Shear wave velocity (Vs) is one of the most important parameters of a geological model to assess the site effect and the ground response. In this paper the spatial variability of shear wave velocity in Mashhad capital city are investigated. For this purpose, 243 Vs profiles of different projects throughout the city were used. Based on the Vs profiles the iso-level maps of the Vs interfaces 300, 500, 750, 950 and 1200 m/s were obtained by kriging interpolation method. The best semivariogram models were obtained with changing the effective parameters and assessing the components of the models and spatial dependence. The best models for the entire interfaces were exponential. Based on these models, the spatial dependence of depth data was moderate to strong. The performance of interpolations was checked by cross-validation and its indices i.e. mean standardized prediction errors (MSPR), root mean square prediction errors (RMSPE), average kriging standard error (AKSE), and root mean square standardized prediction errors (RMSSPE) were assessed. A trend of depth increasing towards the northeast was observed at all of the interfaces.
A geological model including the geometry of the basin, the soil structure and the dynamic properties of the soil layers with great attention to the shear wave velocity (Vs) is a fundamental requirement for site effect studies [
Geostatistical analyses are powerful tools to obtain a precise understanding of the basin characteristics. Geostatistical analyses help to estimate the value of sample properties at the unmeasured locations. There are different geostatistical techniques such as kriging, inverse distance weighting (IDW), splines and triangulation which convert the point data to continuous surfaces by using the spatial interpolation. Most of these methods assume that the adjacent samples tend to be more similar than those which are further apart. This assumption describes the spatial autocorrelation. Experimental semi-variogram can define the spatial structure of a variable [
In this study, the spatial variability of the Vs throughout the Mashhad city is investigated by kriging technique. For this purpose, data of 243 Vs profiles which have been measure during the period of 2000-2014 are utilized. The accuracy of the interpolations is inspected by the cross-validation analysis.
The Mashhad city is the second largest city of Iran with dense population and high seismicity; it is situated in the Northeast of Iran. The city (36˚18'N, 59˚34'E) is located in the northern slopes of Binalood Mountains and Paleo-Tethys suture zone. It covers an area of 311 km2 and is dominated by an arid and semi-arid climate. It is laid on thick Quaternary deposits which are surrounded by Mafic and Ultramafic outcrops in southern parts, Slate and Phyllite in western and southwestern and Marls in northeastern margins. The city is also located in active tectonic area and bounded with two active and quaternary faults in south and north. The soft sediments are divided into three groups of pediment, alluvial fan and alluvial plain deposits. Pediment and alluvial fan deposits generally contain gravels and sands and extent over the south, southwest and west parts of the city. Alluvial plain deposits usually consist of clays and silts that cover center and eastern parts. Kashafrood River passing through the Northeast margin has significant effects on depositional process of the fine grained deposits and is the most important geomorphic phenomenon of the Mashhad watersheds. The highest part of the city with elevation of 1380 m.a.s.l. is lying in the southwestern outcrops. The lowest part of the city with altitude of about 870 m lies in the northeast. Almost 85% of the city have gradient slope less than 5 percent. Rivers which originated from the southern and southwestern outcrops flow towards the lowlands in the northeast and go into the Kashafrood River.
Physical and mechanical properties of the soft sediments in the study area are influenced by geological condition. Borehole logs of 1500 geotechnical boreholes collected from the city show that the soil texture in the south and south west are gravel and sand but gradually change to silt and clay toward north and east.
We utilized the shear wave velocity information of 243 boreholes. These boreholes were drilled during geotechnical studies for different projects such as hotels, residential and commercial buildings. Downhole shear wave profiling has been done by Zamin Physics Consulting Engineering Company. Mashhad is spiritual capital of Iran and more than 20 million tourists and pilgrims visit the city annually. Hence tendency increases to construct high- raised commercial buildings, malls, and hotels. The main aim of downhole Vs measuring are determining seismic soil classification based on 2800 Iranian Seismic Code. Most of the boreholes were drilled to depth of 30 m although some continue more than 30 meters. The Vs profiles scattered throughout the city are shown in
In the area under study, because special sedimentary environment texture and geotechnical properties of the soil
Vs profiles distributed around the city. Cold colors indicate low velocity and hot colors demonstrate high velocity
change from point to point and finding a continuous layer is very difficult. Hence, we use shear wave velocity to determining the soil layers and construction of the basin model. The Vs information is considered as a base of model and the dominant soil texture is used for more detailed layer separation. For this firstly, variation of the Vs at different depths was discovered by the stock chart. Based on the stock charts, 5 breaking points at the Vs of 300, 500, 750, 950 and 1200 m/s were determined visually as seen in
More detailed information about the geostatistical techniques are noted in literature [
where
Stock plot of Vs against depth class, breakpoints are given by black solid circles
Components of a semivariogram are including nugget effect, sill and range. Range is the distance beyond which there is no spatial dependence and correlation between data set points. Nugget effect
In this study, spherical, Gaussian and exponential models were considered to find the best semivariogram models. Spatial dependency is a way to recognize appropriate model [
Cross-validation was also performed to evaluate the validation and adequacy of the semivariogram model [
Mean standardized prediction errors (MSPR),
Root mean square prediction errors (RMSPE),
Average kriging standard error (AKSE),
Root mean square standardized prediction errors (RMSSPE),
where
For an accurate interpolation the mean MSPR value must be near to zero, the RMSPE value should be small and AKSE value should be near to RMSPE, and the RMSSPE has to be near to 1 (ArcGIS Tutorial).
Classical statistical analysis for the depth variation of the Vs interfaces of 300, 500, 750, 950 and 1200 m/s were performed and the results including min, max, mean, median, Standard deviation (SD), skewness and kurtosis are presented in
Normality of the data distribution is required for kriging interpolation. In this study the graphical histogram and Q-Q plot tests were used to analyze the normality. The depth information is normally distributed for the entire interfaces.
Among kriging methods, including simple, ordinary, universal, indicator, probability and disjunctive, we chose the ordinary kriging. Ordinary kriging is the most often used type of kriging and also the simplest with fewest required parameters.
We need appropriate semivarigram model for interpolating by kriging technique. For this, the effective parameters e.g. the lag size, the search direction, and the anisotropy must be selected. These parameters have great influence on the values of sill, nugget, range and the percent ratio of nugget to sill. The spatial dependence was used to select the great semivariogarm models. The exponential models were determined as the best models for all Vs interfaces. The extracted parameters from determined models are presented in
We also examined the anisotropy on semivariogram modeling. The results indicate the anisotropy on data. As shown in
. Statistical parameters of interface depth values for all of the interfaces.
Vs interface | Interface depth | ||||||
---|---|---|---|---|---|---|---|
Min | Max | Mean | Median | SD | Skewness | Kurtosis | |
300 | 0.0 | 6.4 | 4.2 | 4.0 | 2.2 | 0.789 | 4.38 |
500 | 0.0 | 19.2 | 13.36 | 12.0 | 5.5 | 0.37 | 2.766 |
750 | 0.0 | 45.0 | 24.5 | 24.0 | 8.7 | −0.07 | 2.89 |
950 | 15.0 | 90.0 | 55.3 | 60.0 | 18.8 | −0.20 | 2.2 |
1200 | 20.0 | 160.0 | 106.6 | 110 | 32.4 | −0.4 | 2.8 |
. Geostatistical parameters of fitted semivariogram models.
Vs interface | Model | . Geostatistical parameters of fitted semivariogram models. | . Geostatistical parameters of fitted semivariogram models. | . Geostatistical parameters of fitted semivariogram models. | Major range (m) | Minor range (m) | Angle direction |
---|---|---|---|---|---|---|---|
300 | Exponential | 1.26 | 4.68 | 27 | 5926 | 4282 | 69 |
500 | Exponential | 8.22 | 29.84 | 27 | 5926 | 4417 | 129 |
750 | Exponential | 25.01 | 100.6 | 24 | 17348 | 11569 | 122 |
950 | Exponential | 71.19 | 417.61 | 17 | 13290 | 11279 | 122 |
1200 | Exponential | 0 | 1161.7 | 0 | 11851 | 7762 | 118 |
Large range value is related to the higher spatial structure. Other effective parameters for performing accurate interpolation are the number of neighbors and sector type.
The interpolation performances are analysis by plotting the predicted values versus the measured values and also by cross-validation index [
The cross-validation indexes of interpolations, the MSPR, RMSPE, AKSE, and PMSSPE are shown in
Kriged maps of the velocity interfaces and the attributed best fitted variogram are shown in
Cross-validation scatter plots of the interface depth values
. Cross-validation indices of the interface depth values.
Interface | MSPR | RMSPE | AKSE | RMSSPE |
---|---|---|---|---|
300 | 0.0017 | 1.676 | 1.535 | 1.078 |
500 | 0.0009 | 4.086 | 3.903 | 1.065 |
750 | 0.00086 | 6.19 | 6.209 | 1.018 |
950 | 0.01666 | 10.21 | 9.934 | 1.095 |
1200 | 0.03377 | 11.98 | 15.35 | 1.131 |
Semivariograms and kriged maps of the interfaces depth
m/s interface has depth of more than 80 m depth of the interface is continued to 160 m in eastern and northeastern city.
Clay and silt sediments are located in the central, east and northeast parts of the city. In addition the groundwater level ranges from 15 to 40 m in these regions. Hence these regions are covered by the softer soils and are formed deepest parts in all interfaces.
In this study, statistical analyses are done to interpolate the Vs interfaces occurrence depth at velocity of 300, 500, 750, 950 and 1200 m/s. It is found that ordinary kriging is the best estimator to find the best fitted semivariogram to depth data. The moderate spatial dependence is seen for the depth data of the 300 and 500 m/s interfaces and is observed strong spatial dependence for the depth data of the 750, 950 and 1200 m/s interfaces. The range of resulted semivariogram in various Vs interface is different. The highest range is observed in 750 m/s interface and the lowest range is belonging to 300 m/s interface. The most isotropy in data for 300 m/s interface observed in direction of about 70 degree but for others interfaces occurred in direction of about 120 degree. All of the Vs interfaces became deeper towards northeast. The shallow parts of the entire interfaces are located near the south and southwestern outcrops while the deep parts are laid at the central, eastern and northeastern city. It could be related to the existence of the fine grained soils and shallow groundwater level at these regions.
This research was supported by Zamin Physic Pouya consulting engineering company and authors would like to thank this support.
<
*Corresponding author.