Regional terrain-based VS30 prediction models for China

doi:10.21203/rs.3.rs-2118700/v1

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Regional terrain-based VS30 prediction models for China

https://doi.org/10.21203/rs.3.rs-2118700/v1

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published 06 May, 2023

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Time-averaged shear-wave velocity to 30 m (V_S30) is commonly used in ground motion models as a parameter for evaluating site effects. This study used a collection of boreholes in Beijing, Tianjin, Guangxi, Guangdong, and three other municipalities and provinces, which were divided into three regions with reference to the seismic ground motion parameter zonation map of China, to establish V_S30 prediction models based on terrain categories. Regional effects were verified by comparing morphometric parameters (topographic slope, surface texture, and local convexity) thresholds and terrain classification maps obtained from the global digital elevation model (DEM) data and the regional DEM data of the three regions. Additionally, V_S30 prediction models for the three regions using both types of terrain classification maps were established and analyzed comparatively to provide credible regional V_S30 models for China. Through analysis of the correlations between the measured V_S30 values and the predicted V_S30 values, and with consideration of the geological characteristics of the boreholes, the V_S30 prediction models based on terrain classification maps from regional data were finally applied in developing regional V_S30 models for China. Intercomparison of the V_S30 prediction models for the three regions indicated that subregional consideration is necessary in terrain classification. Finally, a spatial analysis method adopting inverse distance weighting of the residuals was used to update the initial V_S30 models. The developed V_S30 models could be used both in developing regional ground motion models and in the construction of earthquake disaster scenarios.

terrain classification

morphometric parameters

VS30 prediction models

regional features

It is recognized that damage to buildings is severely affected by strong ground motion, which is substantially influenced by local site conditions. The time-averaged shear-wave velocity to 30 m (V_S30) is used widely as an index of site classification in earthquake resistant design code and it is considered as an important parameter for measuring the amplification effect of ground motion. For example, in ground motion models (e.g., Abrahamson and Silva 2008; Boore and Atkinson 2008; Abrahamson et al. 2013; Boore et al. 2013) and ShakeMap (Wald and Worden 2005), V_S30 values were used to quantify the site amplification effects of ground motion. Although V_S30 values can be calculated from drilling profiles and inferred from refraction microtremor data (Thelen et al. 2006; Kanbur et al. 2020), it is impractical to obtain dense sample coverage across a region. Therefore, to achieve regional site classification, available high-precision topographic, geologic, and geomorphic data are used.

Wald and Allen (2007) established a relationship between V_S30 and topographic slope for active and stable tectonic regions based on 30arc-second digital elevation model (DEM) data. On this basis, much subsequent research has involved more detailed study in different countries or regions (Lee et al. 2001; Allen and Wald 2009; Lemoine et al. 2012; Xie et al.2016; Zhou et al. 2022; Zhang et al. 2022). Age, lithology, genesis, and other properties of geological maps have also been used as indicators for estimating V_S30 (e.g., Borchertdt 1994; Park and Elrick 1998; Wills 2000; Wills et al. 2006; Vilanova et al. 2018; Li et al.2022). Furthermore, some studies proposed comprehensive consideration of topographic and geologic information to improve the accuracy of V_S30 predictions (Thompson and Wald 2012; Thompson et al. 2014; Wills et al. 2015; Kwok et al. 2018; Li et al. 2019). However, owing to inadequate recognition of special areas such as volcanic plateaus, carbonate rocks, and glacier continents when using the slope-based method, and the subjective experience of the classification of the geology-based method, the terrain-based method has gradually become the focus of active research in recent years.

The terrain-based unsupervised classification method was proposed by Iwahashi and Pike (2007). Based on decision tree theory, the method was used to calculate three taxonomic criteria (topographic slope, surface texture, and local convexity) using DEM data and to partition the land into 16 undefined categories. The relationship between the undefined categories and the geology/geomorphology was verified, indicating the effectiveness of this method in terrain recognition. On this basis, Yong et al. (2012) used 853 borehole data from California to establish a V_S30 prediction model (the Y12 model) based on 16 terrain categories. They performed iterations of a random selection and applied the cross-validation technique to calculate the mean value of V_S30 at the boreholes under each terrain category. They determined the best predicted value of V_S30 for each terrain category when the iteration achieved the lowest value of the mean squared prediction error. The stability and accuracy of the terrain-based prediction model were verified through comparison with the slope-based method (Wald and Allen 2007) and the geology-based method (Wills et al. 2000). Because most V_S30 data considered in developing the Y12 model were not from measured data, only 503 V_S30 measurements were used in developing the subsequent V_S30 prediction model (the Y16 model) in Yong (2016). Nevertheless, the predictive capabilities of the Y16 and Y12 models were certified as statistically indistinguishable. The prediction results of the Y16 and Y12 models for National Earthquake Hazards Reduction Program (NEHRP) site classification were broadly consistent (approximately 85% of data were classified as Site C, 15% classified as Site D, and none classified as Site A, B, or E). This terrain-based method has been applied successfully in many cases. For example, Seyhan et al. (2014) considered the terrain-based method important for estimating V_S30 values in the construction of the NGA-West2 borehole dataset, and evaluated its reliability against other methods that included the slope-based method (Wald and Allen 2009), geotechnical-based method (originally presented in Chiou et al. 2008), and geology-based method (Wills and Gutierrez 2008) to provide the optimal scheme for determining V_S30 values. Stewart et al. (2014) and Foster et al. (2019) also applied this method in Greece and New Zealand respectively for developing V_S30 predictions. Ahdi et al. (2017) established the terrain-based V_S30 prediction model for the Pacific Northwest region of North America, however, different to Yong et al. (2012), they used the logarithmic mean($\mu \ln {V_{{\text{S}}30}}$) and standard deviation($\sigma \ln {V_{{\text{S}}30}}$) of V_S30 from all the boreholes in each terrain category to represent the predicted results. Contreras et al. (2018) divided the Chile borehole database into southern and northern regions and established separate prediction models to inspect the regional effects of this terrain-based method. The result showed that V_S30 was slower in the southern region than in the northern region for the same terrain categories with abundant data, which indicated the existence of a remarkable regional effect.

The global terrain classification map based on 30arc-second DEM data, provided by Iwahashi and pike (2007), suggests that changes in global surface landforms are consistent. However, Zhang et al. (2022) recalculated the threshold values of three taxonomic criteria using local 30-arcsecond DEM data from Xinjiang and Hebei provinces in China, and reported large differences in the results between the two regions. Moreover, statistical analysis of the V_S30 values also showed clear differences in the lithological characteristics of the two regions. Therefore, to adequately consider regional effects, it is necessary to classify terrain categories and to establish V_S30 prediction models for each region independently.

Based on the research of Yong et al. (2012) and Zhang et al. (2022), a collection of boreholes in this study from seven municipalities and provinces in China was divided into three regions: the GG Region (comprising Guangxi and Guangdong provinces), CD Region (comprising Sichuan and Yunnan provinces), and CM Region (comprising Beijing, Tianjin, and Hebei), with reference to the regional characteristics of seismic tectonic activity given by the seismic ground motion parameter zonation map of China. Threshold values for morphometric parameters (topographic slope, surface texture, and local convexity) and terrain classification maps obtained from the global DEM data provided by Iwahashi and Pike (2007) (hereafter, abbreviated as I07) and recalculated from the regional DEM data of the three regions in this study (hereafter, abbreviated as Z22) were compared. Both types of terrain classification map were used to establish regional V_S30 prediction models, which were analyzed comparatively to provide credible regional V_S30 models for China. Through analysis of the correlations between the measured V_S30 values and the predicted V_S30 values at the boreholes, and with consideration of the geological characteristics of the boreholes, the effectiveness of V_S30 predictions of proposed models were validated. Finally, a spatial analysis method adopting inverse distance weighting of the residuals was used to update the initial V_S30 models. The developed V_S30 models could be used in some other research works such as developing regional ground motion models and constructing earthquake disaster scenarios.

The categories obtained according to the terrain-based classification method are not delineated casually but are related to local geomorphic or geological features. Therefore, to support qualitative analysis of the effect of the classification, the geomorphic features of each region are summarized in the following.

In the CD Region, the geomorphology of Sichuan Province is high in the west and low in the east, dipping from the northwest toward the southeast, and the region can be divided into the eastern Sichuan Basin and the western plateau mountains. The highest elevation is approximately 7556 m, and the relative difference in elevation from the east to the west is almost 7000 m. The Sichuan Basin has specific landforms consisting of flat plains in the west, hills in the central area, and mountains and valleys in the east. The elevation of the hills is 500–1000 m. Overall, the mountains, plateaus, and hills in Sichuan Province account for approximately 97.46% of the entire land area. The geomorphology of Yunnan Province is high in the northwest and low in the southeast. The highest elevation is approximately 6740 m and the lowest elevation is near 76 m, i.e., a relative difference of > 6000 m. The plateau area is undulating and the relatively gentle mountains account for only 10% of the entire land area. Most of the land surface is rugged with some areas of relatively gentle plateau plain.

In the GG Region, Guangxi Province is mostly surrounded by mountains and plateaus. Mountains, hills, and basins scattered widely throughout Guangxi Province account for 10% of the entire land area. The basins and hills vary in size and interlace with each other. The plains account for only 26.9% of the total area. The geomorphology of Guangdong Province comprises mostly platforms and plains in the south and hills in the north, with valleys and basins distributed widely among the mountains. The strike of the mountains, which is generally northeast–southeast, is consistent with the underlying geological structure. Granite, sandstone, and metamorphic rocks are reasonably widespread.

The geomorphology of the CM Region is relatively high in the north and northwest, and relatively flat in the southeast and south. Plains are distributed widely in the area and wetlands are distributed only in the coastal region. Plateaus, mountains, and plains are arranged in order from the northwest to the southeast. The plains in the southeast can be further subdivided into alluvial plains, alluvial fan plains, denudation plains, diluvial plains, alluvial-dilluvial plains, marine plains and marine-alluvial plains. The elevation changes obviously across the entire region from approximately 1300–1700 m in plateau areas, to 500–1000 m in the mountains, to < 200 m in plain areas, and to < 4 m in coastal areas.

Detailed geomorphological maps of the three regions, shown in Fig. 1, reveal marked regional differences; therefore, individual analysis is necessary to consider regional effects.

In this study, there were 1948 boreholes in CM Region, 1597 boreholes in CD Region, and 1408 boreholes in GG Region, which were almost collected from engineering projects. For these borehole sites, V_S30 values can be calculated directly using shear wave velocity profile data for drilling depths > 30 m and estimated using empirical extrapolation models for drilling depths < 30 m. The models used in this study were the linear extrapolation model (Boore, 2004) and the bottom constant velocity model (Kuo et al. 2011). We have found that V_S30 values estimated using the linear extrapolation model are closer to measured V_S30 values when the lithology changes uniformly, while V_S30 values estimated using the bottom constant velocity model are closer to measured V_S30 values when the lithology changes abruptly (bedrock appears within 30 m covered with soil). Therefore, the bottom constant velocity model was used in this study when bedrock was identified within 30 m, and the linear extrapolation model was used in other cases.

The median value (or the mean value of the middle) of V_S30 was adopted for boreholes in the same project that are close enough to be considered as having the same latitude and longitude. For example, in the same project as borehole No. 20M-GD-ZK44M03301, there are 19 other boreholes with the same latitude and longitude. The distribution of the V_S30 values of the boreholes in this project is shown in Fig. 2. The maximum and minimum values of V_S30 of the boreholes are 607.85 and 128.07 m/s, respectively, and the mean and median values are 222.45 and 185.03 m/s, respectively. The V_S30 values of most of the boreholes are concentrated in the range of 150–300 m/s, and only one borehole has a V_S30 value that exceeds 600 m/s. Therefore, in comparison with the mean value, the median value of V_S30 of boreholes can avoid the influence of some extreme values. Through analysis of the borehole data, 572 V_S30 values in the GG Region, 705 V_S30 values in the CD Region, and 1312 V_S30 values in the CM Region were finally screened. Statistical histograms and cumulative percentages of the V_S30 values in the three regions are shown in Fig. 3.

It can be seen from Fig. 3 that boreholes with V_S30 <300 m/s account for approximately 76% of all boreholes in the CM Region, while they account for only 42% and 38% of all boreholes in the GG Region and the CD Region, respectively. Generally, the characteristics of boreholes correspond to the regional lithology. A large area of alluvial plains with sand, gravel, sandy clay, and clay covers the CM Region, resulting in a relatively soft field. In contrast, hills and mountains with low–medium elevation in the GG Region, which composed of sandstone, glutenite, slate, and granite, result in a relatively hard field. The large area of great relief mountains with high elevation and the special sedimentary environment of the Sichuan Basin (different from deep sedimentary basins, which are composed of plentiful low-elevation hills with pebbles and gravel) in the CD Region result in a very hard field. Additionally, the boreholes with V_S30 >700 m/s account for < 1% of all boreholes. This is a consequence of the quality limitation of boreholes in engineering projects, i.e., most boreholes are drilled through a weathering layer that covers the underlying bedrock rather than being drilled directly into the bedrock.

V_S30 prediction models

Terrain classifications

The terrain classification scheme proposed by Iwahashi and Pike (2007) by using the three surface morphometric features of topographic slope, surface texture, and local convexity automatically identifies 16 terrain categories from DEM data (brief scheme shown in Fig. 4). Mountains and basins can be identified by slope, terraces (convex-upward) and alluvial fans (convex-downward) can be identified by convexity, and alluvial fans with smooth surface and mountain slopes with rough surface can be distinguished by texture (Iwahashi 2001).

Using V_S30 values from California, Yong et al. (2012) proposed a method for estimation of V_S30 based on the I07 terrain classification map. Subsequently, Zhang et al. (2022) found significant differences between the threshold values used for terrain classification in Xinjiang and Hebei provinces of China, and highlighted that there would be a smoothing effect and inadequate recognition of local geomorphology when consistently using the global thresholds provided by Iwahashi and Pike (2007). Therefore, the terrain classification threshold values of the three regions were calculated using regional DEM data (results shown in Fig. 5), and the terrain categories of the three regions were reclassified accordingly. The Z22 and I07 terrain-classification maps of the three regions are shown in Fig. 6.

Using 30arc-second DEM data (http://www.webgis.com/srtm30.html), and in accordance with the terrain classification scheme of Iwahashi and Pike (2007), the taxonomic thresholds of the three regions were calculated, as shown in Fig. 5(a). The threshold values for Xinjiang and Hebei provinces provided by Zhang et al. (2022) and for world provided by Iwahashi and Pike (2007) are compared in Fig. 5(b).

Comparison of Fig. 5(a) and 5(b) reveals that the threshold values of topographic slope, surface texture, and local convexity in the CM Region are approximately the same as those reported for the Hebei province in Zhang et al. (2022) after the addition of the Beijing and Tianjin regions. The topographic slope of the CM Region is the lowest among the four local regions (i.e., the CM Region, CD Region, GG Region, and Xinjiang province) owing to the large area of plain landform in the CM Region. The texture values of both the CD Region and the GG Region are close to 75%, indicating similarity in surface roughness. However, the slope and convexity values are higher in the CD Region than in the GG Region, reflecting the surface characteristic of more mountains in the CD Region and more hills in the GG Region. Therefore, the CD Region has more upward-convex landforms and steeper topographic slopes than the GG Region. Overall, the geomorphological features of steepest topographic slope, roughest surface texture, and most upward convexity all occur in the CD Region, reflecting the most complex changes of terrain.

The 16 terrain categories of each region were partitioned according to the classification scheme of Iwahashi and Pike (2007) (Fig. 4) and the calculated thresholds shown in Fig. 5(a), and the results (Z22) are shown in Fig. 6. The results extracted from I07 are also shown in Fig. 6 for comparison.

For the CM Region, the classification of terrain categories can be more fully identified using the regional taxonomic thresholds. For example, in the North China Plain, the categories according to I07 can be partitioned only as Class16, while the categories according to Z22 can be partitioned as Class11, Class13, Class15, and Class16, which can better distinguish the uneven and rough surfaces of areas with gentle low slopes that correspond to alluvial plains, alluvial–diluvial plains, and diluvial plains (Fig. 1). The grain size of the alluvial plains is coarser than that of the diluvial plains, which results in them having different characteristics of V_S30 (Wills et al. 2006). Therefore, it is necessary to further partition the plain areas.

For the CD Region, I07 unified Sichuan and most of western Yunnan into Class1, whereas the elevation of western Sichuan is actually higher than that of western Yunnan. Matsuoka et al. (2005) found that the V_S30 value of the same geomorphic unit is affected by elevation. Therefore, further division and more detailed analysis of these areas are necessary. For the GG Region, owing to the complex terrain and varied geomorphic landforms, the mountains, hills, and plains are interlaced and the terrain categories obtained from Z22 and I07 are relatively fragmented. Therefore, intuitive comparison of the two results is not possible and detailed analysis in combination with V_S30 data should be conducted later.

Development of V_S30 prediction models

Iterations of random selection and cross-validation methods were used by Yong (2012) and Yong et al. (2016) to establish the Y12 and Y16 V_S30 prediction models, respectively, while Ahdi et al. (2017) and Contreras et al. (2018) considered $\mu \ln {V_{{\text{S}}30}}$ and$\sigma \ln {V_{{\text{S}}30}}$ from all boreholes in each terrain category as representative. To determine the differences in the V_S30 characteristics between the I07 and Z22 terrain classification results, this study adopted the $\mu \ln {V_{{\text{S}}30}}$ and $\sigma \ln {V_{{\text{S}}30}}$ from all boreholes in each terrain category as representative as used by Ahdi et al. (2017). The number of boreholes and the results of the predicted V_S30 values for each terrain category from I07 and Z22 are listed in Table 1, and the predicted V_S30 values corresponding to the NEHRP site classification boundary are shown in Fig. 7.

Table 1

Predicted values and standard deviations of V_S30 in logarithmic coordinates derived from I07 and Z22.
	CD Region(I07)			CD Region(Z22)			CM Region(I07)			CM Region(Z22)			GG Region(I07)			GG Region(Z22)
	$\mu \ln {V_{{\text{S}}30}}$	$\sigma \ln {V_{{\text{S}}30}}$	Num	$\mu \ln {V_{{\text{S}}30}}$	$\sigma \ln {V_{{\text{S}}30}}$	Num	$\mu \ln {V_{{\text{S}}30}}$	$\sigma \ln {V_{{\text{S}}30}}$	Num	$\mu \ln {V_{{\text{S}}30}}$	$\sigma \ln {V_{{\text{S}}30}}$	Num	$\mu \ln {V_{{\text{S}}30}}$	$\sigma \ln {V_{{\text{S}}30}}$	Num	$\mu \ln {V_{{\text{S}}30}}$	$\sigma \ln {V_{{\text{S}}30}}$	Num
Class1	348.25	0.25	183	314.49	0.18	39	507.65	0.38	3	459.44	0.39	15	478.16	0.61	5	534.48	0.59	8
Class2	321.42	0.00	1	392.81	0.24	51	NaN	NaN	0	NaN	NaN	0	364.95	0.00	1	324.30	0.07	2
Class3	331.12	0.22	46	359.17	0.19	6	454.49	0.36	30	410.37	0.41	10	340.27	0.27	34	309.98	0.40	7
Class4	350.12	0.30	22	346.30	0.27	12	338.95	0.27	11	349.70	0.34	2	310.61	0.00	1	335.73	0.26	17
Class5	330.77	0.34	56	371.42	0.28	30	319.97	0.27	7	394.94	0.35	51	399.01	0.37	18	397.30	0.45	11
Class6	NaN	NaN	0	379.06	0.29	11	NaN	NaN	0	276.92	0.00	1	NaN	NaN	0	270.70	0.00	1
Class7	286.61	0.28	105	336.42	0.30	7	412.04	0.28	63	362.75	0.27	72	366.13	0.31	107	388.45	0.23	23
Class8	296.13	0.21	30	318.20	0.26	26	297.61	0.20	36	311.51	0.22	19	273.73	0.27	6	307.98	0.27	16
Class9	316.33	0.20	18	330.57	0.22	27	341.30	0.31	4	270.16	0.21	281	369.33	0.29	9	442.79	0.23	18
Class10	340.37	0.09	7	342.22	0.37	9	291.20	0.14	18	226.97	0.21	17	NaN	NaN	0	300.02	0.26	11
Class11	308.00	0.26	68	312.27	0.32	8	383.14	0.23	58	284.71	0.32	144	340.54	0.33	117	346.46	0.27	24
Class12	311.37	0.17	33	328.22	0.25	36	283.36	0.21	43	220.66	0.29	58	256.99	0.50	5	334.64	0.29	23
Class13	319.32	0.04	4	344.20	0.38	21	318.83	0.28	4	231.05	0.19	210	298.79	0.13	19	365.09	0.28	34
Class14	353.57	0.07	2	358.26	0.24	21	265.14	0.17	180	193.92	0.12	110	208.88	0.24	2	287.16	0.32	60
Class15	305.70	0.18	61	296.63	0.24	44	330.98	0.23	74	268.35	0.25	47	342.29	0.38	122	396.01	0.32	52
Class16	334.03	0.19	71	305.58	0.23	359	208.54	0.20	706	186.80	0.17	200	226.53	0.31	37	310.10	0.38	176
Note: “NAN” means there is no data under this terrain category.

It can be determined from Table 1 that from the I07 results for the CM Region, no boreholes are listed under Class2 and Class6 and only 3 boreholes are listed under Class2, while the 706 boreholes listed under Class16 account for approximately 57% of the overall data. Additionally, only 4 boreholes are listed under Class9 and Class13. The Z22 results indicate that no boreholes are listed under Class2 (similar to the I07 results) and that only 1 and 2 boreholes are listed under Class6 and Class14, respectively, while over 200 boreholes are listed under Class9, Class13, and Class16.

In the CD Region, the I07 results show that the boreholes under Class6 is empty, and that fewer than 3 boreholes are listed under Class2 and Class14. The terrain category with the largest number of boreholes (183) is Class1, and that with the largest standard deviation (0.34) is Class5 with 56 boreholes. The Z22 results show that each of the terrain categories has more than 5 boreholes, and that Class16 has the highest number (359). These boreholes are mainly located in the plain area of the Sichuan Basin, with similar components comprising sands and pebbles. The terrain category with the largest standard deviation (0.38) is Class13 with a total of 21 boreholes.

In the GG Region, the I07 results indicate that no boreholes are listed under Class6 and Class10, only 1 borehole is listed under Class2 and Class4, and just 2 boreholes are listed under Class14. The exceptionally small numbers of boreholes under these terrain categories reflect both the uneven distribution of boreholes and the smoothing effect in I07 with the application of global DEM data resulting in the absence of some terrain categories in local regions. The terrain category with the largest number of boreholes (122) is Class11. The Z22 results indicate that boreholes are listed under each of the terrain categories, but only 2 boreholes are listed under Class2. The terrain category with the largest number of boreholes (176) is Class16.

It can be seen from Fig. 7b that in the CD Region, the predicted V_S30 values derived from I07 under all categories are located in Site D of the NEHRP classification. The V_S30 fluctuates between 280 and 360 m/s, with only a small range of variation. The predicted V_S30 values derived from Z22 under the Class2, Class5, and Class6 categories are located in Site C of the NEHRP classification, and the remaining categories are in Site D, which is considered relatively reasonable in terms of site identification. With the exception of Class1 and Class16, the predicted V_S30 values of each terrain category derived from Z22 are higher than or close to the predicted values derived from I07. In the CM Region, only the predicted V_S30 value under Class5 from Z22 is significantly higher than that from I07, but the trends of the predicted V_S30 values with the variation of terrain categories derived from the two terrain classification results are almost parallel. The predicted V_S30 values under all terrain categories are located in Site D or Site C of the NEHRP site classification, and the predicted V_S30 value under Class16 derived from Z22 is only 186.80 m/s, approaching that of Site E of the NEHRP site classification. In the GG Region, the predicted V_S30 values under all terrain categories derived from Z22 are higher than those from I07, but the differences between the highest predicted values and the lowest predicted values of the two are close, i.e., 263.3 m/s from Z22 and 251.63 m/s from I07.

To compare the validity of the predictions from Z22 and I07, the linear relationship between the predicted V_S30 values and the measured V_S30 values was analyzed, and the correlation coefficient is shown in Fig. 8. It can be seen that in the CD Region, the correlation coefficient between the predicted V_S30 values and the measured V_S30 values derived from Z22 is 0.32, while the equivalent correlation coefficient derived from I07 is 0.24, i.e., significantly lower. A similar result is evident for the GG Region; however, in the CM Region, the correlation coefficient derived from I07 (0.73) is higher than that derived from Z22 (0.65). A possible reason is that the boreholes with lower V_S30 values are clustered in Class16 with a smaller standard deviation, resulting in a higher overall correlation.

Cross validation of classification considering geology dependency

It can be determined from Table 1 that the I07 and Z22 terrain classification results might lead to concentration of boreholes under a certain terrain category. For example, the Z22 result lists 359 boreholes under Class16 in the CD Region and 176 boreholes under Class16 in the GG Region. Similarly, the I07 result lists 706 boreholes under Class16 in the CM Region. The concentration of boreholes under a certain terrain category also corresponds to concentration of boreholes under a geological unit. For example, in the CD Region, 226 of the 359 boreholes under Class16 in the Z22 result belong to the Holocene unit, comprising mainly modern river alluvial, diluvial, mud, sand, and gravel material. These 226 boreholes connect to the I07 results classified as Class8, Class10, Class12, Class13, Class15, and Class16. Note that it is impossible that these 226 boreholes fall into the same terrain category of I07, only the terrain category with boreholes belonging to the Holocene unit that accounted for > 50% of the total number of boreholes under this terrain category in the I07 result were considered. It is considered that if the number of boreholes belonging to the Holocene unit under a certain category does not exceed 50% of the total number of boreholes under this category, a relationship between the terrain category and the geological unit cannot be inferred; therefore, such terrain categories were not considered. Given the similarity and variability of boreholes under the same geological units (Wills et al. 2006, Thelen et al. 2006), it is necessary to confirm whether it is reasonable to divide these boreholes into the same category or multiple categories, and to verify whether the V_S30 data between the categories are statistically different. For this purpose, the F-test was adopted in which absence of statistical difference between the two terrain categories under the same geological unit was consider the null hypothesis, and evidence of statistical difference between the two terrain categories under the same geological unit was considered the alternative hypothesis. For the terrain categories mentioned above that belong to the Holocene unit in the I07 result, the cross-validation results of the F-test are shown in Table 2. It can be determined that Class8–Class13, Class12–Class13, Class13–Class15, and Class13–Class16 show statistically significant differences, which can only indicate that Class13 is different from other the categories; however, there is no evidence to suggest that the remaining categories differ from each other. Therefore, it is unreasonable to divide the boreholes under the Holocene unit into different terrain categories in the CD Region, whereas it is more reasonable to divide them into the same category in the Z22 result.

Table 2

Cross-validation results of categories belonging to the Holocene unit in I07 in the CD Region
Group-pairs	p-value	Null hypothesis
Class8-Class10	0.166	Accept
Class8-Class12	0.792	Accept
Class8-Class13	0.032	Rejected
Class8-Class15	0.434	Accept
Class8-Class16	0.322	Accept
Class10-Class12	0.128	Accept
Class10-Class13	0.162	Accept
Class10-Class15	0.300	Accept
Class10-Class16	0.066	Accept
Class12-Class13	0.027	Rejected
Class12-Class16	0.449	Accept
Class12-Class15	0.267	Accept
Class13-Class15	0.048	Rejected
Class13-Class16	0.018	Rejected
Class15-Class16	0.047	Rejected

In the CM Region, 518 of the 706 boreholes under Class16 in theZ22 result are Holocene alluvial units, which connect to I07 classification results classified as Class10, Class12, Class13, and Class14. The remaining terrain categories that even include a few Holocene alluvial boreholes but with numbers of < 50% of the total under this category were not considered. The differences of V_S30 between the different terrain categories of the same geological unit were verified by the F-test, and the results are shown in Table 3. Almost all categories show statistical differences and therefore the Z22 classification is more reasonable.

Table 3

Cross-validation results of categories belonging to Holocene alluvial unit in I07 in the CM Region
Group-pairs	p-value	Null hypothesis
Class10-Class12	0.031	Rejected
Class10-Class13	0.033	Rejected
Class10-Class14	0.001	Rejected
Class10-Class16	0.424	Accept
Class12-Class13	0.001	Rejected
Class12-Class14	0.001	Rejected
Class12-Class16	0.001	Rejected
Class13-Class14	0.001	Rejected
Class13-Class16	0.017	Rejected
Class14-Class16	0.001	Rejected

For the GG Region, given that the boreholes were not concentrated in any specific geological unit in particularly large numbers in either classification result, comparative analysis was not performed. However, it can be seen from Fig. 8 that the correlation between the predicted V_S30 values and the measured V_S30 values derived from Z22 was better than that from I07, confirming that the Z22 terrain classification is more reasonable.

Based on the above analysis, regional V_S30 models were established for China using the predicted V_S30 values derived from Z22.

Comparison of V_S30 prediction models

The V_S30 prediction model results derived from Z22 in the CD Region, GG Region, and CM Region and the V_S30 prediction model results of Zhang et al. (2022) for the Xinjiang province are shown in Fig. 9. It can be seen that the predicted V_S30 value under Class1 for the CD Region (314.49 m/s) is significantly lower than that predicted for the other three regions, despite the fact that the boreholes are located in mountain areas with higher elevations and steeper slopes than in the other regions. It might be related to the characteristics of the engineering boreholes involved in the study, i.e., only a few boreholes had values of > 500 m/s, or it might reflect problems inherent in the application of the decision tree theory. Comparison of the correlation between the V_S30 values and slopes in the four regions revealed that the correlation was least significant in the CD Region (Fig. 10). Because the classification scheme based on the decision tree method takes slope as an important taxonomic threshold, V_S30 cannot be distinguished by slope in the CD Region. Therefore, it is insufficient to achieve V_S30 prediction models that rely only on terrain. Instead, geological age, lithology, and other information available in geological maps can be used as supplementary conditions to provide more reasonable estimates in conjunction with measurements from boreholes. On this basis, application of spatial interpolation and geostatistical Kriging interpolation can improve the accuracy of V_S30 prediction and reveal the trend of V_S30 across a region.

Figure 9 also shows that among the four regions the Xinjiang province has relatively high predicted V_S30 values under all terrain categories, and that the CD Region has minimal variation in the predicted V_S30 values with the various terrain categories. The difference in V_S30 value between the GG Region and the CD Region in Class1 (219.99 m/s) is the largest among the four regions under the same terrain. The highest predicted V_S30 values are for Class1 in the GG Region, and the lowest predictions are for Class16 in the CM Region. Significant differences in the predicted V_S30 values between different regions under the same terrain category demonstrate the necessity for delineating terrain by region.

Spatial distributions of predicted V_S30

The predicted V_S30 value at any point in the four regions can be obtained using the model established in the above, but there is substantial limitation in that all the predicted V_S30 values in Site C and Site D of the NEHRP site classification are < 540 m/s, which is obviously impractical. Therefore, we calculated the residuals of the boreholes between the measured V_S30 values and the predicted V_S30 values, analyzed the spatial variation trend of the residuals, and updated the initial V_S30 prediction results through multiplying the residual results with the V_S30 prediction model results. The residuals were calculated using the following equation:

$${R_i}={V_{{\text{S}}30,i}}^{{{\text{measured}}}}/{V_{{\text{S}}30,i}}^{{{\text{predicted}}}}$$

where ${V_{{\text{S}}30,i}}^{{{\text{predicted}}}}$ represents the predicted V_S30 values at the borehole points, and ${V_{{\text{S}}30,i}}^{{{\text{measured}}}}$ represents the measured V_S30 values at the borehole points.

Methods commonly used for analyzing spatial trends include inverse distance weighting and Kriging interpolation, which estimate the attribute value of any point in space through a certain attribute of several discrete points known in space.

In application of Kriging spatial interpolation, the attribute value is usually required to approximate the normal distribution. Moreover, the spatial distribution of boreholes is not uniform; thus, Kriging interpolation results would not be smooth. Therefore, the inverse distance weighting method was used in this study to analyze the spatial variation trend of the residuals. The formula for inverse distance weighting can be expressed as follows:

$$c=\sum\limits_{{i=1}}^{n} {\frac{1}{{{d^\alpha }}}} {c_i}$$

where c is the estimated value of the residuals at an unknown point in space, c_i is the calculated value of the residuals at the i-th borehole, d is the distance from the i-th borehole, and $\alpha$ is the power value.

The inverse distance weighting method mainly depends on the power value of the inverse distance. The power value can control the influence of the sampling points on the interpolation based on the distance from the output point. By defining a higher power value, the nearest point can be further emphasized. Therefore, as the power value increases, the adjacent data will be most affected, the surface will become more detailed (less smooth), and the interpolation will gradually approach the value of the nearest sampling point. Conversely, a smaller power value will have greater impact on the surrounding points further away, resulting in a smoother surface. The power parameter is a positive real number, and the general value of 2 was used in this study.

The spatial variation trends of the residuals obtained by the inverse distance weighting method for the CM Region, CD Region, and GG Region are shown in Fig. 11(a), 11(c), and 11(e), respectively. It can be seen that the variation of the residuals in the GG Region is the most remarkable, with a maximum value of 2.65 and a minimum value of 0.34. The variation of the residuals in the capital circle is relatively moderate, with a maximum value of 2.48 and a minimum value of 0.50. The residuals were used to update the initial regional V_S30 prediction results (Fig. 6, Table 1), and the final V_S30 prediction maps for the CM Region, CD Region, and GG Region are shown in Fig. 11(b), 11(d), and 11(f), respectively. In comparison with the initial V_S30 prediction results, the updated results based on the residuals can identify the coastal areas of Site E (V_S30 < 180 m/s) and the northern mountain area with V_S30 > 540m/s in the CM Region, Furthermore, the updated results can also identify the region with shear wave velocity of > 540 m/s, which represents high mountains, plateaus, and platforms in the CD Region and western parts of the GG Region, which is more consistent with the actual site conditions.

This study used terrain-based methods (Iwahashi and Pike 2007; Yong et al. 2012; Zhang et al. 2022) to establish regional V_S30 prediction models for China. Considering regional differences in morphometric features, the boreholes considered in the study were divided into three regions (the CD Region, CM Region, and GG Region), with reference to the fifth seismic zoning map of China, and models for prediction of V_S30 were established. To verify the regionality of this method, we recalculated the terrain classification threshold values of topographic slope, surface texture, and local convexity and reclassified the landforms into 16 categories for the three regions using regional DEM data. The terrain classification results for the three regions were compared with results extracted from the I07 global classification map. Results proved that using regional DEM data instead of global DEM data can distinguish uneven and rough surfaces in the region of gentle low slopes in the CM Region and the region of mountains with steep slopes and high elevations in the CD Region.

The V_S30 prediction models for the three regions derived using the I07 and Z22 terrain classification maps were compared to evaluate the prediction performance of these two results. Comparison of the correlations between the measured V_S30 values and the predicted V_S30 values, and verification of the geological characteristics of the boreholes, revealed that the V_S30 prediction models based on the Z22 results performed better. Moreover, the necessity for delineating terrain by region was proven by means of the significant differences in the predicted V_S30 values between different regions under the same terrain category. Finally, by analyzing the spatial variation trends of the residuals between the measured V_S30 values and the predicted V_S30 values at the boreholes, the initial regional V_S30 prediction model was updated, and the updated model was proven to be more consistent with the actual site conditions.

Analysis also revealed that the effectiveness of the model is closely related to the statistical characteristics of the V_S30 of collected boreholes. The insignificant correlations between V_S30 and slope in the CD Region confirmed that it is insufficient to use V_S30 prediction models that rely only on terrain. The geological age, lithology and other information available in geological maps can be used as additional supplementary data to provide a more reasonable estimation.

V_S30: time-averaged shear-wave velocity to 30 m

NEHRP: National Earthquake Hazards Reduction Program

Y12 model: V_S30prediction model provided by Yong et al. (2012)

Y16 model: V_S30prediction model provided by Yong (2016)

DEM: digital elevation model

I07: Threshold values for morphometric parameters and terrain classification maps obtained from the global DEM data provided by Iwahashi and Pike (2007)

Z22: Threshold values for morphometric parameters and terrain classification maps recalculated from the regional DEM data of the three regions in this study

CM Region: comprising Beijing, Tianjin, and Hebei

CD Region: comprising Sichuan and Yunnan provinces

GG Region: comprising Guangxi and Guangdong provinces

V_S30^predicted: the predicted V_S30 values at the borehole points

V_S30^measured: the measured V_S30 values at the borehole points

Ethics approval and consent to participate

Not applicable

Consent for publication

Not applicable

Availability of data and materials

The DEM data used in this study can were obtained from the NASA site (courtesy of NASA/NGA/USGS) at http://www.webgis.com/srtm30.html. The regional geomorphic maps were obtained from National Earth System Science Data Center, National Science & Technology Infrastructure of China (http://www.geodata.cn). The boreholes were obtained from non-public seismic safety assessment reports of engineering projects in China.

Competing interests

The authors declare that they have no competing interests.

Funding

This work is supported by National Key R&D Program of China under grant number 2019YFE0115700; Chinese National Natural Science Fund under grant number 51878632; Natural Science Foundation of Heilongjiang Province under grant number YQ2019E036; Heilongjiang Touyan Innovation Team Program.

Authors' contributions

YTZ organized the geomorphic maps, analyzed the data, interpreted the results, and drafted the manuscript. YFR collected and encoded the borehole data, interpreted the results, and corrected the manuscript. RZW designed the study and made the conclusions. HWW and KJ collected the borehole data and processed these data. All authors read and approved the final manuscript.

Acknowledgements

We appreciate sincerely Prof. Saburoh Midorikawa from the Tokyo Institute of Technology, Dr. Hongjun Si from the University of Tokyo and Dr. Tadahiro Kishida from Khalifa University for their constructive suggestions when we imitated this research in 2019. We also appreciate for the data support from "National Earth System Science Data Center, National Science & Technology Infrastructure of China. (http://www.geodata.cn)".

Endnotes

No endnotes in this study

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Regional terrain-based VS30 prediction models for China

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Regional Geomorphic Features

Borehole Database

V_S30 prediction models

Terrain classifications

Cross validation of classification considering geology dependency

Discussions

Comparison of V_S30 prediction models

Spatial distributions of predicted V_S30

Conclusion

List Of Abbreviations

Declarations

Ethics approval and consent to participate

Consent for publication

Availability of data and materials

Competing interests

Funding

Authors' contributions

Acknowledgements

Endnotes

References

Supplementary Files

Status:

Journal Publication

Version 1

	CD Region(I07)			CD Region(Z22)			CM Region(I07)			CM Region(Z22)			GG Region(I07)			GG Region(Z22)
	\(\mu \ln {V_{{\text{S}}30}}\)	\(\sigma \ln {V_{{\text{S}}30}}\)	Num	\(\mu \ln {V_{{\text{S}}30}}\)	\(\sigma \ln {V_{{\text{S}}30}}\)	Num	\(\mu \ln {V_{{\text{S}}30}}\)	\(\sigma \ln {V_{{\text{S}}30}}\)	Num	\(\mu \ln {V_{{\text{S}}30}}\)	\(\sigma \ln {V_{{\text{S}}30}}\)	Num	\(\mu \ln {V_{{\text{S}}30}}\)	\(\sigma \ln {V_{{\text{S}}30}}\)	Num	\(\mu \ln {V_{{\text{S}}30}}\)	\(\sigma \ln {V_{{\text{S}}30}}\)	Num
Class1	348.25	0.25	183	314.49	0.18	39	507.65	0.38	3	459.44	0.39	15	478.16	0.61	5	534.48	0.59	8
Class2	321.42	0.00	1	392.81	0.24	51	NaN	NaN	0	NaN	NaN	0	364.95	0.00	1	324.30	0.07	2
Class3	331.12	0.22	46	359.17	0.19	6	454.49	0.36	30	410.37	0.41	10	340.27	0.27	34	309.98	0.40	7
Class4	350.12	0.30	22	346.30	0.27	12	338.95	0.27	11	349.70	0.34	2	310.61	0.00	1	335.73	0.26	17
Class5	330.77	0.34	56	371.42	0.28	30	319.97	0.27	7	394.94	0.35	51	399.01	0.37	18	397.30	0.45	11
Class6	NaN	NaN	0	379.06	0.29	11	NaN	NaN	0	276.92	0.00	1	NaN	NaN	0	270.70	0.00	1
Class7	286.61	0.28	105	336.42	0.30	7	412.04	0.28	63	362.75	0.27	72	366.13	0.31	107	388.45	0.23	23
Class8	296.13	0.21	30	318.20	0.26	26	297.61	0.20	36	311.51	0.22	19	273.73	0.27	6	307.98	0.27	16
Class9	316.33	0.20	18	330.57	0.22	27	341.30	0.31	4	270.16	0.21	281	369.33	0.29	9	442.79	0.23	18
Class10	340.37	0.09	7	342.22	0.37	9	291.20	0.14	18	226.97	0.21	17	NaN	NaN	0	300.02	0.26	11
Class11	308.00	0.26	68	312.27	0.32	8	383.14	0.23	58	284.71	0.32	144	340.54	0.33	117	346.46	0.27	24
Class12	311.37	0.17	33	328.22	0.25	36	283.36	0.21	43	220.66	0.29	58	256.99	0.50	5	334.64	0.29	23
Class13	319.32	0.04	4	344.20	0.38	21	318.83	0.28	4	231.05	0.19	210	298.79	0.13	19	365.09	0.28	34
Class14	353.57	0.07	2	358.26	0.24	21	265.14	0.17	180	193.92	0.12	110	208.88	0.24	2	287.16	0.32	60
Class15	305.70	0.18	61	296.63	0.24	44	330.98	0.23	74	268.35	0.25	47	342.29	0.38	122	396.01	0.32	52
Class16	334.03	0.19	71	305.58	0.23	359	208.54	0.20	706	186.80	0.17	200	226.53	0.31	37	310.10	0.38	176
Note: “NAN” means there is no data under this terrain category.

Regional terrain-based VS30 prediction models for China

Status:

Journal Publication

Version 1

Abstract

Figures

Introduction

Regional Geomorphic Features

Borehole Database

VS30 prediction models

Terrain classifications

Cross validation of classification considering geology dependency

Discussions

Comparison of VS30 prediction models

Spatial distributions of predicted VS30

Conclusion

List Of Abbreviations

Declarations

Ethics approval and consent to participate

Consent for publication

Availability of data and materials

Competing interests

Funding

Authors' contributions

Acknowledgements

Endnotes

References

Supplementary Files

Status:

Journal Publication

Version 1

V_S30 prediction models

Comparison of V_S30 prediction models

Spatial distributions of predicted V_S30