V_s30 Derived from Geology: An Attempt in the Province of Quebec, Canada

Abstract

The influence of local site conditions is important when assessing the distribution of building damage and seismic risk. The average shear-wave velocity of the top 30 m of soil, V_s30, is one of the most commonly used parameters to characterize site conditions. Topographic slope is one of the proxies used to estimate V_s30 and is often used as a preliminary estimate of site conditions since a dataset is available worldwide at a resolution of 30 arc-seconds. This paper first proposes to compare the accuracy of V_s30 derived from topographic slope against detailed V_s30 zonation in five regions of the province of Quebec, Canada. A general underestimation of V_s30 is observed and site class agreement varies between 18 and 36% across the regions. Secondly, an approach is proposed to improve regional estimates of V_s30 where detailed site characteristics are not available other than the local topography and surface geology information. The surface deposit types from the geological map of Quebec are compared to V_s30 data previously obtained for zonation maps of Montreal, Saguenay and Gatineau in order to estimate V_s30 as a function of sediment deposit types as an alternative to the slope approach. A site class map for the province of Quebec is then proposed.

1. Introduction

Local site conditions play an important role in the distribution of the intensity of ground motions in the event of moderate to large earthquakes. Indeed, different types of soil can amplify or de-amplify seismic waves, leading to variations in shaking intensity over small geographic areas. Loose, less compacted soils, such as sand or clay, tend to amplify seismic waves more than stiffer, more compacted materials. In particular, soils with lower stiffness are more prone to significant deformation under seismic shaking, while stiffer soils tend to resist deformation [1,2,3,4,5,6,7]. This phenomenon, known as site amplification, occurs because softer soils have lower shear-wave velocities, which causes seismic waves to travel more slowly and become more focused in these layers, resulting in stronger shaking at the surface. For example, during the 1995 M6.8 Kobe earthquake in Japan, Finn et al. [1] described that both vertical and horizontal seismic waves traveling into the layer of alluvium (mainly clay) were amplified to a factor up to 4 compared to their amplitude measured in the underlying rock of the Rokko mountain zone, resulting in liquefaction phenomena at the surface. An increase in the duration of the ground shaking up to a factor of 1.5 was also measured.

In the region of Montreal, clay deposits from the ancient Champlain Sea can result in an average amplification factor of up to three depending on the frequency content of the incoming seismic waves [8,9,10,11,12]. Local amplification effects are exemplified by the observed damage to the masonry of the Montreal East City Hall during the M5.9 1988 Saguenay earthquake [13,14]. Chouinard and Rosset [15] estimated an amplification factor of four for the 17 m clay deposit layer with a frequency of 2.5 Hz that matched the frequency of the building. Since 2000, extensive field studies have been performed to characterize the dynamic properties of local soils in the region of Montreal [6,16,17,18].

The most common descriptor of site characteristics is the time-average shear-wave velocity of the top 30 m of soil (V_s30), which is commonly used by researchers and practitioners to define site classes and to estimate the local amplification factors [5,6,8,19,20,21,22,23]. In many instances, information may not be available at some locations, and a common proxy is to use the US Geological Survey (USGS) relation between V_s30 and the topographic slope [19,24,25,26], which is available at the global scale on a regular grid of 30-second arc. However, in regions of glacial deposits, this method may be less reliable due to the complex and heterogeneous nature of these deposits. Glacial regions often feature a mix of unconsolidated materials like sand, gravel and till, as well as solid bedrock, leading to significant variations in shear-wave velocities over short distances [27]. In the region of Montreal, Rosset et al. [28] compared seismic residential risks by using a detailed microzonation map and the USGS proxy map. The USGS proxy map resulted in 30% higher losses than the ones calculated with the detailed map due to an underestimation of V_s30 in flat areas where glacial till sediments are observed.

The regional biases of the USGS approach can be reduced by including geological information in the estimation of V_s30 and evaluating the bias related to the slope and the geology [29,30,31,32]. Other models that correlate geological data to V_s30 or site classification have been proposed in Europe. For instance, Weatherill et al. [33] have developed a model of V_s30 for Greece that combines data on terrain type, surface geology (age) and surface gradient information. In Italy, Di Capua et al. [34] created a model based on surface geology (lithology) and additional criteria such as geological age, consistency and terrain structure. In Portugal, Vilanova and al. [35] similarly have used a stratigraphic classification from geological data at 1:500,000 to 1:50,000 scales and V_s30 measurements.

In the province of Quebec (Canada), several V_s30 maps have been produced for the most populous and seismically active urban areas: Montreal, Quebec City, Ottawa-Gatineau and Saguenay ([36,37,38,39,40,41], respectively), as shown in Figure 1a. The maps are derived from a combination of region-specific borehole and seismic data. For the Saint Lawrence River Valley, Nastev et al. [42] developed a four-layer model using borehole data and associated shear-wave velocity (Vs) profiles to create a V_s30 map over a regular grid of points (Figure 1b).

In the following, the V_s30 mappings from detailed studies are compared to the USGS model site estimates. Next, the surface geology information is correlated to the V_s30 from the detailed zonation maps in order to derive the distribution of the V_s30 value for each type of soil. A relation with depth to bedrock is then derived to improve local estimates of V_s30 over unmapped regions.

2. Materials and Methods

2.1. V_s30 Comparison Between Zonation Map and USGS Model

V_s30 data derived from the slope topography by the USGS are available on a regular grid in a raster format with a resolution of 30 arc-seconds (0.008 degrees), which corresponds to a 600 by 900 m grid in longitude and latitude for Quebec [24]. A comparison of site classes, as given in the National Building Code of Canada [43], between the USGS-based estimates and the detailed map is performed on a regular grid of 500 m. This grid corresponds to the resolution for the Saint Lawrence Valley, which has the lowest resolution of the different regions. Considering a higher resolution could increase the discrepancy between the V_s30 data from the zonation map and the USGS. A score of 0 is given when the classes are similar between the two maps, and a negative score is given when the USGS site class is higher than the detailed zonation (from –1 to –4, depending on the difference in the number of site classes). Conversely, a positive score is given similarly (

Table 1. Score applied to compare site classes from USGS and zonation.

Score		USGS Site Class					Vs30 (m/s)
		A	B	C	D	E
Zonation Site Class	A	0	−1	−2	−3	−4	>1500
	B	+1	0	−1	−2	−3	760–1500
	C	+2	+1	0	−1	−2	360–760
	D	+3	+2	+1	0	−1	180–360
	E	+4	+3	+2	+1	0	<180

). Rosset et al. [36] used a similar approach to perform the comparison of maps for the Greater Montreal Area. For Greater Montreal, Ottawa-Gatineau, Saguenay and the Saint Lawrence Valley, maps are provided in terms of V_s30, while in Quebec, it is provided as site classes.

2.2. Distribution of V_s30 in Each Region

The second part of the analysis concerns the comparison of the sediment types from the geological map and available V_s30 data in the different regions, as shown in Figure 1.

In Greater Montreal, the V_s30 dataset is complemented by values estimates from the borehole profile of the Quebec Transport Ministry considering a simplified 3D geological model with associated relations between shear-wave velocity (Vs) and depth for backfill, alluvial sand, marine clay and glacial deposits, as detailed in Rosset et al. [6].

The zonation of Gatineau (included in the Ottawa zonation) has been developed using similar data from seismic non-invasive methods and borehole and is reported in detail in Hunter et al. [38,39].

In the Saguenay region, the mapping of V_s30 was performed using a 3D geological model and the representative Vs-depth functions derived from SPT/CPT data [40]. The authors shared a map in a raster format V_s30 sites derived from the 3D geological model with a pixel resolution of 75 m.

The Saint Lawrence Valley zonation [42] is based on a simplified 3D model as proposed in Greater Montreal with a larger extent, as shown in Figure 1b. The authors provided us with a grid of points with a distance between points of about 500 m.

Finally, the Quebec zonation provided by Perret et al. [37] consists of a map in vector format with zones in terms of site classes. It has been developed using an extensive dataset of boreholes calibrated in several areas with non-invasive seismic measurements and completed by geological information in areas without boreholes.

3. Results

3.1. V_s30 Comparison Between Zonation Map and USGS Model

The score matrix in Table 1 is used to compare the V_s30 values between USGS and the ones detailed by microzonation for the Greater Montreal, Saguenay, Quebec City and Ottawa-Gatineau (Figure 2, Figure 3, Figure 4 and Figure 5, respectively). Figure 6 shows the distribution of the scores for the Saint Lawrence Valley zonation from Nastev et al. [42].

In general, the percentage of matching site classes is less than 30% (16 to 29%). Positive scores vary between 9 and 34%, and negative scores are the most frequent with a ratio of up to 64% for the region of Montreal. This indicates that V_s30 from the USGS underestimates the true velocity for most sites. In the regions of Montreal, Quebec City and Saint Lawrence Valley, a negative bias of one-site-class difference dominates with 40% of the sites (Figure 2, Figure 4 and Figure 6, respectively). For other regions, the scores are distributed almost equally between −1 and −2 scores.

For most regions, a reasonable agreement has been reported between slope and V_s30 [35,36,37,38,39,40,42,43,44]; however, the predictive performance of slope to V_s30 models is highly dependent on the geological and stratigraphic unit, and may not be appropriate for some regions. As mentioned in Salsabilli et al. [40], in regions where changes in soil deposit composition are relatively gradual, geological data are often sufficient, but in regions such as glaciated or river basins with complex layering, stratigraphic details improve accuracy. The best results could be obtained by combining both slope and geological data with geotechnical data.

3.2. Distribution of V_s30 in Each Region

The most accurate data are first considered and concern the V_s30 sites derived from seismic measurements and geotechnical or borehole profiles in the case of Gatineau and Greater Montreal. For Saguenay, each centroid of the raster map is considered to identify the sediment type. Similarly, for the Saint Lawrence Valley, the points of the grid are used to identify sediment types. The polygons in terms of site classes in Quebec City are converted into a grid of points with an equidistance of about 500 m and associated with sediment types. They are not directly used to correlate V_s30 and sediment types since they are given only in terms of site classes.

The distribution of V_s30 values in the five regions highlights significant variations in soil stiffness, as reflected by median and mean values listed in

Table 2. Statistical data for the different regions.

Investigated Regions
Statistical Parameters	Greater Montreal	Gatineau	Saguenay	Saint Lawrence Valley	Quebec City *
Number of samples	53,966	1474	95,189	182,857	2312
Mean	1055	690	711	1167	1.9 (B)
Median	1109	480	494	1125	1.0 (A)
First quartile	444	212	281	638	1.0 (A)
Third quartile	1600	1300	1040	1500	3.0 (C)
Minimum	110	152	172	159	1.0 (A)
Maximum	3288	2380	2330	2500	4.0 (D)
% in class A	38	20	9	17	54
% in class B	23	22	19	52	15
% in class C	24	15	35	18	20
% in class D	14	24	35	11	12
% in class E	1	19	1	2	0

* The Quebec City zonation is expressed in terms of site classes converted to integers with the site class indicated in brackets (A = 1 to E = 5).

.

The Saint Lawrence Valley zonation region, the largest surface of the investigated ones, has the highest median (1125 m/s) and mean (1167 m/s) V_s30 values and the smallest variance, indicating a relatively homogeneous geology with predominantly rock (52% of site class B).

In contrast, the Saguenay region has the lowest median (480 m/s) and mean (690 m/s) V_s30 with the highest percentage of site class D (35%), indicating predominantly softer sites in the riverbeds of the Saint-Jean Lake and Saguenay River.

In Gatineau, the distribution of V_s30 values is more uniform than in other regions with the percentage in each of the site classes from A to E around 20% and the highest percentage of site class E. For Greater Montreal, median (1055 m/s) and mean (1109 m/s) indicate predominantly stiff soils, with site classes A and B representing 61% of the total.

The distribution in Quebec City is more homogeneous over the site classes A to D, but the comparison with other regions is difficult due to the low number of samples and the missing V_s30 values, which are replaced, by site classes.

The boxplots in Figure 7 are a graphical representation of the distribution of Vs₃₀ from Table 2 for the four regions where V_s30 data are available. In the Greater Montreal Area, stiffer sites are predominant compared to other regions, with 61% of the sites in classes A and B, and high maximum values for V_s30. This is mainly a result of the approach used by Rosset et al. [6] to calculate V_s30 as a function of Vs for the different geological bedrock units in the region.

3.3. Correlation Between V_s30 Data and Surficial Sediments

The Ministère des Ressources naturelles et des Forêts of Quebec provides a detailed mapping of the surficial geology [45]. It shows recent sediments grouped by deposition types and bedrock (Figure 8).

For each zonation map, each site with a V_s30 value is associated with the types of sediment in the geological map. For that purpose, the code associated with a type of sediment is assigned in each site of the V_s30 zonation for the Gatineau, Greater Montreal and Saint Lawrence Valley zonation. For the Saguenay raster map, the centroid is selected, and for the vector map of Quebec City, a regular grid of points is created and associated with the corresponding site class converted to integer values between 1 and 5 for classes A, B, C, D and E, respectively. This procedure applied to the Quebec City map increases the number of data points, which may reduce the accuracy of the approach if the data are used in the correlation.

The mean and standard deviation of V_s30 are then calculated for each type of sediment and for each region with a zonation map (

Table 3. V_s30 mean and standard deviation values were obtained in each investigated region by sediment types and associated site classes based on the calculation using Equation (1). The Quebec City data are not included in the weighted calculation. (* site class A = 1 to E = 5).

Type of Surficial Deposit (Geological Description)	Code	Vs30 (m/s)															Weighted Average	Weighted Standard Deviation	Site Class
		Quebec *			Gatineau			Saguenay			Greater Montreal			St-Lawrence Valley
		N	Mean	Stdv	N	Mean	Stdv	N	Mean	Stdv	N	Mean	Stdv	N	Mean	Stdv
Aeolian sediment	Ed							312	338	247	873	504	379	1586	818	366	604	427	C
Undifferentiated organic sediment	O	9	1.4	0.9	6	451	351	3152	501	362	3898	552	327	6661	936	493	659	477	C
Indefferentiated slope deposit	C													24	525	342	525	342	C
Landslide deposit	Cg				7	491	449	3095	243	160	75	750	383	114	469	368	260	171	D
Undifferentiated alluvium	A	33	2.6	1.2	125	678	650	8591	570	456	23,501	502	320	15,544	604	478	537	432	C
Current alluvium	Ap	12	2.9	1.0	21	1247	887	5110	892	469	13,114	805	446	7537	733	475	813	499	B
Lake Sediment	L	2	2.0	1.4				3758	1122	547	250	816	370	2399	1578	687	1212	641	B
Fine deep-water glaciomarine sediment	MGa	23	2.7	1.0	829	574	602	50,136	603	436	62,234	619	353	32,281	642	515	615	439	C
Coastal and pre-coastal glaciomarine sediment	MGb	40	2.8	1.1	61	976	733	5408	736	511	16,467	810	429	29,674	876	515	826	616	B
Deltaic and prodeltaic glaciomarine sediment	MGd	5	2.4	1.3	34	462	517	15,052	420	356	1927	837	453	5662	913	722	531	469	C
Deep-water fine-grained glaciolacustrine sediment	LGa													516	1026	359	1026	359	B
Coastal and pre-coastal glaciolacustrine sediment	LGb				2	680	721	944	1228	659	11,700	461	287	7127	689	549	556	437	C
Deltaic and prodeltaic glaciolacustrine sediment	LGd										1244	439	198	802	833	409	535	294	C
Subaerial proglacial outwash sediment	Go	7	1.3	0.8				815	545	355				1337	1696	774	1063	785	B
Subaqueous proglacial outwash sediment	Gs													272	1017	462	1017	462	B
Juxtaglacial sediment	Gx	8	2.6	1.1	31	907	621	1469	799	530	817	963	419	2209	1119	483	942	572	B
Frontal moraine sediment	GxT													248	832	550	832	550	B
Undifferentiated till	T	39	2.8	1.0	43	1124	549	5429	1697	684	37,506	991	394	81,005	1297	551	1185	692	B
Melt-out or ablation till	Tf													86	1097	395	1097	395	B
Altered ancient Quaternary formation	Q													88	1416	127	1416	127	B
Undifferentiated bedrock	R	54	2.2	1.1	315	1496	609	4737	1720	708	9147	1472	256	61,552	1703	584	1657	974	A

). V_s30 is then averaged again for each type of sediment using a weighted average of the values from each of the four regions (Gatineau, Saguenay, Greater Montreal and Saint Lawrence Valley) where the weight corresponds to the number of samples in each region. In the case of the Saint Lawrence Valley, this number is reduced by 50% on the basis of a previous study for the Greater Montreal Area that indicated 50% matching accuracy for a similar region [28]. The following equation is adopted to calculate the weighted average:

$$Average {\mathrm{V}}_{\mathrm{s}30}=(\sum _{i=1}^3\left(N_i\times {\mathrm{V}}_{\mathrm{s}{30}_i}\right)+(0.5\times N_4\times {\mathrm{V}}_{\mathrm{s}{30}_4}))/(\sum _{i=1}^3{N}_i+\left(0.5\times N_4\right))$$

(1)

where N_i is the number of samples in one of the four zonation maps i, with i = 4 being the Saint Lawrence Valley, and V_s30i is the average for the ith region (Table 3).

The weighted average standard deviation SD is calculated using the following equation:

$$Average SD=\sqrt{{\displaystyle \frac{\left(N_1-1\right){s_1}^2+\left(N_2-1\right){s_2}^2+\left(N_3-1\right){s_3}^2+0.5(N_4-1){s_4}^2}{N_1+N_2+N_3+{(0.5\times N}_4)-4}}}$$

(2)

where N_i is the number of samples and _i is the calculated standard deviation for the ith region.

The results of this approach are given in Table 3. It lists the calculated average V_s30 for each sediment, its standard deviation in the different regions studied as well as the number of samples.

The average V_s30 for each type of sediment in the different regions is provided, as well as the number of samples and standard deviation in Table 3. Site classes are averaged in the Quebec City zonation by giving an integer value from 1 to 5 for classes A, B, C, D and E, respectively, and, later, converted again to site classes.

Most of the deposit types are classified in B, landslide deposits are in D and rocks are in site class A. Site class C concerns recent deposits (Ed, O, C and A), one glacio-marine (MGa) and two lacustrine (LGb, LGd) deposits. Mean V_s30 values are consistent within the different regions for seven deposit types (A, Ap, L, MGa, MGb, Gx and R); as for the other ones, the values differ of one site class from one region to another one. For the glacio-fluvial deposits (Go), the site classes differ from C to A. The standard deviations for each soil type are shown to be larger for the Gatineau region in comparison to other regions, certainly due to the lower number of samples than in the other regions.

In a second step, the V_s30 data in the three regions with detailed zonation (Gatineau, Greater Montreal and Saguenay) are grouped by main deposit types corresponding to their age of deposition, as ordered in the geological map. The boxplots in Figure 9 show the calculated statistical values, excluding the outliers (red crosses). The results indicate that deposit types C (slope deposits) and E (Aeolian) are predominantly associated with soil class D. Site class C is distinctly identified in deposit types G (glacio-fluvial), MG (glacio-marine) and O (organic). The two latter also exhibit a proportion of samples in site class D. Lake deposits (L) are distributed across site class C, as till (T) and rock (R) are predominantly associated with soil class A. The glacio-lacustrine (LG) and alluvial (A) types are situated between site classes C and B. The median and mean values in five deposits (C, E, A, L and G) differ by less than 25%, while in the other deposits (O, MG, LG, T and R), the difference is up to 43%. Finally, the large number of outliers observed for a given type of deposit (mainly C and MG) may be indicative that the depth to bedrock should also be considered to account for sites with shallow deposits.

Table 4. Statistical values of V_s30 (in m/s) for each main deposit’s type as described in Table 3 grouping the data in Greater Montreal, Saguenay and Gatineau. The site class is given using the mean value. Mean and median values are highlighted with a grey background.

Type of Deposit	Description	Mean	Median	25th Percentile	75th Percentile	Min	Max	Number of Samples	Site Class
All		695	487	281	1047	110	2195	97,617	C
O	Organic	508	356	239	714	110	1411	2773	C
C	Slope	234	189	182	237	170	319	2652	D
E	Eolian	314	284	230	334	128	490	289	D
A	Alluvial	692	568	298	1085	117	2230	11,741	C
L	Lake	1100	1103	745	1149	271	1576	3288	B
MG	Glacio-marine	565	440	269	729	110	1414	68,519	C
LG	Glacio-lacustrine	970	763	374	1168	124	2230	774	B
G	Glacio-fluvial	659	554	348	825	146	1479	1938	C
T	Till	1627	2230	1061	2230	126	2380	5090	A
R	Rock	1901	2230	1658	2230	803	2380	3326	A

lists the values calculated in the boxplots in Figure 9. The mean values are higher than the median up to 43% for organic sediments (O) in general, except for lacustrine sediments (L) and rock (R) where they are close. The site class is derived from the mean value but a similar site class would be obtained from the median one, except for the O type at the boundary of the D class and glacio-fluvial ones (LG) at the limit between the B and C site classes. The range of V_s30 values between the first and third quartiles varies from 50 and 1200 m/s on average with an average of 530 m/s. The relatively high value suggests that the uncertainty in the estimation is large and around one site class, except for alluvial deposits (A) where it is two site class, and for C and E, deposits included in site class D.

The estimated site class is given to each sediment type available in the three maps to create a site class mapping for the province of Quebec, as exemplified in Figure 10. The next step could be to repeat the procedure with geological maps at a 1/25,000 scale when available.

3.4. Correlation of V_s30 with Depth to Bedrock

V_s30 sites where depth to bedrock is available from borehole data with a sufficient number of samples (N) are plotted in Figure 11 for each type of sediment. Calculated parameters of the fitted power–law in the form of ${\mathrm{V}}_{\mathrm{s}30}=\mathrm{a}\times {\mathrm{Z}}^{\mathrm{b}}$, where Z is the depth to bedrock in meters, as listed in

Table 5. Power–law regression parameters for the different sediment types. N is the number of samples and R² is the determination coefficient. All types exclude till and rock.

Power–Law Regression Parameters by Sediment’s Type (Vs30 = a × Zb)
	A	Gx	LG	MG	O	Ed	All Types
N	608	34	175	2886	62	21	3789
a	1274.5	2764.9	428.2	1417.5	1414.9	165.2	1274.5
b	−0.47	−0.62	−0.27	−0.54	−0.60	0.06	−0.47
R2	0.43	0.56	0.32	0.52	0.40	0.13	0.43

. The calculated coefficient of determination R² is relatively good and in the range of 0.32 to 0.56, except for the Aeolian deposit (Ed) where it is 0.12 explained by a low number of samples. The latter deposit is not investigated further as it covers a very small part of the province of Quebec and is often very shallow. The graph with all sediment types excludes the till and rock types, which are the most consolidated and oldest deposits.

Table 5 provides the power–law regression parameters a and b used to fit the V_s30 data over the depth to bedrock for several sediment types found in the province of Quebec.

4. Discussion

The V_s30 distribution in the four regions with local or regional zonation in the province of Quebec is compared to the zonation based on the topographical slope as provided by the USGS (Figure 2, Figure 3, Figure 4, Figure 5 and Figure 6). In general, the latter underestimates V_s30 values compared to the detailed zonation. The percentage of agreement between the two types of maps varies from 18 to 36%. The number of sites with underestimates of V_s30 varies between 59 and 70%, and with overestimates from 1 to 22%, depending on the region. In the USGS approach, the slope is highly dependent on the resolution of the Digital Elevation Model (DEM), and the results are especially sensitive in regions with relatively flat alluvial valleys or with ancient glacial shields. This limitation could be explored by including topographic slope data at the highest resolution available as a third parameter of comparison. This would allow checking which region in terms of V_s30 or soil types are most influenced by topographic slope variation. The difference in resolution between the USGS grid and the grid used to compare the V_s30 data from the zonation maps is small enough that it does not have a major impact on the results.

This paper proposes to estimate V_s30 for several sediment types in order to complement the Saint Lawrence Valley zonation [42] in regions without a 3D geological model or detailed zonation (Figure 10). For that, an approach to correlate the detailed geological mapping of surficial soil deposits and V_s30 in regions with local or regional zonation is proposed. V_s30 values from the zonation are associated with the soil deposits in the geological map and averaged within the different regions with zonation. Rather than using the same resolution for all selected regions as was done to compare USGS V_s30 data, it was decided to use the most accurate data in regions where V_s30 sites were available (Gatineau, Greater Montreal and Saint Lawrence Valley) and, in Saguenay, the resolution of the raster map. This assumption leads to a variation in the number of sites used per region (Table 2). However, as shown in Table 3, the site classification for a given soil type remains relatively constant from one region to another. Soil types showing the greatest discrepancy need to be investigated further.

A weighted average is then calculated that considers equally the three main regions of Gatineau, Greater Montreal and Saguenay and a weight ponderation of 50% for the Saint Lawrence Valley map based on previous analysis of its accuracy [6]. This approach, expressed in Equation (1), is based on expert judgment, which influences the results because the number of samples and the geographical extent of the data in the Saint Lawrence Valley is large in comparison with the other regions. Despite this, the average site class calculated is consistent within the different regions for most of the soil deposits, the majority of which are classified as class C and B. Landslide deposits are the only site class D of the list in Table 3. Rock (R, Q) and till (T, Tf) types are identified as site class A or close to A considering the standard deviation. Alluvial and ancient lake sediments have global V_s30 values in the lower bound of site class C. Glacio-marine and glacio-fluvial sediments are clearly in site class C, as glacio-lacustrine sediments are in site class B. A total of 4 of the 21 types (O, A, MGa and LGb) have similar site class C in the five regions, with the exception of O, which is B in the Saint Lawrence Valley and Quebec data. For the other types, the difference is of one class in one or other of the regions, except for the types L (lake sediment), Ed and Go (glacial sediment), which differ in two site classes. Such a difference in one site class is in agreement with the calculated standard deviation in each type.

In the second step, soil types are grouped by episodes of deposition in order to increase sample size and to generalize the approach to geological maps with lower spatial resolution (Table 4). Aeolian (Ed) and slope (C) sediment are in class D. A total of 5 over 11 sediment types are in site class C. Lake and glacio-lacustrine are in class B as rock and till is classed as A.

The attempt to correlate V_s30 and sediment type using geological information from the regional map of the province of Quebec is relatively conclusive since the uncertainty in estimating the site class from one region where V_s30 data are available to another is relatively large (one site class). Nevertheless, the discrepancy between V_s30 estimated for this region and the other ones is never larger than one site class. In the two regions (Gatineau and Greater Montreal) with V_s30 data derived from seismic measurements, the site class is identical for all sediment types and the absolute difference between the estimated V_s30 in both regions is lower than 35%, except for MGb and Ap, where it is 55%. Similar V_s30 data in Saguenay, Quebec City and any other region could help reduce uncertainty and improve the results of this study. In sites where the depth to bedrock is available, a relation between V_s30 and the latter is proposed for several soil deposits. The correlation between the two parameters is intuitively correct with a relatively good coefficient of determination. However, the relationships need to be validated with samples of the different soil deposits including geological profiles. At this stage, estimates of depth to bedrock are based on low-resolution data at a provincial scale, which need to be supplemented by more detailed data for a sufficient number of V_s30 sites and different soil types.

5. Conclusions

The comparison of V_s30 distributions across different regions of Quebec reveals significant discrepancies when using the USGS topographical slope-based zonation, with underestimates of V_s30 values in most cases. It highlights the clear limitation of the slope-based method, particularly in regions with flat alluvial valleys or ancient glacial deposits like in Canada.

The proposed method of correlating V_s30 with geological mapping of surficial soil deposits is encouraging given the relatively small size of the areas where the correlations are applied, in comparison to the overall size of the application area. It offers a more reliable approach, especially in areas lacking detailed zonation or 3D geological models. The results suggest that soil deposits, such as glacio-marine and glacio-fluvial sediments, are predominantly in site class C, while rocks and tills fall under site class A, with landslide deposits classified as site class D.

Furthermore, the approach of this study can be highly cost-effective by incorporating expert judgment for regional average V_s30 estimates. It proves to be reasonably effective despite some uncertainty due to regional differences. The correlation of V_s30 values with sediment types, supported by the regional geological maps, helps reduce the uncertainty of site classification, though further validation is needed considering a larger number of specific sites in flat areas.

Additionally, the relationship between V_s30 and depth to bedrock, if confirmed, could provide another valuable tool for estimating V_s30 in regions with limited seismic data.