## 1 Introduction  
Structural damage, construction defects, and subsurface utilities in civil engineering usually show different electromagnetic properties from the surrounding medium [1]. These anomalies often manifest as high-contrast medium distributions, and it is important to accurately identify these objects before starting any underground construction work, such as road widening or the relocation of utilities [2, 3]. Otherwise, serious accidents may occur, causing damage to underground utilities without clear subsurface imaging [2, 4]. As a widespread non-destructive testing tool in subsurface exploration, ground-penetrating radar (GPR) can effectively identify underground anomalies [5, 6]. The high-precision imaging of subsurface structures through GPR data analysis is significant in civil engineering (such as road exploration, pipe detection, and various types of municipal engineering) [7], as well as in sedimentological-straightpahical, hydrological, and glaciological areas [8]. One promising method providing quantitative information about subsurface media is full-waveform inversion (FWI) [9; 10]. However, its practical application faces challenges, such as instability in dual-parameter (permittivity/conductivity) inversion and computational inefficiency in 3D surveys [11]. At present, FWI technology for GPR data has been successfully applied in reconstructing the distribution of subsurface media, but most studies have been performed in two dimensions [12; 13; 14; 15; 16]. In the field of 3D imaging towards GPR, some researchers have conducted studies on tomography or migration techniques [17; 18], yet these methods lack the capabilities for the quantitative reconstruction of subsurface media parameters. Early research on the 3D inversion of GPR data primarily employed simplified approaches [19], including pseudo-3D inversion constructed from 2D results [20; 21] or the specific feature attribute inversion of 3D anomalies [22; 23; 24; 25], rather than complete 3D inversion schemes. In [26; 27], the first 3D FWI scheme was proposed for GPR applications in the frequency domain, although the implementations were limited to single-parameter (relative permittivity) reconstruction. Subsequently, [PERSON]. [11] developed a dual-parameter 3D FWI algorithm for GPR using a parameter normalization strategy. By introducing a scaling factor for the inverted parameter, 3D relative permittivity and conductivity models were simultaneously reconstructed. While this approach provided some balance between the parameters' influences in model updates, the 3D FWI results for the two parameters usually show differences in boundary clarity and volume effects [28]. Thus, developing a robust dual-parameter inversion framework that optimizes both permittivity and conductivity reconstruction continues to pose fundamental challenges in computational geophysics. Regularization techniques play an important role in geophysical inversion, as they can constrain model parameters and solve the ill-posed problem of inversion [29; 30]. Since the Tikhonov regularization was proposed [29; 31], continuous advancements in parameter constraint strategies using regularization have been constantly emerging [32; 33]. Introducing zero-order, first-order, and second-order difference operators into the traditional Tikhonov regularization framework can, respectively, obtain constraints with the minimum model, the flattest model, and the smoothest model functionals [34]. These smooth regularization methods and the traditional Tikhonov method use the L2 norm for model parameters and gradients [35], which generally leads to stable and smooth inversion results, making them more suitable for cases where the structures of subsurface anomalies vary in a smooth pattern [11; 14]. However, when there are high-contrast subsurface anomalies in underground structures, current 3D FWI methods often lack boundary precision [34] and suffer from artifacts [11]. The fundamental goal of practical GPR surveys lies in finding the positions of subsurface property variations [3].