Extracting Slowness (Velocity) of Mode Waves (Non-Dispersive Waves) from Acoustic Logging Waveform Data

To extract velocity values for each mode wave (non-dispersive wave) from acoustic logging waveform data, a systematic approach involving signal processing and mathematical analysis is required. The first implementation step involves applying digital filters (such as bandpass or Wiener filters) to remove noise and interference from the raw waveform data. Following data preprocessing, mathematical algorithms including time-domain correlation methods or frequency-domain dispersion analysis are employed to calculate wave velocities. A key computational technique involves implementing the Slowness-Time-Coherence (STC) method, which uses coherence-based semblance processing to identify wave modes and their corresponding slowness values across different time windows. This typically involves matrix operations for cross-correlation calculations and peak detection algorithms to identify coherent wave arrivals. Once velocities are calculated, specialized plotting functions (such as MATLAB's contourf or imagesc) can generate STC diagrams that visualize slowness distributions versus time, highlighting coherent energy peaks corresponding to different wave modes. This analytical process provides critical insights for subsurface formation characterization and hydrocarbon reservoir identification by accurately determining acoustic wave propagation properties through various geological layers.