1 Introduction
The groundwater flow or level variation is crucial to groundwater management and site soil pollution control (Tesfaldet et al., 2019). To understand the location and timing of groundwater traveling through the vadose zone, we must investigate groundwater flow characterization and recharge mechanism. The traditional hydrographic groundwater surveys usually include float observation, pressure observation, and automatic tracking observation. However, when measuring the dynamic change of groundwater level or content over a long period, the measurement is usually indirect, difficult, costly, and infrequent, except for the traditional methods such as volume weighing and borehole sampling to detect the properties of groundwater (Ogilvy et al., 2009). In contrast, the nonintrusive time-lapse geophysics tools provide an opportunity to complement hydraulic campaigns (Fetter, 2001) since they can be implemented over a large region with dense sampling in both space and time. In particular, electrical resistivity tomography (ERT) and self-potential (SP) tomography are particularly appropriate to monitoring groundwater dynamics in resistivity and apparent current density because it is sensitive to changes in flow or chemistry (Carey, 2017; Revil & Linde, 2006). The time-lapse method carries out periodic measurements at a fixed location and provides the perception of the 2D/3D groundwater flow by analyzing the response variation in the subsurface. Compared with the hydrographic survey, and it is a non-invasive, practical, and cost-effective method for characterizing and delineating special recharge zones.
The time-lapse ERT is a mature technology for the hydrogeological study. There have been many recent examples of applying this technology for vadose zone soil moisture estimation, groundwater flow monitoring based on the resistivity characteristic (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, the ERT method is an indirect approach that depends on the change of soil moisture content. There are inherent uncertainties, and the sensitivity of ERT is also not enough for small-scale groundwater flow.
The SP method corresponds to the generation of an underground natural current source (Ahmed & Jardani, 2013). This method is used to monitor the groundwater based on the flow characteristic. Sill (1983) uses physical approaches to simulate the SP anomalies related to groundwater flow by solving major mathematical problems corresponding to groundwater flow problems. By observing the SP data on the ground surface, the potential distribution and current density distribution of the underground space can be effectively calculated to quantify the abnormal distribution characteristics. In recent years, the application of the natural potential method in the inversion of geophysical parameters, such as changes in the hydraulic head using SP technology to reconstruct pumping tests, has gradually attracted attention.
The ERT and SP method monitors the groundwater flow from different aspects. ERT utilizes the change of resistivity caused by the variations of moisture content in the soil. The groundwater movement produces the SP signal. These two methods have different physical mechanisms to describe groundwater flow characterization. Therefore, it is necessary to use a variety of geophysics methods for cross-validation and interpretation using ground truth constraints. This study addressed two primary questions: 1) What is the advantage of the joint 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 joint ERT and SP method strategy to monitor the groundwater flow variation in the pumping experiment. The groundwater level is controlled by pumping water from well to create various conditions of groundwater flow. The ERT data invert the resistivity distribution, which relates to the soil moisture content. Then, we combine the SP data and resistivity result to invert the apparent current density and estimate the permeability.
The paper is organized as follows. After the introduction, we introduce the basic forward and inversion theory of SP data. By solving the hydraulic problem and the Poisson equation, the underground current density distribution is restored. Then, the pumping experiment is used to test the ability of ERT and SP data in groundwater flow monitoring. The final sections are the conclusion and discussions.
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, the forward and inverse problems of the SP method will be introduced. Meanwhile, the permeability tensor can be determined directly according to the coupling coefficient. The problem can then be determined independently by resistivity tomography.