# GeoSAE: A 3D Stratographic Modeling Method Driven by Geological Constraint
## 1 Introduction  
Currently, geological modeling methods across various geological formations and applications are being gradually refined and made more comprehensive. Three-dimensional geological modeling is mainly categorized into explicit modeling, implicit modeling [1, 2], and deep learning-based modeling, with greater attention being given to the latter due to advances in machine learning. 1. Geological and geophysical knowledge is relied upon in traditional explicit modeling methods to construct geological interfaces, with data from geological maps, boreholes, and geological cross-sections being utilized [3]. The quality of the model is significantly influenced by the accuracy of the interpreted data. Each stratigraphic surface is explicitly modeled, and constrained grid interpolation is employed to refine the modeland generate more detailed surfaces [4]. Additionally, semi-automated, interactive methods are employed to enable the manual addition of geological constraints [5; 6; 7], ensuring better alignment with geological knowledge. Various interpolation methods, including Bezier curve interpolation [8], non-uniform rational B-Spline (NURBS) interpolation [9], and the discrete smoothing interpretation (DSI) method introduced by [PERSON] in 2002 [10; 11], have been proposed to better fit geological observations and adapt to different geological structures. Although complex, well-constrained models can be produced by explicit 3D geological modeling, the incorporation of geological constraints is time-consuming and labor-intensive, requiring substantial modeling expertise and geological knowledge. Moreover, the process is difficult to reproduce and is prone to topological errors, such as voids and self-intersections, which hinder the widespread application of 3D geological models in practical production environments [5]. 1. Isosurfaces traced from a 3D potential field are used in implicit modeling to represent geological interfaces [12], and discrete geological data--such as interface points and structural observations--are interpolated using implicit functions [13]. Various implicit modeling methods have been proposed, with different mathematical frameworks being employed, including Kriging-based implicit modeling [14; 15], discrete smoothing interpolation (DSI) [16], and radial basis function (RBF) methods [17; 18]. Advantages in grid quality, reproducibility, and dynamic updating are provided by implicit modeling when compared to explicit methods [19]. However, modeling artifacts may be introduced in regions with complex geological structures. To resolve these artifacts, spatial relationships between geological history and features are incorporated as constraints into the implicit modeling process, forming a hybrid implicit-explicit approach [20; 21]. However, reduced reproducibility and modeling efficiency can result from this approach. 1. Intrinsic geological features are mined from large geological data samples through training with different learning paradigms in deep learning methods. Geological prior knowledge is incorporated to explore geological expressions that align with geological laws, observations, and structural anisotropy. Various 3D geological modeling methods based on deep learning are being continuously explored. Classification algorithm-based networks, such as support vector machines and BP neural networks, are employed to automate the construction of 3D geological models from borehole data [22]. Semantic mining is performed using recurrent neural networks (RNNs), where the prediction of stratum types and layer thicknesses is simulated [23]. Three-dimensional geological model parameters are inverted from geophysical data using convolutional neural networks (CNNs), and geological datasets are synthesized [24]. Generative adversarial networks (GANs), including variants such as deep convolutional generative adversarial networks (DCGAN) and Monte Carlo simulation-based GANs (MC-GAN), have been proposed to improve 3D geological modeling [25; 26; 27].