# Research on 3D Geological Modeling Method Based on Deep Neural Networks for Drilling Data
## 2 Related Work
### Implicit Geological Modeling  
Implicit modeling signifies an innovative approach to constructing geological models, deviating notably from traditional methods reliant on profiles. Instead, it leverages mathematical techniques to derive models from data, establishing mathematical relationships among geological elements. These relationships can subsequently be visualized in three dimensions through various methodologies. [PERSON] and colleagues [25] introduced an integrated display-implicit 3D geological modeling method that utilizes a range of modeling techniques tailored for different types of geological structures. Subsequently, they convert the display model into an implicit model, facilitating the comprehensive regional modeling of diverse geological structures. [PERSON] and collaborators [26] introduced an implicit potential field method with the capacity to integrate various data, including geological boundary contacts and their measurement directions. This is accomplished by creating intermediate 3D geological models that correspond to a subset of the data and then consolidating them into a unified, comprehensive 3D geological model while complying with data constraints and geological principles. Presently, the primary aim of implicit modeling is the generation and simulation of geological boundaries, accomplished through automatic construction employing techniques like radial basis functions, variational Gaussian processes, and other methodologies [27; 28; 29]. To address concerns regarding overlap and gaps that arise in the modeling process, [PERSON] and colleagues [30] introduced a reconstruction algorithm based on the labeling of voxel points. This algorithm possesses the capability to resolve issues related to overlap and blanking in geological modeling through a labeling process. The multi-label regularized tetrahedron method introduced by [PERSON] and colleagues [31] can be effectively employed in the surface reconstruction of multi-geoidal bodies.  
As a mathematical model derived from data, the central aspect of the implicit modeling approach revolves around the effective utilization of diverse geological data. [PERSON] and colleagues [32] showcased the automatic construction of boundary surfaces between geological units through the utilization of lithological contact data, along with the location and orientation of potential faults. This method provides a direct assessment of the geological framework and the ability for swift updates with new data. Furthermore, by harnessing limited, sparse, and discrete borehole data, the automatic construction of 3D geological models within a specified range can be accomplished using algorithms such as support vector machines, backpropagation (BP) neural networks, marching cubes, hermite radial basis functions, and various others [33; 34; 35].  
These studies demonstrate the particular aptness of machine learning methods for handling geological data and predicting geological entities. With technological advancements, these approaches are anticipated to become increasingly crucial in the evolution of urban geological information systems. This will enhance the efficiency and accuracy of urban planning and resource management.