# Research Status of and Trends in 3D Geological Property Modeling Methods: A Review
## 3 Interpolation Methods for 3D Property Modeling  
### Traditional Geostatistical Methods  
There is often much spatial variability when dealing with subsurface space modeling in Earth science. Proposed by [PERSON] [47], geostatistics is a tool to quantify this variability to enable geologists to predict behavior and make the most useful decisions under the constraints of limited knowledge and resources. The major techniques for generating a 3D model of the geological variables are the main focus, especially the interpolation methods; thus, the principal component analysis (PCA), maximum autocorrelation factor (MAF), projection pursuit multivariate transform (PPMT), and related methods are not considered. The PCA, MAF, PPMT, and other multivariate transforms methods are commonly used to simulate correlated variables independently without the requirement of fitting a linear model. In addition, these approaches can be applied in the data preparation procedure for the geostatistics approaches dealing with multivariate analysis. Geological phenomena, especially in the petroleum industry, follow a series of complex physical rules that cannot be expressed by simplified models. Reservoir properties, such as porosity and permeability, are needed in reservoir fluid simulation equations to predict oil production and are required at each spatial location; however, porosity and permeability can be obtained only in sparse wells. In other words, for economic reasons, it is generally impossible to accurately and definitively obtain all the information required for a subsurface model. Therefore, spatial uncertainty is a fundamental concept in Earth science. In the early days of the oil industry, practitioners tended to think deterministically and thus expected to obtain a single estimate of oil production. Today, uncertainty is widely accepted. Geostatistics captures this spatial uncertainty by generating multiple reasonable property models (also known as stochastic realization). By integrating information from different sources, such as logging, coring, geological interpretation, or seismic data, the study area and the true expression of this uncertainty can be obtained. [PERSON] [48] introduced the regionalized variable \(Z(h)\) as the value of characteristic \(Z\) of a geological phenomenon at location u. Regionalization means that variables expand in space and exhibit a specific spatial structure. If this concept is ignored, the variables are randomly distributed in the reference region and thus do not exhibit any spatial continuity. However, physical processes in geology are not random in space and have spatial continuity in their properties. For example, the continuity of the river channel formed by a river flowing down the hillside is controlled by the complex physical phenomena along the path of the river, and the mineral deposits tend to be concentrated in certain specific spaces. Thus, the regionalization of variables is the main principle by which geostatistics differs from statistics. It would be impossible to make predictions if spatial continuity does not exist. However, the physical laws that determine spatial continuity cannot be accurately modeled due to the lack of information. To quantify spatial uncertainty, a mathematical model is needed to describe the spatial structure of the variables in the study area. For example, the spatial trends in the data and the isotropy or anisotropy of the variables can be obtained by defining a spatial variable model in geostatistics. Geostatistical methods have evolved over the decades into two-point geostatistical methods (including the kriging method, deterministic simulation method, and stochastic simulation methods), object-based methods, and multiple-point geostatistics. The methods differ in how their spatial continuity and uncertainty models are expressed and how direct data (such as core data) or indirect data (such as seismic data) are integrated for stochastic realization of subsurface conditions.