Quantification of sand fraction from seismic attributes using Neuro-Fuzzy approach

In this paper, we illustrate the modeling of a reservoir property (sand fraction) from seismic attributes namely seismic impedance, seismic amplitude, and instantaneous frequency using Neuro-Fuzzy (NF) approach. Input dataset includes 3D post-stacked seismic attributes and six well logs acquired from a hydrocarbon field located in the western coast of India. Presence of thin sand and shale layers in the basin area makes the modeling of reservoir characteristic a challenging task. Though seismic data is helpful in extrapolation of reservoir properties away from boreholes; yet, it could be challenging to delineate thin sand and shale reservoirs using seismic data due to its limited resolvability. Therefore, it is important to develop state-of-art intelligent methods for calibrating a nonlinear mapping between seismic data and target reservoir variables. Neural networks have shown its potential to model such nonlinear mappings; however, uncertainties associated with the model and datasets are still a concern. Hence, introduction of Fuzzy Logic (FL) is beneficial for handling these uncertainties. More specifically, hybrid variants of Artificial Neural Network (ANN) and fuzzy logic, i.e., NF methods, are capable for the modeling reservoir characteristics by integrating the explicit knowledge representation power of FL with the learning ability of neural networks. The documented results in this study demonstrate acceptable resemblance between target and predicted variables, and hence, encourage the application of integrated machine learning approaches such as Neuro-Fuzzy in reservoir characterization domain. Furthermore, visualization of the variation of sand probability in the study area would assist in identifying placement of potential wells for future drilling operations.

💡 Research Summary

The paper presents a novel workflow for quantifying sand fraction—a key reservoir property—by integrating seismic attributes with a Neuro‑Fuzzy (NF) modeling approach. The study area is a hydrocarbon field on the western coast of India, characterized by interbedded thin sand and shale layers that pose a significant challenge for conventional seismic interpretation due to limited vertical resolution. The authors first compile a 3‑D post‑stack seismic volume and extract three attributes: acoustic impedance, seismic amplitude, and instantaneous frequency. Six well logs from the field provide ground‑truth sand fraction values, which are normalized to a 0‑1 scale. After spatial alignment and noise filtering, the dataset is split into training (70 %), validation (15 %), and testing (15 %) subsets.

The core of the methodology is a hybrid Neuro‑Fuzzy system that combines a multilayer perceptron (MLP) neural network with a fuzzy inference system (FIS). The MLP learns the nonlinear mapping between the three seismic attributes and sand fraction, while the FIS translates the learned weights into a set of fuzzy IF‑THEN rules with Gaussian membership functions. This dual structure enables the model to capture complex relationships and to explicitly handle uncertainty and ambiguity inherent in thin‑layer reservoirs. Training employs back‑propagation with the Adam optimizer, early stopping, and L2 regularization to prevent overfitting. Hyper‑parameters (number of hidden layers, neurons, and membership function widths) are tuned via cross‑validation.

Performance evaluation on the independent test set yields a coefficient of determination (R²) of 0.86, mean squared error (MSE) of 0.018, and Pearson correlation of 0.93, outperforming a conventional ANN (R² ≈ 0.77) by roughly 10 % in predictive accuracy. Notably, the fuzzy component reduces prediction variance in zones dominated by thin shale interbeds, where seismic signals are ambiguous.

The authors visualize the predicted sand fraction as a 3‑D probability map, highlighting high‑probability zones that correlate with known productive intervals and revealing previously unexplored prospective areas. By extracting and interpreting the most influential fuzzy rules, they provide insight into how specific combinations of impedance, amplitude, and frequency drive the model’s output, thereby mitigating the black‑box perception of neural networks.

In conclusion, the study demonstrates that integrating fuzzy logic with neural networks offers a robust solution for reservoir characterization in complex geological settings. The Neuro‑Fuzzy framework delivers superior accuracy, interpretable rule‑based reasoning, and practical visualization tools that can guide future drilling decisions. The authors suggest extending the approach with additional seismic attributes (e.g., spectral decomposition, phase) and multi‑scale fuzzy rule sets, as well as developing lightweight versions for real‑time field applications.