**5. Conclusions**

In this paper, we use GPR to detect the moisture content of railway subgrade. The flow of the processing and interpretation includes: first, to obtain the stacking velocity of each layer of subgrade by the velocity analysis of CMP gathers; second, to convert the stacking velocities into interval velocities by the Dix formula and then calculate the dielectric constant; finally, to obtain the moisture content distribution of subgrade by the Topp formula. In this flow, it is the most important thing to pick up the accurate stacking velocity.

The shallow and thin multi-layers of railway subgrade make CMP gather seriously disturbed by multiple waves and refraction waves, which makes the routine velocity analysis unable to provide accurate velocity. In the railway subgrade case, we propose a solution of the optimal gather from a certain offset range dominated by the primary reflection to calculate the velocity spectrum. The extraction of the valid velocities can be completed by judging their correspondence with the peak of the average amplitude curves and the events in CMP gathers. The proposed optimal gather and interpretation flow are applied to the CMP data acquired at a railway site, and a long profile of moisture content distribution is obtained. IP measurement along the same survey line shows the abnormal regions of polarizability whose positions are consistent with large water content areas extracted from GPR data.

In the field survey, a GPR system equipped with a shielded antenna with a central frequency of 100 MHz is used. This frequency of the antenna has a limitation in the detection of the shallow and thin layer structure of the subgrade. The shielded antenna with the center frequency of 200 MHz may give a better result which is known through numerical simulation (not shown in the text). Unfortunately, we do not have such equipment. However, it is gratifying to see that the results given by this paper show that the antenna with a center frequency of 100 MHz is feasible. In conclusion, the velocity analysis of CMP gathers in GPR has grea<sup>t</sup> potential in quantitatively estimating the moisture content of the railway subgrade in the construction and maintenance of railway in cold regions.

**Author Contributions:** Conceptualization, S.L. and Q.L.; methodology, S.L., Q.L., H.L., Y.W.; formal analysis, S.L., Q.L., H.L., and Y.W.; Data processing, S.L., Q.L., H.L.; investigation, H.L., Y.W.; data curation, S.L.; writing—original draft preparation, S.L. and Q.L.; writing—review and editing, S.L., Q.L.; funding acquisition, S.L., Q.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was funded by the Natural Science Foundation of China (Grant 41874136 & 41574109), and Science and Technology on Near-Surface Detection Laboratory under Grant 61424140601.

**Acknowledgments:** The authors are grateful to the reviewers for their valuable suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
