IMF-Slices for GPR Data Processing Using Variational Mode Decomposition Method

Xuebing Zhang,Zhijia Zhang,Enhedelihai Nilot,Xuan Feng,Qianci Ren

doi:10.3390/rs10030476

Abstract

Using traditional time-frequency analysis methods, it is possible to delineate the time-frequency structures of ground-penetrating radar (GPR) data. A series of applications based on time-frequency analysis were proposed for the GPR data processing and imaging. With respect to signal processing, GPR data are typically non-stationary, which limits the applications of these methods moving forward. Empirical mode decomposition (EMD) provides alternative solutions with a fresh perspective. With EMD, GPR data are decomposed into a set of sub-components, i.e., the intrinsic mode functions (IMFs). However, the mode-mixing effect may also bring some negatives. To utilize the IMFs’ benefits, and avoid the negatives of the EMD, we introduce a new decomposition scheme termed variational mode decomposition (VMD) for GPR data processing for imaging. Based on the decomposition results of the VMD, we propose a new method which we refer as “the IMF-slice”. In the proposed method, the IMFs are generated by the VMD trace by trace, and then each IMF is sorted and recorded into different profiles (i.e., the IMF-slices) according to its center frequency. Using IMF-slices, the GPR data can be divided into several IMF-slices, each of which delineates a main vibration mode, and some subsurface layers and geophysical events can be identified more clearly. The effectiveness of the proposed method is tested using synthetic benchmark signals, laboratory data and the field dataset.

Highlights

Most of the geophysical data are non-stationary
With empirical mode decomposition (EMD)-based methods, the ground-penetrating radar (GPR) data can be decomposed into a group of stationary sub-components, and the subsequent processing for subsurface information is focused on the analysis of the generated intrinsic mode functions (IMFs) instead [8]
To utilize the benefits of the IMFs mentioned above, and avoid the negatives of the EMD, we introduce a new decomposition scheme called variational mode decomposition (VMD) [12] for GPR data processing as well as for imaging

Summary

Introduction

Most of the geophysical data are non-stationary. Especially for the ground-penetrating radar (GPR) data, which can be treated as a set of time-series signals, such non-stationarity appears more obviously. Non-stationarity can be defined and measured by certain statistical methods [1], geophysicists are prone to using the time-frequency decomposition methods (e.g., wavelet transform [2,3], S-transform [4,5] and matching pursuit [6,7]) to delineate the non-stationary characteristics This is because these methods provide a visualization and are convenient for further applications. The other feature is that the decomposed IMFs correspond to different frequency bands or ranges This means that any operation performed on the IMFs (e.g., removing or extracting a few IMFs) amounts to filtering in the corresponding frequency domain. The mode-mixing effect and the lack of a mathematical foundation limit their further applications in GPR data processing and imaging

Objectives

Methods

Results