# Data Interpretation Technology of GPR Survey Based on Variational Mode Decomposition
## 1 Introduction  
The spatial distribution of underground media may be characterized by data interpretation of the effective reflection electromagnetic waves of ground penetrating radar (GPR). The extraction of echo signals is one of the most critical technologies in GPR measurement data interpretation, which is directly related to the detection accuracy towards the underground target of interest [1]. The collected GPR signal typically possesses non-stationary and random characteristics due to the complexity of the underground medium and the interference factors during the measurement. In general, Fourier transform the power spectrum estimation are the representative theories in GPR signal processing, whereas they are suitable in nature for application in stationary signal analysis [2]. With these methods, the frequency components of the whole signal can be produced, but the joint time andfrequency resolution of the signal cannot be simultaneously obtained. For non-stationary GPR signals, the change in signal characteristics with time is essential in reflecting the variation in the underground medium being investigated. To this end, the instantaneous frequency characteristic of GPR signals plays an important role in the recognition of underground media [3, 4]. The instantaneous frequency of a non-stationary signal is commonly examined while using time-frequency analysis methods, typically short-time Fourier transform and wavelet transform. These methods are competent for obtaining the energy intensity of the instantaneous frequency at different frequencies and times [5, 6, 7]. However, the above methods are based on Fourier analysis theory, so they are limited by the disadvantages of Fourier analysis. Conventional GPR is a broadband signal, while the instantaneous frequency analysis method is based on the Hilbert transform and it is unable to separate signals at different scales [8, 9]. Since [PERSON] proposed the Hilbert-Huang Transform (HHT), the instantaneous spectrum of the intrinsic mode function (IMF) of GPR signals can be obtained by using the empirical mode decomposition (EMD) [10, 11, 12]. Due to some problems in the EMD methods, such as mode aliasing and endpoint effects, the HHT method and its use are limited to a certain extent [13, 14, 15, 16]. A noise-assisted data analysis method, the ensemble empirical mode decomposition (EEMD) is applied in order to overcome this problem, which represents one improvement of EMD. By adding finite white noise to the investigated signal, the EEMD method can automatically eliminate the mode mixing automatically [17]. The reconstructed signal from IMFs includes residual noise and different realizations of signal plus noise may produce different number of modes with EEMD. [PERSON] proposed the complete ensemble empirical mode decomposition (CEEMD) in order to overcome these situations [18]. Furthermore, some scholars have proposed that the EEMD and the CEEMD could both be used in GPR signal analysis [19, 20, 21, 22]. However, these methods also have limitations, for example, the lack of mathematical theory and the degrees of freedom will reduce the algorithm's robustness, which leave room for theoretical development and the improvement of the robustness of the decomposition [23]. Recently, the variational mode decomposition (VMD), which encompasses multiple adaptive Wiener filter groups, was discovered to have good robustness with the ability to overcome the disadvantages of mode aliasing, small end effects, and pseudo components when compared to other conventional algorithms [23, 24]. The VMD algorithm has been applied to some fields, such as mechanical fault diagnosis or structural damage identification, and it has achieved significant results [25, 26, 27, 28]. VMD has also been applied to analyze seismic data [29, 30]. However, relevant reports on utilizing VMD to analyze GPR data are lacking.