Automatic Variogram Inference Using Pre-Trained Convolutional Neural Networks
Creators: Mokdad, Abdelkerim
Publisher: name: University of Alberta Library
Year: 2023

<p>Calculating and modeling a variogram from sparsely sampled data can be complex and time-consuming due to the need for expertise in selecting the appropriate parameters and fitting functions to the experimental variogram. To assist with variogram modeling, a novel approach based on Convolutional Neural Networks (CNNs) are implemented in this research to automatically calculate and model variograms from sparse data. CNNs are known for effectively processing grid-like data such as images and spatial maps making them suitable for geostatistical applications. To train the CNN model, a large set of Sequential Gaussian Simulation (SGS) realizations, each with different variogram model parameters, is resampled to generate the training data. Training a CNN directly on sampled data was not effective so each dataset is modeled using inverse distance; other interpolation techniques such as kriging and nearest neighbors were also tested, but inverse distance was found to be the most efficient for training data, the minimal number of input parameters for inverse distance is attractive.<br>
The approach consists of the implementation of three CNNs: CNN-A predicts the major direction of continuity, CNN-1 estimates key variogram model parameters, and CNN-2 predicts the experimental variogram values at pre-set lag distances. Considering these CNNs, two workflows are implemented: (1) train CNN-1 to directly predict variogram model parameters (range, anisotropy ratio, nugget effect) followed by the inference of an automated model based on the predicted parameters (2) train a second CNN-2 to predict the experimental variogram values at specified lag distances which are easily autofitted. Mean squared error (MSE) is used as the loss function in the training process. Once trained, the CNNs can predict the azimuth of the major direction, key variogram model parameters, and the experimental variogram of a given dataset. When applying CNN to datasets, data augmentation (rotation) is performed to obtain a set of variogram predictions that improve prediction robustness.<br>
Hyperparameter tuning and sensitivity analysis are performed to determine optimal parameters for the CNN by choosing configurations that minimize MSE and avoid overfitting. The testing and validation of variogram prediction are conducted on various datasets, including the Walker Lake, and a data validation consisting of 110 geological images transformed to grayscale values. The results indicate that the prediction of variogram model parameters (CNN-1) is limited by a fixed number of variogram structures and the second workflow (CNN-2) involving predicting values at pre-set lag distances performs better without limiting the number of variogram structures.<br>
CNN-2 results in the prediction of an experimental variogram that can be easily fit with automated variogram programs achieving an R-squared value of 0.95 for the validation dataset. The workflows are fully automated and applicable to sparse or dense data but are currently limited to 2D datasets and the output consists of normal score variograms.</p>