# Research Status of and Trends in 3D Geological Property Modeling Methods: A Review
## 3 Interpolation Methods for 3D Property Modeling
### Traditional Geostatistical Methods
#### 3.1.3 Object-Based Method  
Geostatistical interpolation algorithms include sequential simulation methods [51; 52; 60; 61; 62], iterative methods [63], and noniterative and nonsequential simulation methods [64; 65]. However, these are all two-point statistical methods based on the definition of variograms and cannot simulate complex spatial patterns, such as rivers. Simulating complex spatial patterns is very important in fluid simulation. Therefore, many attempts have been made to reproduce nonlinear spatial structures. For example, the anisotropy directions of the variogram are modified at local locations, and the continuity of geological features is improved by modifying the range of the variogram [66]. However, none of these approaches can truly reproduce complex geological patterns.  
The object-based method [67; 68; 69; 70; 71] distributes geometric objects by using the marked point process based on some probability theory. This method directly inputs geometric objects into the grid until certain predefined constraints are met. This process requires iterative trials and constantly editing and modifying the shape and location of the object  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Kriging Method** & **Applicability** & **Advantages** & **Disadvantages** \\ \hline \multirow{6}{*}{Sequential Gaussian Simulation} & Random variables conform to Gaussian distribution, or & With different random paths & It is not suitable for \\  & Gaussian distribution, or & each time, different simulation & continuous variables with \\  & conform to Gaussian & effects are obtained. & strong anisotropy; The \\  & distribution after data & According to geological & accuracy of simulation results \\  & transformation; For & experience, the most suitable & is closely related to the \\  & continuous variables & simulation results are selected & variation function \\ \hline \multirow{6}{*}{Sequential Gaussian collocated collaborative simulation} & Random variables conform to Gaussian distribution after data & & \\  & transformation; Applicable to & Using external parameter & It is not suitable for \\  & transformation; Applicable to & collaborative simulation, the & continuous variables with \\  & continuous variables; At the & interpolation result is & strong anisotropy; The \\  & position of the estimation & interpolation result is & accuracy of simulation results \\  & point, the spatial distribution & more accurate & is closely related to the \\  & of external variables is known; & variation function \\  & The main variable and & & \\  & external variable satisfy the & & \\  & second-order stationary & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of different sequential Gaussian simulation methods.  
to achieve a result conforming to the constraint information. A major advantage of the object-based method is that the model can achieve good visual effects, thereby allowing geologists to see familiar sedimentary objects and directly adjust the objects' shape and size. For example, a river channel can be characterized by sinuosity (amplitude and wavelength), channel width, channel length, and channel thickness. Thus, by defining the aforementioned attributes using a random distribution function, several channels can be employed in the model to form meandering stream facies, as shown in Figure 3. Nevertheless, the object-based method still has some drawbacks. First, it is difficult to constrain the data faithfully, and it is quite complicated to consider dense well point data while repeatedly modifying the object position. Second, the multivariate distribution of the marked point process is also very complex and difficult to analyze and define.