1 Introduction
Knowledge of groundwater flow and groundwater level variation is crucial to groundwater management and water quality control (Tesfaldet et al., 2019). A better understanding of the mechanism governing groundwater movement in the vadose zone requires investigations on both groundwater flow characterization and the recharging process (Nielsen et al., 1986). Traditional hydrographic groundwater surveys include float, pressure, and automatic tracking observations. However, when measuring the dynamics of the groundwater level over a long period, the measurement is usually indirect, costly, and infrequent (Ogilvy et al., 2009). In contrast, the nonintrusive time-lapse geophysics tools provide an opportunity to complement traditional measurements (Fetter, 2001), especially given that geophysical surveys can be implemented over a large region with dense sampling intervals in both space and time. In particular, electrical resistivity tomography (ERT) and self-potential (SP) tomography are appropriate to monitor groundwater dynamics due to the sensitivity of resistivity and apparent current density to changes in flow or water chemistry (Carey, 2017; Revil & Linde, 2006). The time-lapse method carries out periodic measurements at a fixed location and determines the 2D/3D groundwater flow by analyzing the response variation in the subsurface over a specific period (Doetsch et al., 2012).
The ERT is sensitive to changes in pore water electrical conductivity and temperature. Therefore, it has been used to track the subsurface migration of conductive tracers and image the hydraulic conductivity of heterogeneous aquifers (Bowling et al., 2006). The time-lapse ERT method has been well established for soil moisture estimation and groundwater flow monitoring (Jongmans & Garambois, 2007; Niesner, 2010). It measures the resistivity of the subsurface by using an electrode dipole to inject direct current into the ground and using additional dipoles to measure the resulting voltage. Many studies have explored the challenges and uncertainties associated with predicting groundwater flow using ERT. However, for small-scale groundwater flow, there is not apparent resistivity change, and the ERT is not sensitive to describe the groundwater movement (Fagerlund and Heinson, 2003). The SP method is used to monitor the groundwater based on its flow characteristic. The SP signal has two main components: (1) the electrokinetic contribution associated with groundwater flow through the permeable soil and (2) oxide-reduction phenomena (Naudet et al., 2003).  Sill (1983) used physical approaches to simulate the SP anomalies related to groundwater flow by solving the constitutive equation corresponding to groundwater flow. By observing the SP data on the ground surface, both potential and current density distributions of the underground space can be effectively calculated to quantify the abnormal distribution characteristics. In recent years, the application of the geophysics potential method in the inversion of geophysical parameters, such as changes in the hydraulic head using SP technology to reconstruct pumping tests, has attracted increasing attention (Revil & Linde, 2006).
The ERT and SP methods have different physical mechanisms to describe groundwater flow characterization. ERT utilizes the change of resistivity caused by the variations of moisture content in the soil, while the groundwater movement produces the SP signal. Combining the two methods for cross-validation will provide a more robust result (Fan et al., 2020; Guo et al., 2020). This study addressed two primary questions: 1) What is the advantage of the combined time-lapse strategy; and 2) How does the magnitude and timing of water input change groundwater flow dynamics? To answer these questions, we propose the combined ERT and SP method strategy to monitor the groundwater flow variation in a pumping experiment. The groundwater level is controlled by pumping water from shallow water well to create various conditions of groundwater flow. The time-lapse ERT data can be used to derive the dynamics in resistivity distribution, which reflects the evolution of soil moisture content over time. Then, the SP data and ERT result can be combined to invert the resistivity and estimate the permeability distribution. The proposed method was tested in a pumping experiment, and the geophysical results agreed well with direct monitoring of the groundwater level in wells. The results of this study provide a reliable and low-cost way to identify and monitor the groundwater movement in the vadose zone.
2 The Self-potential Inversion Theory
Self-potential (SP) refers to passively measure electric potentials that are generated through coupling with some other forcing mechanism, which is often hydraulic, chemical, or thermal. This coupled flow mechanism in this stratigraphic setting was detected on the surface by Minsley, (2007). Over the years, there has been a growing interest in the application of the SP method in various fields of earth science, including hydrology, geothermal and geotechnical and environmental engineering (Darnet& Marquis, 2004). In many cases, this method is relatively easy to use and convenient for qualitative interpretation. In this section, we present the forward and inverse theory of the SP method. Meanwhile, the permeability tensor can be determined directly according to the coupling coefficient. The problem can then be solved independently by resistivity tomography.