VMD-TCN-Transformer-based approach for logging curve reconstruction under complex conditions

Acoustic logging curves, particularly compressional wave slowness (DTC) and shear wave slowness (DTS), serve as fundamental data for petrophysical analysis, synthetic seismogram generation, and refined reservoir characterization. However, during actual drilling operations, these curves are prone to distortion or gaps due to factors such as borehole conditions and complex environmental measurement noise, which constrains their practical application. Traditional empirical formulas and statistical regression methods struggle to capture the complex nonlinear relationships between logging curves. Although machine learning and deep learning methods introduced in recent years have improved reconstruction accuracy to some extent, they still exhibit limitations in comprehensively representing the non-stationary features, local variations, and long-range geological dependencies of logging signals under complex borehole conditions.

To address these issues, this study proposed an acoustic logging curve reconstruction method based on a fusion architecture combining variational mode decomposition (VMD) and temporal convolutional network (TCN)-Transformer. The method first employed VMD to perform multi-scale decomposition of the original logging signals, preserving the effective formation signals to the greatest extent while effectively filtering out high-frequency environmental noise. Subsequently, TCN was introduced to characterize the local variation features of the logging curves, while the Transformer’s multi-head self-attention mechanism was employed to extract long-range dependencies within the logging sequences, enabling holistic modeling of complex sedimentary cyclicity. Based on measured logging data from a block in Shanxi, comparative model analysis, ablation experiments, curve reconstruction experiments under conditions of severe borehole enlargement, and blind-well prediction validation were conducted.

The results demonstrated that the proposed method performed well in terms of accuracy and stability for acoustic logging curve reconstruction. The coefficients of determination (R²) for DTC and DTS predictions in the test intervals reached 0.9142 and 0.9165, respectively. Both the VMD signal decomposition and the TCN-Transformer hybrid architecture contributed significantly to the model’s performance. In intervals with significant borehole enlargement, the model effectively suppressed environmental noise interference, producing reconstructed curves with continuous and geologically reasonable morphology. The synthetic seismograms generated from the blind-well prediction results showed good consistency with the measured seismic profile in terms of wavelet characteristics and phase features.

The proposed method exhibits strong adaptability and practicality under complex borehole conditions. It can provide reliable foundational data for the correction and completion of low-quality logging data, as well as for subsequent seismic inversion and refined reservoir characterization.