‟ Distribution of Shallow Isochronous Layers in East Antarctica Inferred from Frequency-Modulated Continuous-Wave (FMCW) Radar „

7 During the 32nd Chinese National Antarctic Research 8 Expedition, the Frequency-Modulated Continuous-Wave (FMCW) 9 radar was used for the first time to obtain the distribution of 10 shallow isochronous layers within the East Antarctic region 11 extending from Zhongshan Station to Kunlun Station. Taking a 12 typical area as a case study, this article describes the complete 13 workflow used in radar data processing, including signal 14 processing and extraction of isochronous layers. The wave 15 velocity model is established according to an empirical formula 16 to calculate the depth of the layer, and the result is compared and 17 corrected with the volcanic record in ice core DT263; the relative 18 error of depth is only approximately 5%. The echograms of the 19 isochronous layers in three regions is presented, including the 20 area around the dome A, the area 100 km from the dome A and 21 the area in the Lambert Glacier. A comparison of the echograms 22 within the three regions shows that the isochronous layers are 23 relatively stable in the Dome A and change more intensely in the 24 Lambert Glacier region, while the folding of the layer occurs in a 25 concentrated area near Dome A. This folding may be due to the 26 local layer mixing and compression caused by the ice flow and 27 wind-driven processes. The analysis of the distribution of the 28 shallow isochronous layers and age-depth information from 29 different regions provides important data that support the 30 calculation of large-scale accumulation rates and flow history in 31 the Antarctic region. 32

shallow isochronous layers within the East Antarctic region 11 extending from Zhongshan Station to Kunlun Station. Taking a  12 typical area as a case study, this article describes the complete 13 workflow used in radar data processing, including signal 14 processing and extraction of isochronous layers. The wave 15 velocity model is established according to an empirical formula 16 to calculate the depth of the layer, and the result is compared and 17 corrected with the volcanic record in ice core DT263; the relative 18 error of depth is only approximately 5%. The echograms of the 19 isochronous layers in three regions is presented, including the 20 area around the dome A, the area 100 km from the dome A and 21 the area in the Lambert Glacier. A comparison of the echograms 22 within the three regions shows that the isochronous layers are 23 relatively stable in the Dome A and change more intensely in the 24 Lambert Glacier region, while the folding of the layer occurs in a 25 concentrated area near Dome A. This folding may be due to the 26 local layer mixing and compression caused by the ice flow and 27 wind-driven processes. The analysis of the distribution of the 28 shallow isochronous layers and age-depth information from 29 different regions provides important data that support the 30 calculation of large-scale accumulation rates and flow history in 31 the Antarctic region.  Glacier were selected to map the isochronous layers. These 101 regions are illustrated in Figure 1 as Profiles 2, 3, and 4, 102 respectively. By analyzing the echograms of the long-distance 103 isochronous layers in these regions, they exhibit completely 104 different characteristics, which are closely related to the 105 accumulation rate between regions. The data presented in this 106 paper facilitate calculations of large-scale accumulation rate and 107 can be used to analyze the temporal and spatial distribution of 108 SMB in the 1280 km range (from Zhongshan Station to Dome A). 109 These data also provide the foundation for reconstructing past 110 climates in the Antarctic region and analyzing the flow history. 111

Materials and methods 115
Considering the need for precise detection of shallow 116 isochronous layers and the lack of a large amount of convenient 117 energy, FMCW sounding radar was used in this work.

118
Compared to sounding radars with a depth of several 119 kilometers, the FMCW sounding radar sweep bandwidth used in 120 this study was 1.5 GHz, and the period was 4 ms, resulting in a 121 high vertical resolution of 6.16 cm in firn/ice. The trace repetition 122 rate was 100 traces/s; each trace contained 24,576 points at a 123 sampling rate of 6.25 MS/s and was able to measure the 124 isochronal layer within 10-100 m. The system power was 2 W,

Signal processing 147
The main purpose of this stage is to optimize the quality of the 148 data and prepare for the subsequent layer mapping. The specific 149 process is shown in Figure 3. 150

152
The raw data contain considerable coherent noise when they 153 are collected. The presence of this noise will affect the extraction 154 and analysis of ice structure, making the echogram blurry and 155 unable to effectively show the isochronal layer. Taking into 156 account the signal-to-noise ratio, only the last of every 8 traces 157 received by the radar was preserved to suppress coherent noise [S 158 Urbini, et al., 2010].

159
The original data were stored in the time domain; a fast Fourier 160 transformation (FFT) was applied to the original data to obtain a 161 spectrum plot, and a Hanning window was applied to the data to 162 reduce the range sidelobes. Because there is a 1/r 2 reduction in 163 power with range, we applied a lowpass filter to the spectral data, 164 and a filter with a very low cutoff frequency was used. The 165 original spectra were then multiplied by the inverse of the 166 lowpass filter response to correct for the gain. us to effectively distinguish isochronous layers. Figure 4 shows 187 that the distribution of the layers is more obvious after this 188 intensive processing. 189 After a clear image was obtained, the distance and depth of this 190 echogram could be calculated. When calculating the distance of 191 the profile, according to the principle of sounding radar and 192 referring to the radar parameters in Section 2, the distance of 193 the profile can be accurately calculated from the number of traces 194 N: where is the horizontal movement speed of the sounding radar; 196 a snowmobile can carry the radar at a constant speed of 14 km/h. 197 is the sweep period of 10 ms.

198
When calculating the depth, to complete the transition between According to the basic formula: 206 where 0 is the velocity of electromagnetic waves in a vacuum; 207 thus, the wave velocity is closely related to the relative actual 208 dielectric constant of the ice. A Kovacs et al. [1995] presented an 209 empirical formula for the relative true dielectric constant : 210 Firn is a mixture of air and ice. With the increased depth, the 211 content of air decreases gradually, which leads to the increasing 212 density of firn. When the density exceeds the critical value 213 (0.83 g/cm 3 ), firn is converted into ice [J Ren et al., 2001]. In this 214 process, the density changes greatly, which has a considerable 215 impact on the velocity of the wave. The detection area of the 216 sounding radar used in this paper includes firn and ice; therefore, 217 the process of snow densification must be considered. According 218 to the densification model formula proposed by KM Cuffey et al. 219 [2010], we can calculate the ice layer density ρ at a depth of : 220 where is the density value of pure ice (0.917 g/cm 3 at -20 °C) 221 and is the snow density on the surface of the ice sheet. The 222 surface density of ice sheets at ice cores LGB69 and DT263 is The present study area is consistent with this previous paper, so 228 this value can be corrected according to the geographical position. According to Equations (2)-(4), we can derive the functional 243 relationship between the wave velocity and the depth and use it to 244 perform the conversion between travel time and depth. After 245 post-processing of the raw data, the profile shown in Figure 4 was 246 obtained, which shows the lateral variation characteristics within 247 the range of 5 km.

Mapping of isochronous layers 252
After signal processing, the information of different layers can 253 be distinguished in the echogram. In this step, we mapped an 254 isochronous layer with a length of 5.8 km and arbitrarily selected 255 several clearly defined isochronous layers for tracking and 256 extraction. 257 In the subsequent accumulation rate study, the accumulation 258 rate model can be used to analyze the effect of depth on the SMB 259 [I Das et al., 2015]. In Figure 4, the continuity of the layers is 260 better, and the depth of the layers is characterized by greater 261 depth in the middle of the echogram and relatively shallower on 262 both sides. According to the standard SMB equation, 263 where is the depth of the layer, the density of the layer can be 264 calculated according to Equation (4), and is the age of the layer. 265 The depth of the isochronous layer is proportional to the 266 accumulation rate, so the accumulation rate in the middle of this 267 area is higher. Figure 5 corresponds to the elevation in the 268 echogram. Since the length of this area is only 5.8 km and the 269 surface altitude change is not severe, the influence of the terrain 270 on the isochronous layer can be observed. We need to analyze the 271 distribution of the layers on a larger scale to determine whether 272 the difference in the rate of accumulation is ubiquitous. And this 273 finding proves that the FMCW sounding radar can help us study 274 the differences in the spatial and temporal distributions of 275 accumulation rate. 276 By connecting all of the cross sections, as shown in Figure 5, 277 the distribution of shallow isochronous layers from Zhongshan 278 Station to Kunlun Station in East Antarctica can be obtained. We 279 chose an echogram of the isochronous layers over a distance of 280 30 km in the Lambert Glacier area as an example and selected 5 281 isochronous layers for tracking and extraction ( Figure 6). 282 However, when we added the elevation in an area of 70 km 283 (Figure 7), the results were not satisfactory because the terrain 284 changes usually exceed 200 m in a large area (more than 100 km), 285 whereas the shallow ice sounding radar can measure isochronous 286 layers only within a range of 100 m, and the elevation change far 287 exceeded the depth that FMCW radar can detect. To clearly 288 observe the distribution characteristics of the isochronous layer 289 and calculate the SMB according to the depth (Equation (5)  Thus, layer 1 ( Figure 6)  isochronous layer 2 ( Figure 6) can be related to a particular time 323 in the past. 324   thickness of the snow added in this area was estimated to be 347 1.76 m. 348 In Figure Table 1, which shows that the relative error 357 between the depth of D13-D16 and the volcanic record in the ice 358 core is approximately 5%, which is consistent with the findings 359 of M Frezzotti et al. [2005]. 360 The difference between the two data sets is due in part to the 361 increased snow thickness error within AD1999-2015. The firn 362 formed during this period has not yet reached the critical density 363 (0.55 g/cm 3 ), and the process of snow densification is obvious in 364 this range [Herron M M et al. 1980]. Therefore, the present paper 365 has a certain degree of overestimation of the inversion results. In 366 addition, although Equation (4) is an often useful empirical 367 formula for the depth-density relationship and has a high 368 correlation with the measured data of DT263, it still contains the 369 biases. 370 However, when using a constant wave velocity of 0.168 m/ns 371 (the electromagnetic wave velocity in pure ice), the relative error 372 reached 15.5%, which shows that the velocity model used in this 373 paper has higher precision when calculating depth. If the model is 374 used in a deeper range, it will exhibit greater advantages, which 375 provides a foundation for accurate calculations of accumulation 376 rate. 377 The depth of internal reflection horizons can be calibrated by 378 the corresponding ice core, and the depth-year information in the 379 vicinity of the ice core can also be determined. As shown in 380 Figure 7, the isochronous layer in the region is extended, and 381 continuous isochronous layers within a few hundred kilometers 382 can be obtained so that the SMB can be studied on a larger scale.

383
This method can also be used to plot the three-dimensional 384 distribution of a particular isochronous layer after multiple 385 investigations [MJ Siegert et al., 2010]. 386

Presentation of isochronous layers over large areas 387
At the end of this paper, a number of typical areas are also 388 analyzed, including the Dome A area, a region 100 km away from 389 Dome A [Sun Bo et al., 2009], and the region surrounding the 390 Lambert Glacier, which is the largest glacier in the world. These 391 regions present a wide range of layers. 392 In Figure 7, the randomly selected images of different depths 393 and layers in these regions show the shallow ice structure and the 394 depth variation in the horizontal direction within ~130 m. The 395 depth information of the isochronous layers is shown in Figure 7. 396 Therefore, we can, as in the Section 5, track and map specific 397 isochronous layers using the corresponding ice core data and 398 determine the ages corresponding to specific depths. 399 The   processes also have a great influence on the distribution of 462 accumulation rate.

463
After analyzing these three regions, it can be found that the 464 distribution of isochronous layers differs among regions. These 465 phenomena are closely related to the spatial transformation of the 466 accumulation rate. Therefore, further analyses can be conducted 467 using geographic and meteorological factors. 468

Conclusion 469
This paper mainly describes the shallow exploration radar 470 observation work conducted by CHINARE 32 from Zhongshan 471 Station to Kunlun Station in 2015. The process of collecting data 472 for the entire section is described, detailed processing was then 473 carried out, the isochronous layers were drawn, and the 474 correspondence of the results with the ice core was demonstrated.

475
The results are summarized below. 476 1) FMCW sounding radar is a high-resolution radar system. 477 After signal processing, a clear echogram of the isochronous 478 layers can be obtained. And layers within ~100 m can be 479 distinguished and extracted.. flow movement and wind-driven processes. 504 5) As seen from Table 2 and Table 3