# GeoSAE: A 3D Stratographic Modeling Method Driven by Geological Constraint
## 1 Introduction
Reliable 3D geological models are constructed by combining drill holes, outcrops, and 2D geological cross-sections as strong constraints in these methods. Stochastic processes are modeled, and scale conversion is facilitated in these methods, while geological observations are integrated into graph structures using graph neural networks (GNNs), thereby extending the range of constraints [28]. Geological constraints are often added to the inversion function or applied during post-processing of the inversion model after each inversion step to align it with geological characteristics in the construction of 3D geological models with geological constraints [29]. For specific geological formations, seismic voxels are used to estimate relative geologic time (RGT) for stratigraphy interpretation and fault detection, and fault models consistent with geological structures are generated [30]. However, the modeling of non-integrated structures is still considered difficult. A framework combining deep learning with implicit modeling has recently been proposed to improve the application of implicit methods in structural geology, with a multilayer perceptron (MLP) architecture being utilized [31]. Despite considerable progress in research, significant limitations are faced in the practical application of deep learning-based 3D geological modeling methods. The data required for 3D geological modeling are typically scarce and difficult to obtain, contradicting deep learning's reliance on large datasets. Consequently, the extraction of more features from sparse data has become a significant challenge in applying deep learning methods to 3D geological modeling. The construction of 3D geological models requires the consideration of complex geological bodies, and the data scale is often large. High-precision models necessitate significant computational resources, presenting challenges for deep learning networks, computational methods, optimization algorithms, and hardware performance. The non-visible nature of underground spaces introduces uncertainty in the mechanisms of deep learning models, making it difficult to provide reliable explanations or practical support for the generated 3D geological models. The design of a suitable neural network capable of capturing the intrinsic features and distribution patterns of geological data is a key step in using deep learning for 3D geological modeling, allowing geological structures in uncharted areas to be inferred [32]. In this study, an auto-encoder (AE) is used to learn feature representations of a dataset through network training, and the original data is subsequently reconstructed from these features. For 3D geological modeling, useful features are learned from the input data by the auto-encoder during training, which can be applied to tasks such as constructing 3D potential fields, noise reduction, and classification [33]. Furthermore, incomplete input data can be accommodated by the auto-encoder's decoder, offering advantages in handling missing data in 3D potential fields and proving particularly suitable for sparse and heterogeneous geological data inputs. The analysis above highlights the critical issue of insufficient constraints related to geological evolution in the construction of 3D geological models, which remains an urgent challenge in the field of 3D geological modeling. To address this challenge, this work presents GeoSAE, a geological constraint-driven 3D modeling method that incorporates geological constraints into the modeling process. In GeoSAE, the \"S\", \"A\", and \"E\" represent Stacked Autoencoder, which is a neural network architecture where multiple autoencoders are stacked to simultaneously predict several potential field values.