or out of the confidence interval of our scatter plots, we set cs_k equal to 1 or 0, respectively.

We first selected 935 sites where real V_S profiles are accessible, and we then homogeneously computed the other indicators assuming a 1D velocity model. Soil class, depth of engineering bedrock (H₈₀₀) defined as the depth where shear-wave velocity is equal or first exceeds the conventional EC8 (CEN 2004) value of 800 m/s, V_S30 and theoretical f₀ from SH amplification were evaluated using the reflectivity method (Kennet, 1983), whereas the seismic bedrock (H_{seis_bed}) came from the depth for which the resonance frequency, provided by simplified Rayleigh’s method (Dobry et al. 1976), is close to the value of the measured f₀. The V_S profiles were selected from 935 real sites: 602 are from Kiknet network (http://www.kyoshin.bosai.go.jp/), 243 from California (Boore, 2003; http://quake.usgs.gov/~boore), 21 from European strong-motion sites (Di Giulio et al. 2012), 33 from French (Hollender et al. 2018), and 36 are Italian sites from ITACA database (D’Amico et al. 2020). The complete list of the 935 stations is given in Di Giulio et al. (2019). The maximum depth of investigation is 600 m, but the majority of the sites does not exceed the depth of 300 m. For 15 profiles having shear-wave velocity larger than 800 m/s starting from the surface, we set H₈₀₀ equal to 1 m. A number of 18 sites within the analyzed profiles never reach a shear-wave velocity of 800 m/s.

Scatter plots for the different pairs of indicators are shown in Fig. 2: f₀ & V_S30; f₀ & H_{seis_bed}; f₀ & H₈₀₀; and H₈₀₀ & V_S30. As expected, the seismic (H_{seis_bed}) and the engineering (H₈₀₀) bedrock depths are inversely proportional to f₀: the deeper the seismic interface, the lower the corresponding resonance frequency (Fig. 2b, c). V_S30 is increasing with f₀ (the softer the surface layer, the lower the resonance frequency; Fig. 2a), and is decreasing with increasing H₈₀₀ (the softer the surface layer, the deeper the engineering bedrock depth; Fig. 2d).

Fig. 2

Scatter plot for the pairs of indicators: a f₀-V_S30, b f₀-seismic bedrock depth, c f₀-H₈₀₀, d H₈₀₀-V_S30. The gray circles show the values computed at 935 sites, the square symbols indicate the values at the real sites listed in Table 4. The geometric mean and the mean ± 2 standard deviation are computed assuming logarithmic bins along the x-axis and they are reported as black thick and thin lines, respectively. The mean curves and associated variability are given in the "Appendix" material ("Appendix" Tables 17, 18, 19 and 20)

Spearman’s rank correlation coefficient (Spearman, 1904) was also computed between each pair of indicators used in the scatter plots. This coefficient (Fig. 3) describes how well the relationships in the scatter plots can be described by a monotonic function, and the sign of the coefficient reflects the direction of the relationships between indicators. The histograms of Fig. 3 show that the highest degree of correlation is shown by the pair f₀-V_S30 (coefficient equals to 0.79), which is the only one with a positive sign. The remaining pairs show a Spearman’s correlation coefficient fairly high (from 0.69 to 0.75 as absolute value), except the pair H_{seis_bed}-V_S30 that shows the lowest value (− 0.36).

Fig.3

Spearman’s correlation coefficient for the pairs of indicators

However, the plots of Fig. 2 show a larger scatter, together with a shortage of data (i.e. few samples) at low frequencies (panels a, b, c). They thus cannot be considered representative for deep sites, i.e. when f₀ is less than 0.3 Hz or when the depth of the stiff interface (H_{seis_bed} or H₈₀₀) is larger than 200 m, because of the limited number of samples in our data set. A large scatter is also observed in the high-frequency (> 10 Hz) range in the f₀—H_{seis_bed} scatter plot (Fig. 2b), where H_{seis_bed} varies from a few meters up to 100 m.

From the plots of Fig. 2, we assume that the consistency between a pair of indicators is quantified in a binary way depending on whether or not it falls within the confidence interval given by ± 2 standard deviations around the geometric mean (black lines in Fig. 2): we precautionary assume cs_k = 1 when the values of a site is within this range.

As shown in Fig. 2, the resonance frequency f₀ is a very important indicator in our strategy and is therefore present in three over four scatter plots of Fig. 2. However, in case of a site that does not show a resonance peak, the scatter plots of Fig. 2a, b, c cannot be used to verify the consistency between indicators. This is why cs_k in Eq. 3 can be assumed equal to 1 (for k = 1,2,3) even when a site does not show a resonance peak (e.g. flat H/V curves), but is classified as a stiff soil or bedrock site from geological and geophysical consideration (Pilz et al. 2020; Lanzano et al. 2020).

Regarding the consistency between V_S30 and surface geology, we recommend to check it by using the velocity ranges associated to the different lithological groups listed in literature data or based on regional V_S30—surface geology relationships (if available). Specifically, some reference range of shear-wave velocity for different European soils (soft and stiff clay, loose and dense sand, gravels) and rocks (weathered and competent rocks) can be found in Foti et al. 2018 (Table 3 in their work). Other indication of the expected V_S30 for different geological categories (on the basis of age, grain degradation and depositional environment) are reported in Stewart et al. (2014) for Greece, in Parker et al. (2017) for Central and Eastern North America, in Xie et al. (2016) for China area, in Michel et al (2014) for Swiss sites and Mital et al. (2021) for different terrain classes in United States. For Italy, Forte et al. (2019) proposed a soil classification considering 20 geological-lithological complexes; they made available a stand-alone software for database interrogation that gives the median and standard deviation of V_S30 after defining the coordinates of the site. All these studies dealing with V_S30 and surface geology depend from a starting soil-profile database built on site-specific measurements, and then extrapolated to a large scale using geological information or terrain map-based models including topographic slope or geomorphic terrain classifications (Yong 2016). It is also possible to have values of V_S30 at a finer spatial scale using available observations from previous studies performed in the area where the station is located, e.g. information from microzonation activities (such as Amanti et al. 2020 for the Central Apennine or Saroli et al. 2020 at municipal scale), or from existing geotechnical-engineering database (Passeri et al. 2021).

Studies investigating the distribution of V_S30 are still few (Mital et al. 2021), and almost all the works cited above give a mean value of V_S30 for a certain geological-lithological layer, with the uncertainty that are expressed as standard deviation or through a range within a minimum and maximum value. For evaluating cs_k between V_S30 and surface geology, especially in case of regional relationships, we suggest in a precautionary way to select as velocity uncertainty two standard deviations, or the full range between the minimum and maximum value in the provided distribution.

In the QI3 computation, we didn’t consider the V_S30 & H_{seis_bed} pair because the shallow depth limitation of V_S30 makes its relationship to the seismic bedrock depth meaningful only when the stiff interface is very shallow (i.e. at a depth < 30 m). The scatter plot of this pair of indicators is actually shown in Fig. 4 and displays a very large variability over the entire range of x- or y- axis, consistently to the low value of Spearman’s correlation.

Fig. 4

Scatter plot for the couple H_{seis_bed}-V_S30. The color scale is proportional to the soil class category, following the classification of EC8 building code (CEN 2004)

3 Quality metrics computation at real sites

Once the three quality indices (QI1, QI2 and QI3) are computed, the final quality index (Final_QI) for the overall characterization of a site is conclusively computed as arithmetical average between QI2 and QI3:

$$ {\text{Final}}\_{\text{QI}} = \left[ {{\text{QI}}2 + {\text{QI}}3} \right]/2 $$

(4)

As previously described, QI2 accounts for the presence of the relevant indicators (Eq. 2) and QI3 for the consistency of their values (Eq. 3). The range of Final_QI is spanning from 0 to 1: a value of 1 is assigned to a site with a detailed and good seismic characterization, 0 is for a site poorly or not characterized.

We verify this quality procedure by applying it to seven seismic stations (Table 4) of two permanent seismic networks of Italy: INGV National seismic network (network code IV; https://doi.org/10.13127/SD/X0FXnH7QfY) and the strong-motion network operated by Presidency of Council of Ministers-Civil Protection Department (network code IT; https://doi.org/10.7914/SN/IT). The soil class of the investigated stations (Table 4) following the EC8 seismic code (CEN 2004) is B or C; these are the most common classes for sites of the seismic networks in Europe (Felicetta et al. 2017).

Table 4 List of indicators extracted at seven real sites from the available reports

The location of the seven sites and the information on their site characterization are available online through public reports at the Italian Accelerometric Archive (ITACA; http://itaca.mi.ingv.it; D’Amico et al. 2020) and at the Engineering-Strong Motion database (ESM; https://esm-db.eu; Luzi et al. 2020). The geological and geophysical reports can be downloaded from the stations section of these databases. Table 4 shows the available indicators extracted from the reports; the corresponding values are also plotted in the scatter plots of Fig. 2 as squared symbols. All the sites of Table 4, with the exception of IT.CSM, have several information provided from ad-hoc geophysical and geological surveys carried out within recent national projects for site characterization of permanent networks (e.g. Bordoni et al. 2017; Cultrera et al. 2018) or from microzoning studies. IT.PNG has partial information due to the lack of direct measurements of shear-wave velocity profile in proximity of the station, and V_S30 is inferred by correlation with topography (https://esm-db.eu; Luzi et al. 2020) and soil class by first-level microzonation study (Zarrilli and Moschillo 2020).

We detail below the step-by-step quantitative quality assessment at IV.ROM9. Many geophysical measurements were performed at this site for recovering the local velocity profile, such as down-hole (DH) and cross-hole (CH) tests (up to 70 m deep; Cercato et al. 2018), and 2D passive surface-wave array experiments, together with a geological map based on ad hoc field survey (Bonomo et al. 2017). The 2D passive array analysis should be considered as independent from invasive surveys because it was done before the profiles from DH and CH were made public. As an example of the information available at IV.ROM9, Fig. 5 illustrates a set of H/V noise spectral curves (panels a and b), the comparison of the velocity profile V_S obtained from different methods (panel c) and the geological map (scale 1:5000) in panel d. A total of 36 points of noise measurements of a few hours, through three 2D passive arrays of increasing spatial aperture around the location of IV.ROM9, showed consistently a resonance frequency at 1 Hz (see Fig. 5b). This ensures the spatial stability of the 1 Hz peak, which is also stable with time (Fig. 5a), with a possible additional and weaker peak also at 0.4 Hz. In the next of the quality evaluation, we consider the f₀ value of IV.ROM9 equal to 1 Hz (Fig. 5b). Three different V_S profiles (Fig. 5c) are available from direct measurements but none of them was indicated at the best model before our analysis. The “amv” model shows i) a deeper interface, with a velocity contrast of about 2, at about 170 m that is related to the f₀ peak at 1 Hz, and ii) a lower velocity at the surface in comparison to the profiles obtained by invasive methods (Fig. 5c). It is not so uncommon to get different V_S profiles by using different data and techniques, especially when data are collected at different times and analyzed by different teams in a blind way. In general, amv methods based on surface-wave analysis can provide lower velocities in the uppermost part of the profile with respect to DH and CH surveys (Passeri et al. 2021). This discrepancy may be related to the grouting hole operations, to the different volumes investigated by the methodologies, and to the lower resolution of surface-wave methods in resolving very thin layers. As authoritative choice of the best V_S profile, we considered a combined one, obtained by the CH up to a depth of 70 m (the invasive method which is considered as the most reliable for the near-surface part; Di Giulio et al. 2018), and by the joint surface-wave amv model that is characterized by a deeper investigation capability (inset of Fig. 5c). In similar cases, when more measurements for the same indicator are available, it is recommended that the authoritative solution, obtained by expert judgement, is indicated in the seismic databases collecting information for the stations together with a synthesis report.

Fig. 5

IV.ROM9 station. a H/V noise spectral ratios using the continuous recording of IV.ROM9 (sensor Trillium 120 s); the results of the first two months of 2015 are shown. H/V noise spectral ratios of the geophysical survey (sensor Lennartz 3d-5 s); the mean curves of 12 measurements (each of about 2 h of time length; recording day 9 March 2017) are overlaid. c V_S profile obtained through surface-wave inversion of ambient vibration data (amv), from crosshole (CH) and downhole (DH). The inset shows the best velocity profile obtained combining the CH and the amv model. d Geological map (scale 1:5000) after the field survey (Bonomo et al. 2017)

QI1 evaluation at IV.ROM9 of each indicator is summarized in Table 5, together with an explanation of the chosen values. Three indicators (f₀, surface geology and soil class) give a QI1 equal to 1, i.e. the maximum value, meaning that they have been computed with reliable methods (factor a_MS = 1 in Eq. 1), direct measurements (b_ID = 2), confident estimates (c_MI = 1) and well documented reports (d_RC = 1). One of the SESAME (2004) criteria uses a threshold of 2 in the H/V peak amplitude (assuming a squared average of the horizontal components in the H/V analysis). The amplitude peak is not above 2 for all the 36 points of noise measurements at IV.ROM9, although very close to this threshold value (Fig. 5b). For the indicator f₀ the factor c_MI, which is connected to the proper method implementation and interpretation of the results, was evaluated equal to its maximum value (c_MI = 1) due to the consistent shape of the H/V curves around 1 Hz (Fig. 5b), and to the spatial and time stability of the H/V peak obtained from multiple measurements.

Table 5 QI1 computation (Eq. 1) for the 7 recommended indicators at station IV.ROM9, together with the factor values and the indication on how they have been evaluated. Similar tables for the other selected stations are shown in the "Appendix" (from "Appendix" Tables 11, 12, 13, 14, 15, 16)

The remaining four indicators have a lower QI1 value: 0.67 for V_S, V_S30 and H_{seis_bed}, 0.33 for H₈₀₀. This is related to the factor c_MI which was set to 0.5 for both V_S, V_S30 and H_{seis_bed} considering the discrepancies observed in the velocity profiles (Fig. 5c), and equal to 0 for H₈₀₀ (Table 4).

Concerning the V_S30 value, the measurements return 532 m/s for down-hole survey (DH), 605 m/s for Cross-Hole test (CH) and 414 m/s for surface-wave inversion of passive data (Table 4). Each method is considered a direct measurement (factor b_ID = 2) and has its own resolution in resolving thin layers (Fig. 5c), and the surface-wave inversion was performed independently with respect to the invasive methods. Such discrepancy in the V_S30 value is also due to the presence of a velocity inversion that is identified by the CH and DH methods, which was not considered during the model parameterization in the surface-wave array analysis, and to the difference between areal and discrete measurements. For these reasons the factor c_MI of the V_S30 indicator was set equal to the intermediate value of 0.5.

About the seismic bedrock (H_{seis_bed}), the surface-wave analysis only is able to find it at a depth of about 170 m (Fig. 5c). However, the factor c_MI relative to H_{seis_bed} was set equal to 0.5 (Table 5). This because the assumption of considering the H/V as Rayleigh-wave ellipticity during the inversion step of analysis, not including the possible bias from Love or body waves (Hobiger et al. 2009; Knapmeyer-Endrun et al. 2017), as well as the presence in the area of further H/V peaks at lower frequencies (Marcucci et al. 2019), needs to be verified more in detail.

For the H₈₀₀ indicator, the shear-wave velocity profile derived from surface-wave analysis exceeds 800 m/s only in the deep basement layer (at a depth of 170 m), conversely the CH and DH surveys exceed 800 m/s several times in the uppermost profile: the first time is at a depth of 6 m (CH) and 14 m (DH). The velocity value of 800 m/s is maintained for very thin layers (Fig. 5c), while at the bottom of such layers the velocity returns to lower values than 800 m/s. The factor c_MI for the H₈₀₀ indicator was set equal to 0 (Table 5) for such discrepancy among the CH, DH and surface-wave profiles, too large even if we take into account the lower resolution of the ambient vibration methods in solving thin surface layers. However, H₈₀₀ in the European code is defined as “the depth of the bedrock formation identified by shear-wave velocity larger than 800 m/s” and it is not specified if it is the depth which it first exceeds 800 m/s (as assumed in this and companion paper), or the depth below which the velocity is always larger than 800 m/s.

Finally, the c_MI values indicated in Table 5 reflect the lack of consistency for certain indicators (H₈₀₀, V_S30, V_S) caused by the absence of a final site characterization summary report which combines the various V_S estimates providing an authoritative V_S profile, e.g. as proposed by the Swiss Seismological Service (SED) at ETH Zurich (2015); https://stations.seismo.ethz.ch//. The presence of such a summary report (see companion paper Cultrera et al. 2021) will most probably increase the c_MI value and related Q1.

Once the QI1 for each available indicator is computed (Table 5 and "Appendix" material), it is straightforward to compute the second index QI2 by applying Eq. 2 with the weights of Table 3. QI2 accounts for the number and importance of the most appropriate indicators, and it is equal to 0.79 in the case of IV.ROM9; the low QI1 for V_S30 and H₈₀₀ does not significantly affect the QI2 value because of the smaller weight of these indicators.

To evaluate QI3 (Eq. 3), we checked the consistency cs_k between pairs of indicators on the basis of the scatter plots in Fig. 2 (mean values with uncertainties are available in Tables 17, 18, 19 and 20 of the "Appendix"). The square symbols of Fig. 2 referring to IV.ROM9 fall within the confident area (mean ± 2 standard deviations), except for the pair f₀—H₈₀₀ (in panel c) where the values given by DH and CH surveys are out the standard deviation limit. Therefore, cs_k is set equal to 1 for the pairs corresponding to the scatter plots of panels a, b and d, and cs_k is set equal to 0 for the pair f₀—H₈₀₀ of panel c (Table 6). The cs_k is set 1 also for the correlation between V_S30 and surface geology: although the different surveys give three values of V_S30 spanning from 414 to 605 m/s (see Table 4), such velocity range is compatible with the ignimbrite tuff formation (Fig. 5d) described in the geological report, and within the expected velocity values of the near-surface layer in the area (Pagliaroli et al. 2014; Marcucci et al. 2019). The QI3 value at IV.ROM9 is then equal to 0.8 and the resulting Final_QI (Eq. 4) is 0.8.

Table 6 Quality indices for the selected seismic stations

The evaluation of QI1, QI2, QI3 and the Final_QI are reported in Table 6 for all the analyzed stations. The station IV.CDCA has the best site characterization, meaning that all the indicators are well computed and their consistency is verified. The worst classification is for IT.CSM, where direct measurements were not performed and only surface geology (from geological map 1:25,000) and soil class (from topography) are available in seismic databases.

IT.MCA is also well characterized; at this site the H/V noise curve does not exhibit any peak (flat H/V curve) and consistently the basement in the geological report is indicated as nearly outcropping although fractured and weathered (soil class is B). The cs_k for four pairs were set equal to 1 (Table 6) because the absence of a f₀ agrees with the geological description (stiff rock outcrops) and with the values retrieved for V_S30 and H₈₀₀ from station reports. However, the depth of bedrock H_{seis_bed} is ambiguous because H₈₀₀ is found at a depth of 29 m, and presumably H_{seis_bed} is at larger depth and then not properly outcropping as indicated in the report. QI3 was 0.8 because the cs_k for the pair f₀-H_{seis_bed} was set equal to zero.

IV.LAV9 has approximately the same Final_QI of IV.ROM9, even though it is characterized by a lower QI2 and higher QI3; the former is due to some mismatches between the outcome of the nearby geophysical surveys, and the latter because the indicators values are all consistent according to the scatter plots of Fig. 2. IT.ORC has the maximum value for QI1 and consequently QI2, but it is penalized by the inconsistency between pairs of indicators as derived from scatter plots (Fig. 2).

IT.PNG has a Final_QI with intermediate value among the other stations, and the 0.42 overall quality value is fairly low (Table 6). This is due mostly to the lack of direct measurements of V_S and H₈₀₀. The absence of the H₈₀₀ indicator leads to cs₃ and cs₄ equal to 0. cs₂ is also 0 because there is inconsistency for the couple f₀-H_{seis_bed} (0.54 Hz and 45 m), suggesting a wrong identification of (at least) one of these indicators. A specific study (Saroli et al. 2020), although focused in a neighboring area located a few kilometers North of IT.PNG, seems indeed to suggest a deeper seismic bedrock.

In summary, Table 6 shows very clearly that stations with direct and reliable measurements at a large number of indicators get a much higher quality assessment than stations with only inferred values, but that consistency checks between pairs of indicators significantly modulate the final_QI.

4 Discussion and conclusion

We propose a strategy to assess the quality of site characterization at seismic stations, through relatively simple metrics based on the available information at the station. The quality metrics strategy needs to be as much as possible independent from subjective choices, and an expert judgment is requested to compute the final quality index, because a careful examination of the site information when present from past studies is required by our strategy. We believe that the quality indices evaluation, and the crosscheck of each selected indicator is in the responsibility of the analysis team and/or of the network operators involved in site characterization, with the final aim to associate high-quality metadata to the ground-motion recordings.

The quality evaluation is provided by a single scalar value (Final_QI; Eq. 4), ranging from 0 to 1, that takes into account the number and reliability of a few (7) relevant indicators (through QI1 and QI2), and their mutual consistency (QI3) evaluated between five pairs of indicators. In the absence of locally calibrated analyses, the consistency is evaluated using scatter plots based on the shear-wave profiles of 935 real sites.

In particular, in the QI and QI2 evaluation we make use of a weighting scheme which assigns a larger grading to direct measurements compared to inferred values. It is worthy to note that a similar classification criteria was recently proposed by Lanzano et al. (2020) for Central Italy seismic stations. Whereas our finality is to rank the site characterization at strong-motion stations whatever their stiffness, these authors were interested in discriminating reference rock sites, i.e. seismic stations unaffected by local amplifications to be used for improving the prediction of site-specific ground motion.

Moreover, to correctly compute the quality index in our classification criteria, it is necessary to have an unambiguous definition of the main indicators used for seismic site characterization, and recommendations on how to compute them including uncertainties. The details of measurements and computation methods should be reported in a concise form to allow the evaluation of their reliability as addressed in Cultrera et al. (2021).

Our strategy has been applied to seven real seismic stations; the Final_QI values (Table 6) prove the feasibility of the approach in obtaining a quantitative assessment of the overall quality of site characterization for seismic applications. In general, direct and rigorous measurements yield better results and allow a reliable picture of the site condition through the selected indicators. However, we are aware that some significant open issues emerge from this work:

• f₀ enters in three over the four pairs of indicators for which the consistency of QI3 is computed (see Fig. 2). f₀ is actually the indicator that obtained the largest consensus from the online questionnaire as explained in the Cultrera et al. (2021), and a proper evaluation of f₀ is thus very important in our strategy. For this aim, it is preferable to analyze large time-periods of ambient noise rather than some hours. This kind of analysis can be easily implemented in seismic networks for many modern stations, which are typically six-channels (i.e. velocimeter and accelerometer) recording in continuous mode (Fig. 5a). When this is not possible, several single-station noise measurements of a few hours (Fig. 5b) and repeated in time should be performed in a target site. Anyhow, our strategy is not applicable when a site, although with a good seismic characterization, doesn’t show a clear resonance frequency and simultaneously cannot be classified as a bedrock site from geological or geophysical consideration. This family of stations, i.e. stiff and soft sites with no recognizable f₀, needs other proposals to be properly included for the evaluation of the quality metrics. These sites could be possibly characterized by the absence of a sharp seismic contrast, or by valley edge effects that bias the 1D resonance behavior.

• It is important to homogenize site information at seismic networks, and increase the number of case studies in different environments to enlarge the samples used for the scatter plots. Scatter plots are built using a simplified 1D approach with the aim to check the consistency between different indicators. Some sites with 2D or 3D effects may behave as outliers in the present (1D) scatter plots, and low-quality metrics could suggest the occurrence of such complex site effects.

• Subjective criteria of the analyst in the indices evaluation should be reduced as much as possible. Nevertheless, an expert judgment is required by our strategy in the QI1 definition and in particular in the evaluation of factor c_MI, because QI2 is automatically and independently computed through Eq. 2, and QI3 can be evaluated using scatter plots. In order to avoid an incorrect judgment of QI1 for the seven site indicators, we recommend that an expert team on site characterization should be in charge of the evaluation of the quality factor on the basis of available information retrieved from seismic databases, public reports or specific studies. The tables and examples supplied in the main text and appendix of this work, although not exhaustive of all situations that can be found at real sites, are aimed at providing indication and assisting in a proper attribution of the quality indices.

This study represents a tentative proposition to quantify the quality of site characterization at seismic stations. Such a proposition can certainly be improved, and should be modified after a few years to take into account the experience and feedback from users, possible discussions and improvements about the list of “most recommended” indicators, and the availability of new, widely accepted guidelines for the acquisition of site parameters. Further studies are needed to test the performance of our strategy on a large number of real sites, expanding the discussion into the scientific community with other end-users including building code operators. The quality values (especially QI1 and Final_QI) can be introduced easily in the station book of online seismic databases. As proposed by the SERA project, the metadata site xml file with enclosed quality values can be indicated in the station xml file (Cornou et al. 2020).

Some decades ago, the site characterization was only binary: rock or soil. It was progressively replaced in the late 90 s by some continuous parameters, mostly V_S30, the use of which is now so common that it is included in all strong motion databases as the main site information, and can therefore be used also in ground motion prediction equations (GMPEs). In a similar way, the “quality” of such a site information has been recently introduced in a simple, binary way, i.e., “measured” or “inferred”, and the within-event variability modulated according to this binary classification (Chiou and Youngs 2008; Derras et al. 2016). The “continuous” quality index proposed here might help, once implemented in strong (and weak) motion data-bases, to improve GMPEs by including a continuous (rather than binary) dependence of the within-event variability of the quality of site metadata, and to obtain more appropriate hazard estimates at a target site. It could constitute a strong incentive for all network operators, GMPE developers, and the whole earthquake engineering community, to emphasize the importance of the quality of site metadata, and the need to invest on direct site measurements. We are aware however, that it is only a long term objective, as the concept presented in these two companion papers needs first to be accepted, then probably improved after comprehensive feedback from various worldwide network operators, and finally routinely implemented in the strong motion databases.

Appendix

The next Tables 7, 8 and 9 report examples (after Di Giulio et al. 2019) for the assignment of factors a_MS, b_ID, and c_MI in the QI1 definition (Eq. 1 of the main text). Tables 10 refers to histograms of Fig. 1 of the main text. Tables 11, 12, 13, 14, 15 and 16 show the QI1 assignment for the real stations that were analyzed in this paper. Tables 17, 18, 19 and 20 refer to the scatter plots of Fig. 2 of the main text.

Table 7 Example of some peer-reviewed papers connected to each indicator to estimate factor a_MS in Eq. 1. The list is not exhaustive

Table 8 Criteria to estimate the factor b_ID in Eq. 1 (direct or inferred evaluation of the target indicator)

Table 9 Some examples to estimate factor c_MI in Eq. 1

Table 10 Background data for the histograms of Fig. 1

Table 11 QI1 (Eq. 1) for the 7 recommended indicators at station IV.CDCA

Table 12 QI1 (Eq. 1) for the 7 recommended indicators at station IV.LAV9

Table 13 QI1 (Eq. 1) for the 7 recommended indicators at station IT.ORC

Table 14 QI1 (Eq. 1) for the 7 recommended indicators at station IT.MCA

Table 15 QI1 (Eq. 1) for the 7 recommended indicators at station IT.CSM

Table 16 QI1 (Eq. 1) for the 7 recommended indicators at station IT.PNG

Table 17 Scatter plots of Fig. 2: mean values and related standard deviation

Table 18 f₀-seismic bedrock depth

Table 19 f₀-H₈₀₀

Table 20 H₈₀₀-V_S30