## 1 Introduction
[20] applied the time-lapse inversion algorithm to the CSAMT. Through the study of the synthetic data test, it was found that time-lapse inversion cannot only eliminate false anomalies but also obtain reliable inversion results in high noise or when there is a large amount of missing observation data. The controlled source audio-frequency magnetotelluric method (CSAMT) circumvents reliance on random weak natural field source signals, mitigates issues related to the dead band of natural field sources, and remains impervious to high-resistance shielding. This method offers advantages such as a high signal-to-noise ratio and economical observation costs. Due to the utilization of artificial sources in field construction, electromagnetic noise environments are present; nevertheless, reliable signals can still be measured. This characteristic makes it the preferred technology for electromagnetic monitoring applications. CSAMT typically defines apparent resistivity similarly to MT Cagniard apparent resistivity but is unsuitable for large-area three-dimensional observation due to the need to observe the magnetic field. The method involves the simultaneous observation of two mutually orthogonal electric and magnetic fields while sharing magnetic channels among multiple electric channels during the production process. Any loss or noise contamination in the magnetic data can impact the calculation of Cagniard apparent resistivity at multiple sites [21]. Furthermore, a deviation in the horizontal direction of the magnetic probe arrangement can introduce measurement errors in Cagniard apparent resistivity [22]. By altering the inversion strategy of the controlled source audio-frequency magnetotelluric method to exclusively utilize the electric field component for inversion, the need for magnetic field measurements is avoided. This not only avoids the issues caused by the Cagniard effect but also leads to a significant reduction in the number of sites, equipment costs, and field work expenses. Consequently, large-scale three-dimensional observations using the CSAMT become more feasible. To address the challenge of comparing separate inversions in large-area three-dimensional measurements, a 3D time-lapse electric field inversion algorithm for CSAMT is proposed. This algorithm leverages the electric field component for inversion, reducing instrument layout requirements and rendering fieldwork more suitable for large-area three-dimensional measurements. The algorithm discontinues the calculation of Cagniard apparent resistivity, thereby avoiding potential errors in the magnetic field measurement process. The designed objective function not only incorporates model terms to impose constraints on the inversion in model space but also introduces time-lapse terms to establish connections among the inversion data at different time steps, thereby enforcing temporal constraints. A function with temporal and spatial constraints is defined, and through formula derivation and synthetic testing, the feasibility of the 3D time-lapse electric field inversion algorithm is discussed. We designed two constantly changing high and low resistivity anomalous bodies in the theoretical model. In the dynamic model, three time steps are selected to calculate the forward responses and perform synthetic data testing. Various levels of noise are introduced to the forward response for time-lapse inversion, testing the reliability of the algorithm. The synthetic test results indicate that the 3D time-lapse electric field inversion algorithm for CSAMT performs well, effectively addressing the challenge of comparing data with different noise levels. The observation method aligned with the algorithm proves suitable for large-scale three-dimensional measurements. The algorithm, which incorporates dual constraints in both temporal and spatial dimensions, demonstrates stability and feasibility in the field of monitoring.