## 2 The TL-ERT Method: Data Processing and Inversion
### Novel Algorithms for Data Processing and Inversion  
After these seminal works, the TL-ERT method has found an impressive and large spectrum of applications, and many authors have proposed new methods for TL-ERT data analysis and inversion [4]. In past years, the number of papers on this topic has constantly grown. Here, an overview of selected papers published during the last ten years is presented. [PERSON] et al., 2010 [51], proposed a structural joint inversion using cross-gradient constraints of the time-lapse GPR and ERT data. They analyzed synthetic and experimental data collected during a water injection experiment. The structure is imposed when the updates of the model, with respect to the background, is in the same or opposite directions. Synthetic and experimental tests confirmed the capacity of the structural joint inversion to better describe the plumes geometry, with respect to the single individual inversion. [PERSON] et al., 2011 [52] investigated the possibility to calibrate the hydrogeophysical inversion with the time domain electromagnetic (TDEM) and ERT data. A geophysical model was simultaneously inverted with a groundwater model by coupling the groundwater and geophysical parameters. [PERSON] et al., 2013 [53] used a stochastic joint inversion of resistivity and self-potential data integrated with in-situ measurements of hydrogeological parameters. The main results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity. [PERSON] et al., 2015 [54] analyzed the performance of coupled and uncoupled inversion approaches in the reconstruction of heterogeneous saturated hydraulic conductivity patterns. The comparison was carried out in the framework of a model inversion based on the ensemble Kalman filter. The results highlighted some advantages of the coupled approach, but it requires massive computational resources. The joint inversion of geophysical data and the coupled inversion of hydrogeophysical data are extremely complex issues and challenging scientific problems, for this reason, there are not many papers about the joint inversion of the TL-ERT data with other geophysical measurements. Furthermore, there is a growing interest in the studies on hydrogeophysical and petrophysical relationships. Many works are focused on improving and modifying the full 4D inversion algorithm based on the regularization in space and time [50]. [PERSON] et al., 2011 [55], introduced the concept of simultaneous inversion. They proposed two different approaches: in the first one, the inversion of two consecutive ERT datasets was performed under a single optimization procedure and constraints, to ensure that the changes from one time to another were smooth; in the second method, the inversions were performed simultaneously and constraints of smoothness and closeness to a reference model were applied to the difference image produced. [PERSON] et al., 2011 [56] modified the method for the full 4D inversion based on the regularization in space and time. They introduced the concept of the 4D active time-constrained (4D-ATC) inversion. The main feature of the modified algorithm is that it allows the time regularization to vary between different time steps depending on the degree of spatial resistivity changes occurring among different monitoring stages. As a result, the 4D-ATC algorithm uses all the benefits of the 4D algorithm, but also introduces increased flexibility in terms of temporal regularization, which can help in focusing on the dynamic resistivity changes. In a successive work, [PERSON] et al., 2014 [57], proposed an inversion scheme based on distributed and non-uniform parameters, considering the time-related noise and the reduction of the sensitivity in ERT measurements as purely random. Other improvements were based on the concept of the adaptive approach and the use of minimum gradient in TL-ERT data inversion. [PERSON] et al., 2015 [58] proposed, for the first time, an adaptive survey technique for geoelectrical monitoring.