Borehole acoustic logging is an acquisition method that is regarded as the most efficient and reliable method to measure subsurface rock elastic property. It plays an important role in both well construction and reservoir evaluation. The acquisition is carried out downhole by firing a transducer and then collecting waveforms at an array of receivers. A signal processing technique such as the slowness-time-coherence method is used to process array waveform data to resolve slownesses from different arrivals. To label these slowness values, a classification algorithm is then required to first determine if a primary (P) or a secondary (S) arrival exists or not, and then label out the existing ones at each depth of the entire logging interval to deliver continuous compressional and shear slowness logs. Such a process is referred as automatic sonic log tracking process. Clearly, it is of great importance to be able to track log as accurately as possible. Traditional approaches either use predefined slowness or arrival time boundary to distinguish them or treats slowness peaks in consecutive depths like “moving particles” and use a particle tracking algorithm to estimate their trace. However, such a tracking algorithm is often challenged by a sudden change in formation types at bed boundary, fine-scale heterogeneity, downhole logging noise, as well as unpredicted signal loss due to bad borehole shape or gas influx. Consequently, the tracking process is often a tricky task that requires heavy manual quality control and relabeling process, which poses significant bottleneck for a timely delivery of sonic logs for downstream petrophysical and geomechanical applications. In this paper, we propose a new physical based multi-resolution tracking algorithm that can improve the robustness of the tracking process. The new algorithm is inspired by the fact that different resolution sonic logs can sense different rock volumes and therefore response differently to a thin layer or an interval with bad borehole conditions. It works by grouping slowness-time peaks with different resolutions to form clusters, which are then tracked by the connecting with its neighboring depths. As different resolution slownesses are physically constrained by the convolution response of heterogeneous layers, the cluster-based multi-resolution tracking approach exhibits better logging depth continuity than the traditional single-resolution methods. Outliers due to noise can be confidently avoided. Finally, remaining gaps due to shoulder bed boundary can be patched by a convolution constrained optimization process from coherences from different resolutions. This new approach is therefore referred as a multi-resolution approach and can significantly improve sonic log tracking accuracy than the single resolution approach. This new algorithm has been tested on several sonic logging field data and demonstrates robust tracking performance of sonic P&S logs. Additionally, with the multi-resolution processing, sonic logs with different resolution can be reliably obtained and a high-quality high-resolution sonic log can also be automatically delivered, which can then be used to match resolution of other petrophysical logs for various types of interpretation.
Precise inversion of logged slownesses for elastic parameters in a gas shale formation