esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Sum-Rate Performance with RVQ-Based CSI Feedback
### Similarity between RVQ Error and Gaussian Channel Error
Therefore, the Gaussian channel error model equivalent to the original RVQ model can be denoted by  
\[\mathbf{H}=\sqrt{1-E(z)}\mathbf{\hat{H}}+\sqrt{E(z)}\mathbf{E}. \tag{14}\]  
Figure 2: Comparison of \(\beta^{2}\) and the expectation of the equivalent VQ error. According to Lemma 1 in [4], effective direct channels \(\mathbf{u}_{k}^{mH}\mathbf{H}_{kk}\mathbf{v}_{k}^{m}\) are independent and Gaussian-distributed complex variables with unit variance. Thus, the effective direct channel in each IA data stream is equivalent to a Rayleigh fading channel, and the achievable sum-rate of IA with perfect CSI can be represented by  
\[R_{IA}\approx E\left(\sum_{k}\sum_{m}r_{k}^{m}\right)\approx Kd\text{log}_{2}(e )e^{1/\rho}E_{1}(\frac{1}{\rho}), \tag{15}\]  
where \(\rho=\frac{P}{d\sigma^{2}}\) is the effective SNR in each stream, and \(E_{1}(\eta)=\int_{1}^{\infty}t^{-1}e^{-\eta t}dt\) is the exponential integral function [4]. In the Gaussian channel error model, the channel matrices obtained by the receivers are \(\sqrt{1-\beta^{2}}\mathbf{\hat{H}}_{ki}\); then, the precoding and decoding vectors \(\mathbf{u}_{k}^{m}\) and \(\mathbf{v}_{k}^{m}\) are solved based on imperfect \(\mathbf{\hat{H}}_{ki}\). Thus, for \((k,m)\
eq(i,l)\), \(\mathbf{u}_{k}^{mH}\mathbf{\hat{H}}_{ki}\mathbf{v}_{i}^{l}=0\) holds, and the intra-stream interference can be written as  
\[\mathbf{u}_{k}^{mH}\mathbf{H}_{ki}\mathbf{v}_{i}^{l}=\mathbf{u}_{k}^{mH}\bigg{(} \sqrt{1-\beta^{2}}\mathbf{\hat{H}}+\beta\mathbf{E}\bigg{)}\mathbf{v}_{i}^{l}= \beta\mathbf{u}_{k}^{mH}\mathbf{E}\mathbf{v}_{i}^{l}, \tag{16}\]  
where \(\mathbf{u}_{k}^{mH}\mathbf{E}\mathbf{v}_{i}^{l}\) are also independent and Gaussian-distributed complex variables with unit variance. Finally, the achievable sum-rate of IA with RVQ-based CSI feedback can be approximated by  
\[R_{RVQ}\approx E\left(\sum_{m,k}\text{log}_{2}\left(1+\frac{ \frac{P}{d}|\mathbf{u}_{k}^{mH}\mathbf{H}_{kk}\mathbf{v}_{k}^{m}|^{2}}{\sum \limits_{(k,m)\
eq(i,l)}\frac{P}{d}\left|\beta\mathbf{u}_{k}^{mH}\mathbf{E} \mathbf{v}_{i}^{l}\right|^{2}+\sigma^{2}}\right)\right)\approx Kd\text{log}_{2} (e)e^{1/\rho_{\textit{eff}}}E_{1}(\frac{1}{\rho_{\textit{eff}}}),\] (17) where \[\rho_{\textit{eff}}=\frac{\rho}{\rho(Kd-1)\beta^{2}+1}=\frac{\rho}{\rho( Kd-1)2^{B}Beta(2^{B},\frac{NM}{NM-1})+1}\] (18) denotes the effective SNR with the introduced quantization error from RVQ. The accuracy of (17) is demonstrated in Section 6. Figure 3: PDFs of RVQ error \(z\) and equivalent VQ error \(z\) with \(B=20\), \(\beta=0.0938\).
# CAVVPM: Challenge-Based Authentication and Verification of Vehicle Platooning at Motorway
## 5 Evaluation
### Security of CAVVPM  
A virtual opponent cannot pass the PoF verification without fulfilling the challenging situations, as shown in Section 4.2. The only possibility for the opponent is if an independent vehicle \(R\) follows the verifier at the platooning distance \(R\). As stated in Proposition 1, we calculated the likelihood that M will pass verification owing to \(R\)'s movement. Vehicle R, driving at 30 m/s, was simulated approaching the verifier at the same time. The vehicle \(R\) performed a random walk with a step size of 0.3 m inside the checkpoint range (30 m-60 m away from the verifier). The verifier provided physical challenges with a tolerance of 0.3 m regularly. \(R\)'s distance from V as a function of time for five checkpoints is shown in Figure 13A. At the time of the limit, as seen in Figure 13B, \(R\)'s range from every security check was apparent. We find that \(R\) often resides far from the designated checkpoint since it makes no effort to go there.  
In Figure 14A, \(M\)'s pass percentage as a result of the number of physical challenges, computed using the formula over 2000 challenges, is shown in greater detail. Note that \(M\) failed all of the PoFs after \(K=2\), (\(PM=0\)). As a point of reference, we have included \(PM\) as a numerical value derived from Proposition 1. The odds of overcoming even a few minor physical obstacles are quite low. \(PM\) is unaffected by the checkpoint space attribute \(M\). This is because \(R\) must meet a deadline for a certain checkpoint. The uniform distribution of this probability can easily be demonstrated using a random walk (with slightly higher probabilities for the two boundaries).  
Figure 12: Shows the change in C’s acceleration, velocity, and distance from \(d_{\mathit{off}}=45\) m to milestone D = 42 m when the verifier’s speed drops from 30 m/s to 27 m/s. (**A**) Acceleration; (**B**) Velocity; (**C**) Following distance.  
Figure 13: _Cont._Figure 14: (**A**) time(s); (**B**) Index of checkpoint. Simulated and numerical passing probability \(P_{M}\) vs. challenges \(K\).  
Figure 13: For example, how long it takes to verify a certain number of challenges and milestones. (**A**) Five challenges are used to calculate the distance between R and V. (**B**) Vehicle R’s range from checkpoints at each deadline. (**B**) shows that, independent of \(M\), \(PM\) and \((1/N)^{K}\) are essentially identical, despite the fact that P1 is smaller than \((1/N)^{K}\).
## 3 Results
### Place of Installation of the Anenometer  
The pitch angle is positioned by a 0.5 Hp direct current motor at 1750 rpm coupled to a gearbox with a 60:1 ratio, and the movement to each blade is transmitted by a worm-screw and a spiral-bevel-gear system. The gearbox increases the torque to counteract the effects of the wind on the rotation of the blades and can rotate without restrictions; however, the positioning speed is reduced to 3\({}^{\circ}\)/s. The pitch angle rotates from 0\({}^{\circ}\) to 90\({}^{\circ}\) in 30 s. The calculated distance to detect the maximum wind speed of 15 m/s 30 s in advance is 450 m.  
Figure 7 shows the location of the SHAWT and the proposed place for the anemometer installation [31]. In A, the generator is installed, and in B, it is proposed to install the anemometer 450 m apart, both places located within the university.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Statistical Wind Analysis** & **Wind Speed (m/s) at 18 m** \\ \hline Mean & 4.44 \\ Median & 4.24 \\ Mode & 3.62 \\ Standard Deviation & 1.98 \\ Range & 15.00 \\ Minimum & 0.00 \\ Maximum & 15.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical analysis of wind speed.  
Figure 6: Historic frequency of wind speed.  
It is considered that local wind gusts do not change their route, as the area of study is in a plain; moreover, according to meteorological analysis, there are no sudden changes in ambient temperature or atmospheric pressure. Route changes could be due to nearby buildings, for which a dynamic wind flow analysis is performed.
## Materials and Methods  
### Data and Preprocessing  
In this study, the basic knowledge database for extracting the spatial distribution information of rocky desertification is the Chinese periodical database provided by the CNKI. The CNKI is a database system based on various literature and documents and it has become the world's largest Chinese knowledge engine and library. By 31 August 2017, the China Academic Journals full-text database (CAJ) in the CNKI included 10,898 journals, 1,700,252 articles and 60,496,267 articles. The authors compiled a special crawler system of the CNKI in JAVA and retrieved all 9345 documents related to rocky desertification from the 1950s to 2016 using the three keywords of 'rocky desertification', 'kast desertification' and 'kast degradation.' The authors also downloaded the title, abstract, keywords, author and other information and saved these data to the local database. The local database was implemented on SQLite. SQLite is an in-process library that implements a self-contained, serverless, zero-configuration, transactional SQL database engine. These merits of SQLite make our information extraction method of research hot regions can be migrated to different computing platform.  
The basic spatial data used for address recognition, toponym matching and spatial mapping in the study came from the 2012 version of the Chinese administrative division map provided by China Cartographic Publishing House. By considering the abbreviation, alias or historical name of administrative divisions, the study also used the 1:250,000 basic geographic database provided by the National Administration of Surveying Mapping and Geoinformation of China and the China's historical-level administrative division database provided by the National Earth System Science Data Sharing Infrastructure to revise partial toponyms and supplement some aliases of toponyms. All of the above databases comprised a standard toponym database (STD) in this study.  
To analyze the sensitivity to rocky desertification and to compare the sensitivity and hot regions of rocky desertification, this study also uses (Figure 1)  
1. The relief amplitude spatial distribution data calculated from a digital elevation model (DEM) with a 1-km resolution;
2. The vegetation coverage spatial distribution data calculated using the dichotomy model with MODIS NDVI data [35; 36];
3. The 1-km grid population dataset of China (2010) based on the data of the Fifth National Census [37];
4. The road network density above the county level, which is based on the 1:25 million basic geographic database provided by the National Geomatics Center of China.
# Research on Panorama Generation from a Multi-Camera System by Object-Distance Estimation
## 3 Proposed Method
### Object-Distance Interpolation Method in the Non-Overlapping Regions  
An interpolation method is adopted to derive object-distance information in the non-overlapping regions. For a pixel point \(p(x_{p},y_{p})\) located in the non-overlapping region between two overlapping regions \(A_{i,j}\) and \(A_{j,k}\), its object-distance can be interpolated from the known object-distance information of two points \(p_{l}\big{(}x_{p_{l}},y_{p}\big{)}\) and \(p_{r}\big{(}x_{p_{r}},y_{p}\big{)}\) using Equation(15), as shown in Figure 7.  
\[r^{l}\big{(}x_{p},y_{p}\big{)}=\Big{(}\frac{x_{p_{l}}-x_{p}}{x_{p_{r}}-x_{p_{l} }-w}\quad\frac{x_{p}-x_{p_{l}}}{x_{p_{r}}-x_{p_{l}}-w}\Big{)}\binom{r^{l} \big{(}x_{p_{l}},y_{p}\big{)}}{r^{l}\big{(}x_{p_{r}},y_{p}\big{)}} \tag{15}\]  
where \(r^{l}\big{(}x_{p},y_{p}\big{)}\), \(r^{l}\big{(}x_{p_{l}},y_{p}\big{)}\), and \(r^{l}\big{(}x_{p_{r}},y_{p}\big{)}\) are the object-distances of pixel point \(p\), \(p_{l}\) and \(p_{r}\), respectively. The object-distance information can be calculated using the object-distance maps in the top-level of the aforementioned pyramid grids.  
The values of \(x_{p_{l}}\) and \(x_{p_{r}}\) are determined by \(x_{j,k}^{L}-\frac{w}{2}\) and \(x_{i,j}^{L}+\frac{w}{2}\), respectively, where \(w\) represents the width of an overlapping region. In this context, \(i\) takes values from 1 to 7, j takes values from 2 to 7, and \(k\) takes values from 3 to 8, including 0. The parameters of \(x_{i,j}^{L}\) and \(x_{j,k}^{L}\) represent the displacements of the centre lines \(gap_{i,j}\) and \(gap_{j,k}\) from the y-axis of the panoramic image system, respectively. In the same way, the object-distances can be estimated for all the pixel points in the non-overlapping regions.  
Finally, a panoramic image can be generated based on Equation (9) with the estimated object-distance information on the overlapping regions and non-overlapping regions.  
Figure 7: Non-overlapping regions of a panoramic image.
# Fine Root Length of Maize Decreases in Response to Elevated CO2 Levels in Soil
## 3 Results
### Relative Diameter Class Length Under Different Levels of Elevated Soil CO2  
The relationships between root length and basal diameters of the whole root systems for CK and the CO2 treatments were determined. As shown in Figure 4a, the data was fitted by an exponential equation, and in Figure 4b, the data, of which root length could be log-transformed, was also fitted with a linear equation.  
\[\mathrm{Y=a+bX} \tag{2}\]  
Here, Y refers to the root length after being log-transformed, and X refers to diameter grouped from 0 to 2.9 mm at intervals of 0.1 mm. The mean values of root diameters are represented by X (x1, x2,..., x30), and the histograms refer to the mean values of the root length Y (y1, y2,..., y30). The values of \(a\) in the exponential equation for CK, G1000, and G2000 were 3.651, 3.432, and 3.351, respectively; in this regard, G1000 and G2000 were less in comparison with the CK treatment. The values for \(b\) were \(-\)0.824, \(-\)0.74, and \(-\)0.744, for CK, G1000, and G2000, respectively; in this regard, G1000 and G2000 were greater compared with CK treatments. The correlations were significant, and the coefficients of determination (R2) were all greater than 0.80 (R2 = 0.924 for CK, R2 = 0.871 for G1000, and R2 = 0.890 for G2000). The slope of the exponential equation for the CK treatment was steeper than that for the CO2 treatments, and the values of \(b\) of linear equations in CO2 treatments were greater compared with the CK treatment, which also demonstrated that the increased CO2 flux was consistent with a great decrease in the root length of the small-diameter class (Figure 4b).  
Figure 3: Basal diameter variation of different nodal-root whorls of maize in the control (CK) and elevated soil CO2 treatments (G1000 and G2000). Medians (solid, lines in box), and 25% and 75% quartiles (lower and upper margins of the boxes) of nodal-root whorl diameters are shown. Different letters (e.g. a, b) indicate significantly difference at a 5% significance level. The total number of root disks of each root system is given in the key.  
difference in the large-diameter class (d \(>\) 2.0 mm) in comparison with the CK treatment (Table 3, \(p\)\(>\) 0.05). The average fine root lengths for G1000 and G2000 within the root diameter range 0-1 mm were 24,529.3 \(\pm\) 1325.5 cm and 18814.3 \(\pm\) 2735.3 cm, respectively, representing decreases of 29.44% and 45.88%, respectively, in comparison to the CK treatment (Table 3, \(p\)\(<\) 0.05). The mean values of root lengths within the root diameter range of 1-2 mm for G1000 and G2000 were 1341 \(\pm\) 85.7 cm and 1202.8 \(\pm\) 83.9 cm, respectively, representing decreases of 36.37% and 42.92%, respectively, compared to the CK treatment (Table 3, \(p\)\(<\) 0.05). The mean root lengths of G1000 and G2000 for diameters of 2-2.9 mm were not significantly different from those of the CK treatment (Table 3).
## 5 Results and Discussion
In Figure 17, the spatial distribution of the power dissipation and electron density distributions are represented according to the electric field components, which are indicated by resolving the radial fields into the \(E_{x}\) and \(E_{y}\) components. In the case of \(E_{x}\), the field strength was the highest for 6 \(\times\) 10\({}^{3}\) V/m near the window surface, and the field direction was perpendicular to the window surface. Similarly, for the case of \(E_{y}\), the field strength was the highest for 1.5 \(\times\) 10\({}^{4}\) V/m, and the field direction was parallel to the window surface. In both these cases, as shown in Figure 17, the spatial distributions of the electron generation and power dissipation coincided with the electric field concentrated region. When the volume-integrated power dissipation value deposited for plasma generation was calculated by resolving into the \(E_{x}\) and \(E_{y}\) field components, the power dissipation value \(E_{x}\approx\) 300 W and \(E_{y}\approx\) 260 W. Among the radial field components involved in the plasma discharge, a dominant component was \(E_{x}\), which was due to the field emitted geometry characteristics of the waveguiding structure. Figure 8:2 Electron density and power dissipation \(Q_{h,x}\) (=Re \((\frac{1}{2}\sigma\cdot E_{x}\cdot E_{x}^{*})\)) distributions according to the \(|E_{x}|\) profile, electron density and power dissipation \(Q_{h,y}\)(=Re \((\frac{1}{2}\sigma\cdot E_{y}\cdot E_{y}^{*})\)) distributions according to the \(|E_{y}|\) profile in the XZ plane of circular TE\({}_{11}\) waveguiding structure. (**a**) Electron density distribution according to the profile of \(|E_{x}|\), (**b**) the distribution of power dissipation value \(Q_{h,x}\) according to the profile of \(|E_{x}|\), (**c**) electron density distribution according to the profile of \(|E_{y}|\), and (**d**) the distribution of power dissipation value \(Q_{h,y}\) according to the \(|E_{y}|\) profile.
# Robust Speed Control of a Multi-Mass System: Analytical Tuning and Sensitivity Analysis
## 3 Development of the Control Algorithm
### Frequency Analysis
#### 3.2.1 Stability Analysis  
The sensitivity of different closed-loop control systems will be evaluated with and without delay quantities: delay from the electrical part of VEL (i.e., represented by the transfer function \(G_{t}\)) and delay from the angular speed sensor (i.e., represented by the transfer function M). Then, the stability will be evaluated using _Nyquist criteria_[35; 36].  
The parameters of the total delay transfer function (\(G_{\Delta}\)) are set according to [10], so that \(\alpha_{t}\) is 1800 rad/s, and \(T_{d}\) equals 0.2 ms. Since \(T_{m}\) depends on the sampling time of the measurement sensor [10; 32], it will vary during this work. However, it will be fixed to 0.7 ms in this section. As a result, \(G_{\Delta}\) can be described as a first-order system with a total delay time of 0.9 ms. The open-loop transfer functions of \(PI\), \(LQ\), and \(LQI\) are determined through Equations (23)-(25), respectively  
\[H_{PI}(s)=G(s)\left[k_{p}+\frac{k_{i}}{s}\right] \tag{23}\]  
\[H_{LQ}(s)=\textbf{{K}}_{\textbf{{LQ}}}\big{(}s\textbf{{I}}-\textbf{{A}}+ \textbf{{L}}_{\textbf{{LQ}}}\textbf{{C}}\big{)}^{-1}+\big{[}\textbf{{L}}_{ \textbf{{LQ}}}G(s)+B_{M}\big{]} \tag{24}\]  
\[H_{LQI}(s)=\textbf{{K}}_{\textbf{{x}}}\big{(}s\textbf{{I}}-\textbf{{A}}+ \textbf{{L}}_{\textbf{{LQ}}}\textbf{{I}}\textbf{{C}}\big{)}^{-1}+\big{[} \textbf{{L}}_{\textbf{{LQ}}}G(s)+B_{M}\big{]}+\frac{\textbf{{K}}_{\textbf{{z} }}}{s}G(s). \tag{25}\]  
The Nyquist plot in Figure 9 shows that the PI closed-loop control system has high robustness with \(M_{Sv}=1\) in the ideal case (i.e., \(G_{\Delta}=1\)), while it shows unsatisfactory robustness of \(M_{Sv}>2\) in the presence of a 0.9 ms delay. The Nyquist contour is very close to the \(-1\) point, explaining the low robustness evaluation. Nonetheless, according to Nyquist stability criteria, the closed-loop with the PI controller is stable.  
Figure 9: Nyquist plot in logarithmic scale [38] for PI-controlled system.  
The maximum sensitivity of the LQ closed-loop control system has insignificantly increased due to a time delay, as illustrated in Figure 10. Therefore, according to Nyquist stability criteria, the closed-loop with an LQ controller is stable and robust.  
In Figure 11, the robustness of the \(LQI\)-controlled system provides the same \(M_{Sv}\) evaluation as the \(LQ\) controller in both cases. In the ideal case, it is worth noting that the \(LQ\) and \(LQI\) have almost identical Nyquist plots. Also, in case of a time delay, both controllers produced the same outer contour, but the inner contour of \(LQI\) forms a spiral pattern. Therefore, according to Nyquist stability criteria, the closed-loop of \(LQI\) is stable and robust.
# Influence of Some Additives on the Properties of OPC Solidified Sandy Silt
## 3 Results
### Indirect Tensile Strength
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Additives**} & \multirow{2}{*}{**Content/\%**} & \multirow{2}{*}{**Mixture**} & \multicolumn{5}{c}{**Curing Days**} \\ \cline{3-8}  & & & **7** & **14** & **28** & **60** & **90** \\ \hline None & 0 & S11 & 0.18 \(\pm\) 0.01 & 0.25 \(\pm\) 0.02 & 0.40 \(\pm\) 0.03 & 0.46 \(\pm\) 0.03 & 0.46 \(\pm\) 0.04 \\ \hline \multirow{3}{*}{Gypsum} & 2 & SS2 & 0.19 \(\pm\) 0.02 & 0.29 \(\pm\) 0.03 & 0.39 \(\pm\) 0.03 & 0.59 \(\pm\) 0.04 & 0.59 \(\pm\) 0.03 \\  & 3 & SS3 & 0.09 \(\pm\) 0.01 & 0.15 \(\pm\) 0.01 & 0.34 \(\pm\) 0.02 & 0.55 \(\pm\) 0.04 & 0.56 \(\pm\) 0.05 \\  & 4 & SS4 & 0.08 \(\pm\) 0.01 & 0.11 \(\pm\) 0.01 & 0.16 \(\pm\) 0.02 & 0.47 \(\pm\) 0.05 & 0.49 \(\pm\) 0.04 \\ \hline \multirow{3}{*}{Clay particles} & 2 & SN2 & 0.22 \(\pm\) 0.02 & 0.27 \(\pm\) 0.02 & 0.36 \(\pm\) 0.03 & 0.40 \(\pm\) 0.03 & 0.40 \(\pm\) 0.05 \\  & 3 & SN3 & 0.23 \(\pm\) 0.05 & 0.30 \(\pm\) 0.03 & 0.38 \(\pm\) 0.03 & 0.41 \(\pm\) 0.05 & 0.41 \(\pm\) 0.06 \\  & 4 & SN4 & 0.23 \(\pm\) 0.02 & 0.30 \(\pm\) 0.02 & 0.39 \(\pm\) 0.04 & 0.43 \(\pm\) 0.06 & 0.43 \(\pm\) 0.05 \\ \hline \multirow{3}{*}{Lime} & 2 & SH2 & 0.10 \(\pm\) 0.01 & 0.15 \(\pm\) 0.02 & 0.19 \(\pm\) 0.02 & 0.21 \(\pm\) 0.03 & 0.21 \(\pm\) 0.03 \\  & 3 & SH3 & 0.07 \(\pm\) 0.01 & 0.09 \(\pm\) 0.02 & 0.12 \(\pm\) 0.02 & 0.14 \(\pm\) 0.02 & 0.15 \(\pm\) 0.02 \\  & 4 & SH4 & 0.04 \(\pm\) 0.01 & 0.06 \(\pm\) 0.01 & 0.07 \(\pm\) 0.01 & 0.08 \(\pm\) 0.03 & 0.11 \(\pm\) 0.03 \\ \hline \multirow{3}{*}{Fly ash} & 2 & SF2 & 0.19 \(\pm\) 0.02 & 0.26 \(\pm\) 0.03 & 0.38 \(\pm\) 0.04 & 0.49 \(\pm\) 0.05 & 0.53 \(\pm\) 0.06 \\  & 3 & SF3 & 0.18 \(\pm\) 0.02 & 0.31 \(\pm\) 0.03 & 0.42 \(\pm\) 0.04 & 0.53 \(\pm\) 0.05 & 0.54 \(\pm\) 0.04 \\ \cline{1-1}  & 4 & SF4 & 0.20 \(\pm\) 0.01 & 0.30 \(\pm\) 0.02 & 0.43 \(\pm\) 0.04 & 0.54 \(\pm\) 0.05 & 0.58 \(\pm\) 0.03 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Test results for indirect tensile strength (MPa).
## 2 Materials and Methods
### Isostatic and Decompensative Gravity Anomalies  
#### 2.3.1 Initial Data  
For computation of the isostatic and decompensative gravity anomalies we employ five principal data set: Bouguer gravity anomalies, topography, initial model of the sedimentary cover (thickness and density), depth to the Moho based on seismic determinations and EET of the lithosphere. All these grids have resolution of \(5^{\prime}\times 5^{\prime}\), they have been obtained in previous studies and summarized in [48]. The Bouguer gravity anomalies (Figure 1) are calculated from the EIGEN-6c4 model [12], which is based on a combination of the recent satellite missions (chiefy GRACE and GOCE) and surface/airborne observations. The resolution of this model is 2190 spherical harmonics degree/order, which approximately corresponds to \(5^{\prime}\times 5^{\prime}\) in space. The topography correction is calculated using the ETOPO-1 data [49]. The density of the topography is assumed to be 2.67 g/cm\({}^{3}\), and of the water--1.03 g/cm\({}^{3}\). The calculation technique accounts for sphericity of the Earth, it is explained in details in [43]. The effect of the initial density model of the sedimentary cover is also removed from the Bouguer gravity anomalies [48]. The residual field is shown in Figure 2b.  
The initial model of sediments (thickness) is shown in Figure 3a. For most of the study area, we used the compilation of Kaban [3], which was supplemented by the data of [PERSON] et al. [43] for the Anatolian block, part of the Lesser Caucasus and Zagros fold belt. These data have been also used for determination of the adjusted topography (Equation (2), Figure 3b). It represents a result of numerical \"densification\" of water and sedimentary toks to the standard density of topography (2.67 g/cm\({}^{3}\)). It is visible that after this procedure, vast areas in the continental part expose negative topography.  
For the Moho boundary (Figure 4a), we used the same model as in [48]. It is based on the EuCRUST-07 data [50], which were supplemented in the eastern part by the model presented in [51]. The effective elastic thickness (Figure 4b) used in this study is calculated with the fan wavelet coherence technique [48].  
Figure 3: (a) Thickness of sediments according to the initial model; (b) adjusted topography calculated by numerical \"densification\" of water and sedimentary toks to the normal upper crust density (2.67 g/cm\({}^{3}\)).  
Figure 2: (a) Bouguer gravity anomalies; (b) residual gravity field after removal of the effect of the initial density model of the sedimentary cover. See text for detailed explanations.