Ground Penetrating Radar (GPR) has become a widely used technology in geophysical prospecting. The Variational Mode Decomposition (VMD) method is a fully non-recursive signal decomposition method with noise robustness for GPR data processing. The VMD algorithm determines the central frequency and bandwidth of each Intrinsic Mode Function (IMF) by iteratively searching for the optimal solution of the variational mode and is capable of adaptively and effectively dividing the signal in the frequency domain into the many IMFs. However, the penalty parameter $\mathsf{\alpha }$ and the number of IMFs K in VMD processing are determined depending on manual experience, which are important parameters affecting the decomposition results. In this paper, we propose a method to automatically search the parameters $\mathsf{\alpha }$ and K optimally by Particle Swarm Optimization (PSO) algorithm. Then the signal-to-noise ratio (SNR) and root-mean-square error (RMSE) are used to judge the best superposition of the IMFs for data reconstruction, and the process is data-driven without human subjective intervention. The proposed method is used to process the field data, and the reconstruction data show that this innovative VMD processing can effectively improve the SNR and highlight the target reflections, even some targets not found in pre-processing are also revealed.

China is strongly dependent on railway transportation, but the frost heaving of the subgrade in cold regions has seriously affected the safety and comfort of trains. Moisture content is an essential parameter in the subgrade frost heave. Non-destructive and efficient geophysical methods have great potential in measuring the moisture content of railway subgrade. In this paper, we use the common mid-point (CMP) measurement of ground penetrating radar (GPR) to estimate the propagation velocity of electromagnetic waves in a subgrade application. We establish a synthetic model to simulate the railway subgrade structure. The synthetic CMP gathers acquired from shallow and thin layers are seriously disturbed by multiple waves and refraction waves, which make the routine velocity analysis unable to provide accurate velocities. Through the analysis of numerical simulation results, it is found that the primary reflection waves, multiple waves, and refraction waves are dominant in different offset ranges of CMP gather. Therefore, we propose a solution of the optimal gather at a certain range of offset dominated by the primary reflection wave to calculate the velocity spectrum and extract the accurate velocities for the subgrade model. The relative dielectric constants of the corresponding layers are calculated after the stacking velocities are converted into the interval velocities. Then, the moisture content is obtained by the Topp formula, which expresses the relationship between dielectric constant and moisture content. Finally, we apply the optimal gather scheme and the above interpretation process to the GPR data acquired at the railway site, and we form a long moisture content profile of the railway subgrade. Compared with the polarizability measured by the induced polarization (IP) method, it is found that the regions with high moisture content correspond to polarizability anomalies with different strengths. The comparison shows the reliability of GPR results to some extent.

The internal layers of ice sheets from ice-penetrating radar (IPR) investigation preserve critical information about the ice-flow field and englacial conditions. This paper presents a new detailed analysis of spatial distribution characteristics of internal layers and subglacial topography of the East Antarctic ice sheet (EAIS) from Zhongshan Station to Dome A. The radar data of 1244 km along a traverse between Zhongshan Station and Dome A of EAIS were collected during the 29th Chinese National Antarctic Research Expedition (CHINARE 29, 2012/2013). In this study, the Internal Layering Continuity Index (ILCI) and basal roughness were taken as indicators to provide an opportunity to evaluate the past internal environment and dynamics of the ice sheet. Except for the upstream of Lambert Glacier, the fold patterns of internal layers are basically similar to that of the bed topography. The relatively flat basal topography and the decrease of ILCI with increasing depth provide evidence for identifying previous rapid ice flow areas that are unavailable to satellites, especially in the upstream of Lambert Glacier. Continuous internal layers of Dome A, recording the spatial change of past ice accumulation and ice-flow history over 160 ka, almost extend to the bed, with high ILCI and high basal roughness of the corresponding bed topography. There are three kinds of basal roughness patterns along the traverse, that is, “low ξ_t low η”, “low ξ_t high η”, and “high ξ_t high η”, where ξ_t represents the amplitude of the undulations, and quantifies the vertical variation of the bedrock, and η measures the frequency variation of fluctuations and the horizontal irregularity of the profile. The characteristics of internal layers and basal topography of the traverse between Zhongshan Station and Dome A provide new information for understanding the ancient ice-flow activity and the historical evolution of EAIS.

Ground-penetrating radar (GPR) is an important tool for measuring soil water content (SWC) at the field scale. The amplitude analysis of the early time signal (ETS) of GPR may provide a rapid way to estimate SWC. By assuming a homogeneous medium, various studies have been conducted on the relationship between the amplitude of ETS and the topsoil layer’s electromagnetic parameters (dielectric permittivity and conductivity) through numerical simulations, laboratory experiments, and field experiments. Soil is a typical inhomogeneous medium, and soil cultivation is a factor affecting its heterogeneity. In this context, we discuss the ability of the amplitude of ETS to estimate the water content of heterogeneous soil. First, we establish a multi-scale stochastic medium model with the inhomogeneous distribution of dielectric permittivity and conductivity and simulate the GPR response by the finite-difference time-domain (FDTD) method to observe the influence of medium heterogeneity on the GPR response. The heterogeneity of the soil models is evaluated by a geostatistical analysis described by two parameters, correlation length and variability. Then, we analyze the relationship between variability and the average envelope amplitude (AEA) of ETS. A strong soil heterogeneity increases the error of the AEA method in estimating SWC. Finally, the AEA method is used to estimate the SWC of two adjacent fields with different heterogeneities, which were caused by different cultivation methods. The results of the numerical simulation and field experiment indicate that the soil heterogeneity can have an impact on the estimation of SWC using EST, with an error lower than 3% within a depth range of 1/2 λ to λ (wavelength). This suggests that the EST of GPR can be applied to soil layers with relatively large lateral changes in water content.

Xiuyan Jade, produced in Xiuyan County, Liaoning Province, China is one of the four famous jade in China. King Jade, which is deemed the largest jade body of the world, was broken out from a hill. The local government planned to build a tourism site based on the jade culture there. The purpose of the investigation was to evaluate the stability of subsurface foundation, and the possible positions of mined-out zones to prevent the further rolling of the jade body. Cross-hole radar tomography is the key technique in the investigation. Conventional travel time and attenuation tomography based on ray tracing theory cannot provide high-resolution images because only a fraction of the measured information is used in the inversion. Full-waveform inversion (FWI) can provide high-resolution permittivity and conductivity images because it utilizes all the information provided by the radar signals. We deduce the gradient expression of the time-domain FWI with respect to the permittivity and conductivity using a method that is different from that of the previous work and realize the FWI algorithm that can simultaneously update the permittivity and conductivity by using the conjugate gradient method. Inverted results from synthetic data show that time-domain FWI can significantly improve the resolution compared with the ray-based tomogram methods. FWI can distinguish targets that are as small as one-half to one-third wavelength and the inverted physical values are closer to the real ones than those provided by the ray tracing method. We use the FWI algorithm to the field data measured at Xiuyan jade mine. Both the inverted permittivity and conductivity can comparably delineate four mined-out zones, which exhibit low-permittivity and low-conductivity characteristics. Furthermore, the locations of the interpreted mined-out zones are in good agreement with the existing mining channels recorded by geological data.