A Stabilized Real-Time Slowness Estimation Method for Compressional Waves by Using Kalman Filtering

In acoustic logging, slowness estimation is always considered as a most essential and fundamental task because of its wide applications in lithology evaluation, rock mechanics analysis, and geological hazard forecasting. To reduce turnaround time for making efficient exploration and production decisions, there is a growing practical demand for stable real-time slowness analysis. At present, the slowness time coherence (STC) method is widely used to analyze slowness characteristics from acoustic array waveforms. It usually requires fine-tuning of the parameters to ensure optimal performance. However, when employed for real-time slowness analysis, its ability to handle wave interferences, low signal-to-noise data, and noises has encountered remarkable challenges. Conventional peak-finding schemes often fail to accurately identify and pick slowness variations in such cases, resulting in considerable errors and unstable fluctuations in the derived slowness estimation. This paper introduces a novel approach that combines Kalman filtering with the STC method to enhance real-time slowness estimation. Kalman filtering is used to update the optimal state of the system in real time, and it can significantly improve the stability of slowness picks, even in cases with poor signal-to-noise ratios and rapid slowness variations. In addition, the accuracy of slowness picks is further improved through an integrated peak-finding mechanism. In general, key parameters of Kalman filtering, such as process noise covariance matrix and observation noise covariance matrix, need to be appropriately specified before model construction. However, in the context of slowness estimation, obtaining these parameters can be challenging due to the uncertainties associated with stratigraphic changes. Consequently, this study proposes an automated method for parameter estimation to achieve acceptable results. The application of Kalman filtering is lightweight and thus poses little burden on data storage and calculation speed, leading to a much-reduced processing time within 20 milliseconds for each depth point. This method has already been applied in many field cases of various lithologies and well types, such as openhole wells, cased wells, soft formations, and large boreholes (diameter exceeding 600 mm), which have verified its stability and time efficiency in dealing with the situation of gradual and sudden changes in different formations. As a result, this method provides a robust and reliable compressional wave slowness estimation, even when faced with challenges like poor signal-to-noise ratios and rapid slowness variations, making it a powerful tool for on-site data processing and evaluation.