# Research Status of and Trends in 3D Geological Property Modeling Methods: A Review
## 3 Interpolation Methods for 3D Property Modeling
### Wavelet Analysis-Based Method  
The use of wavelet analysis for pattern-based classification simulation and continuous variable simulation was first proposed in Reference [100]. Wavelet analysis can decompose the training image into components of different frequencies [101]; this technique is similar to the filtersim algorithm. Wavelet analysis uses a certain scale of wavelet decomposition, rather than a filter, to reduce the dimensionality of the training image patterns. Wavelet subbands capture most of the pattern changes and reduce the dimensionality of the patterns. Then, the obtained approximate subband coefficients of the patterns are used for pattern classification. During the simulation, the same similarity search is performed between the conditional data events and the training image patterns.  
This technique integrates the conditional distribution function (cdf) of each class into the simulation process of categorical variables. The cdf is generated based on each classification frequency of the central node of the template. Therefore, as in the Monte Carlo method, the cdf of a class is used to plot the pattern instead of randomly selecting a pattern from the most similar class (with conditional data events).  
The proposed wavelet-based method does not make any improvements to the previous pattern-based method in terms of methodology, practicality, or quality of results. For example, it is claimed that a better statistical reproduction of the training images can be provided by adding the cdf of each category to the MPS. However, by randomly selecting a pattern for each class, filtersim, for example, inherently considers the probability of the central node (e.g., sandstone or shale in a binary image) in the MPS. Therefore, filtersim simply follows the same cdf through random sampling of the patterns.  
However, a drawback of this method is the complexity the method adds to the overall algorithm, such as the size of the subbands (or, in simple terms, the reduction in pattern dimensionality). In this method, this value needs to be traded off between the final good implementation effect and the computation time of the algorithm, and the modeler needs to adjust this value to obtain the optimal dimensionality reduction suitable for a particular training image to be processed.  
Another similar but important shortcoming of this method is the wavelet function and decomposition level. It is critical to know the optimal decomposition level of the classification model. In other words, there is no spatial correlation between the decomposition level and the classification accuracy. Increasing the decomposition level does not guarantee more accurate clustering as in the linear sense. For example, using two classification levels may produce better results than using three, and including all levels (equivalent to ignoring the wavelet decomposition and using only the original pattern) can even lead to worse classification results. The selection of decomposition level before using the algorithm is still an open question. Other factors related to wavelet transformation are also considered sources of error/uncertainty.