## 1 Introduction  
Electromagnetic exploration and monitoring technology are extensively applied in various domains such as coal [1], water [2], oil [3], gas, geothermal [4], engineering [5], resource exploitation [6], scientific research [7], and environmental studies [8]. It offers technical advantages such as cost-effectiveness, efficiency, and non-invasiveness towards the monitoring target. Despite the widespread use of electromagnetic monitoring technology, challenges persist in the processing of time-lapse monitoring data. Analyzing abnormal positions in monitoring results becomes intricate due to variations in data observation conditions, noise levels, and the inversion fitting degree of the analytical method applied to detect abnormal changes in monitoring targets. Particularly during the data preprocessing stage, subjective human factors introduce variability, rendering the inversion results more challenging to compare. Electromagnetic monitoring typically forecasts the changes in underground structures by comparing inversion results and analyzing resistivity alterations. [PERSON] et al. [9] predicted the Sebei 2 gas reservoir by scrutinizing the resistivity residual profile using two-dimensional inversion. [PERSON] et al. [10] employed a time-lapse long-offset transient electromagnetic sounding method to monitor oilfield waterflooding production. They identified and predicted the underground oil production range through the resistivity profile obtained via subtractive inversion. However, variations in observation equipment, changes in observation conditions, and data preprocessing adversely impact data quality. Concurrently, different noise levels in monitoring data, diverse fitting degrees of data, and the choice of a prior model significantly influence the reliability of inversion results. Consequently, the separation of inversion outcomes from time-lapse monitoring data can lead to inaccurate monitoring results. This was emphasized by [PERSON] et al. [11], who demonstrated that the isolated inversion of monitoring data can create false anomaly blocks, thereby complicating the analysis of monitoring results. To enhance the efficacy of inversion in highlighting changes in monitoring targets and address the challenges arising from the separate inversion of monitoring data, numerous scholars have conducted research. [PERSON] et al. [12] employed the inversion of the ratio between the initial data set and the subsequent data set to emphasize changes in the underground electrical structure. [PERSON] et al. [13] attempted to minimize the data difference between the initial data set and the subsequent data set and its difference from the response model. [PERSON] et al. [14] rectified the initial model parameters of the inversion data in each monitoring stage to mitigate false anomaly blocks generated by inversion. [PERSON] et al. [15] introduced a time-lapse inversion algorithm for the simultaneous inversion of multiple time observation data, capable of handling data with distinct observation times and varying noise levels. The aim is to eliminate random errors in multiple data sets and underscore changes in the underground media over time. After [PERSON] et al. [11] proposed a 4D time-lapse inversion algorithm that put data sets and model parameters into the space-time domain, many scholars continued to study the theory of time-lapse inversion. [PERSON] et al. [16] refined the time-lapse resistivity inversion method by introducing variable time regularization factors and improving the inversion parameter optimization method. [PERSON] et al. [17] simultaneously inverted data sets and model parameters at multiple time points, while [PERSON] et al. [18] utilized the smooth constrained least square method in conjunction with the L-curve parameter optimization method to enhance the speed of time-lapse inversion. [PERSON] et al. [19] refined the time-lapse algorithm by setting inversion weights based on the quality of observation data, thereby improving inversion reliability. [PERSON] et al.