Joint Time–Space–Depth Feature Learning for Multimodal Velocity Estimation from Array Acoustic Logging Waveforms

Accurate velocity estimation from array acoustic logging in unconventional hydrocarbon reservoirs is frequently hindered by complex wavefield interference, limited vertical resolution in thinly interbedded formations, and severe borehole noise. To overcome these challenges, this study proposes a unified deep learning framework, termed CNN–BiConvLSTM–SKAM, designed to synergistically capture the temporal, spatial, and depth-dependent characteristics of measured acoustic waveform data. Specifically, a multi-scale dilated residual convolutional neural network (CNN) is employed to encode local temporal arrivals and spatial move-out correlations across the receiver array. Subsequently, a bidirectional convolutional long short-term memory (BiConvLSTM) network explicitly models vertical stratigraphic dependencies, effectively preserving formation continuity and addressing the constraints of traditional point-wise interpretive workflows. To further enhance feature discriminability, a selective kernel attention mechanism (SKAM) is integrated to adaptively refine salient representations through dynamic spatial and channel weighting. This multi-dimensional feature set is ultimately mapped to synchronized compressional (P-), shear (S-), and Stoneley (ST-) wave velocities curves via an output regression layer. Validation on expert-annotated field datasets demonstrates that the proposed framework significantly outperforms standalone CNN and BiConvLSTM architectures, achieving high coefficients of determination of 0.854, 0.937, and 0.868 for P-, S-, and ST-waves, respectively. These results indicate that the framework effectively exploits joint time–space–depth representations, providing a robust, high-precision, and automated solution for acoustic velocity estimation in complex subsurface environments.