# Petrophysics Parameter Inversion and Its Application Based on the Transient Electromagnetic Method
## 1 Introduction  
The transient electromagnetic (TEM) method is a high-efficiency geophysical technique with deep detection capabilities that is widely applied in mineral exploration and engineering surveys [1, 2]. However, conventional TEM inversion outputs resistivity distributions, which is a physical property lacking direct geological interpretability. Translating resistivity models into actionable petrophysical parameters (e.g., porosity and water saturation) remains a critical challenge for resource evaluation and hazard assessment, particularly in complex hydrogeological contexts.  
Previous studies have established that the electrical conductivity of surrounding rock masses is closely related to petrophysical parameters, such as water saturation, porosity,and permeability, all of which significantly affect bulk resistivity [3, 4, 5]. Based on [PERSON]'s law, [PERSON] et al. showed that both water saturation and the formation factor influence the saturation index, with experimental results confirming the importance of formation water resistivity [6]. [PERSON] et al. further quantified the relationship between resistivity and porosity, applying it to primary rock formations [7, 8]. [PERSON] et al. found strong correlations among permeability, porosity, and resistivity, which were used to infer tunnel rock properties [9]. To account for variations in water connectivity, [PERSON] introduced the water connectivity index (WCI), which has been successfully applied across resistivity models [10]. [PERSON] et al. proposed a stochastic joint inversion approach for shales, revealing statistical links among petrophysical parameters [11]. [PERSON] et al. developed an equivalent resistivity model using parallel circuit theory to relate resistivity and hydrate saturation [12]. These studies collectively highlight the critical role of petrophysical controls on resistivity and support the development of such predictive models. With the growing application of transient electromagnetic (TEM) methods in hydrogeological investigations, quantifying the coupling between EM responses and formation parameters has become increasingly vital [13, 14, 15]. [PERSON] et al. estimated aquifer porosity using TDEM-derived resistivity, improving upon Archie-based methods [16]. [PERSON] et al. linked resistivity with Q-system classifications to assess rock mass quality [17]. [PERSON] et al. used TEM data to quantify aquifer water content using a generalized volume model [18]. Other efforts focused on inversion methods: [PERSON] et al. proposed a Bayesian approach with depth constraints [19, 20]; [PERSON] et al. integrated [PERSON]'s law and deep learning to predict water-rich zones [21]. [PERSON] et al. and [PERSON] et al. applied advanced inversion strategies to map seawater intrusion and subsurface porosity [22, 23]. Additional studies have explored the lithological and hydrogeological influences on resistivity in mining and karst environments [24, 25, 26]. Recent advances in stochastic and constrained inversion methods (e.g., BEL1D and LCI) have further improved the accuracy of resistivity-based characterization, reinforcing the potential of TEM in resolving petrophysical and hydrological conditions [27, 28, 29, 30].  
Based on the above research and analysis, inverting subsurface petrophysical parameters from transient electromagnetic (TEM) data has significant theoretical value. In this study, rock physical parameters such as porosity and water saturation were further estimated using the resistivity model obtained from TEM inversion. Multiple sets of geoelectric models with varying physical parameters were constructed for numerical simulations to verify the reliability of the proposed method. This approach provides a novel pathway for electromagnetic data inversion and facilitates the interpretation of geological data. Finally, a field TEM survey was conducted, and the spatial distribution trends of subsurface porosity and water saturation were delineated by integrating the data with geological data.