## 5 Conclusions  
During the Chinese National Arctic Research Expedition, source bearing estimation experiments using an ice-mounted geophone and a USR were performed at three sites in the central Arctic Ocean. The relationship between the errors of bearing estimation and frequency bands was studied.  
It was found that the bearing estimation errors for an acoustic source in different frequency bands are related to the \(x\)- or \(y\)-direction peak displacements received by the ice-mounted geophone. The higher the peak displacement, the smaller the bearing estimation error. When the value of the \(x\)- or \(y\)-direction peak displacement in some frequency band is lower than a certain threshold, the bearing estimation error corresponding to the frequency band becomes larger, almost larger than 25\({}^{\circ}\).  
Moreover, when the incident angle of the acoustic source and the thickness of the ice meet certain conditions, some modes of the Lamb waves in the ice layer will be excited, and the peak distribution structure of the horizontal displacement will be changed. The bearing estimation errors in the frequency band corresponding to the Lamb waves are reduced, and the efficient frequency band of the signal for the bearing estimation will be widened.  
The study of acoustic signals detected on the surface of ice is not only related to geophones, but also to sound sources. Due to the difficulty in obtaining underwater sound sources and the complex physical characteristics of the ice layer, it has been difficult to obtain variations in cross-ice sound signals with frequency. In experiments at three sites, the x-, y- and z-direction displacements and bearing estimation were measured by using an ice-mounted geophone, and the analysis frequency band was 40-1000 Hz. At same time, the underwater data were received by the USR. By comparing data obtained on the ice with data obtained underwater, we could partly discover the conversion and mechanism of signal energy across ice layers in different frequency bands.  
Considering that there are still some problems with source bearings caused by the anisotropy of the ice layer or small real bearing angles in the experiment, Arctic acoustic experiments and research will need to be continuously performed. Underwater acoustic source bearing estimation and the coupling propagation mechanism of underwater acoustic signals across ice-to-ice surfaces will be further studied.  
Conceptualization, H.W.; Methodology, S.C.; Software, S.C. and H.R.; Validation, S.C. and H.W.; Formal analysis, S.C.; Investigation, H.Z.; Data curation, H.Z. and H.R.; Writing--original draft, S.C.; Writing--review & editing, H.W.; Supervision, Y.Y.; Project administration, Y.Y.; Funding acquisition, H.W. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Key R&D Program of China (2021 YFC2801202), the Natural Science Foundation of Fujian Province of China (2023J011382), the National Nature Science Foundation of China (42276192, 42076236), and the Scientific Research Foundation of Third Institute of Oceanography, MNR (No. 2022020).  
Not applicable.  
The data presented in this study are available on request from the corresponding author. The data are not publicly available due to some intellectual property and preventing abuse.  
We thank the officers and crew of RV Xue Long 2 who were present during the Eleventh Chinese National Arctic Research Expedition.  
The authors declare no conflict of interest.