A Clustering-Based Dispersion Analysis Approach for Borehole Acoustic Waves and Its Application

In borehole acoustic, how to extract the fundamental dispersion modes of guided waves is not an easy task, because the unfavorable borehole conditions and co-existing noises in a dispersion map contribute to an outstanding challenge in utilizing the dispersion features. Such inefficiencies in dispersion analysis routines hinder the availability of many critical insights about near wellbore geology (like lithology, anisotropy, and fractures, etc.). Even though many dispersion analysis methods have been proposed and applied in past decades, the access to reliable dispersion characteristics is still a challenge due to ambient noises and other unfavorable conditions. The Prony method (1795) is commonly used to extract velocity dispersion data, but the method is not reliable in controlling the effect of noise present on estimating dispersive modes. The Weighted Spectral Semblance method (Nolte and Huang 1997) does not generate spurious estimates but does generate aliases. Tikhonov regularization (Aster et al. 2005) is effective in filtering most of the spurious modes. However, multiple propagation modes with different energies make it difficult to estimate the dispersion mode. In this paper, we present a two-level DBSCAN clustering method which is capable of differentiating and extracting dispersion characteristics of the fundamental mode. In specific, we connect outcomes of the inversion-based matrix pencil method with such a hierarchy DBSCAN scheme, which considers both the inverted amplitude and slowness during the density-based clustering optimization. That new approach resolves the problem that conventional slowness time coherence method cannot accurately obtain the reservoir features when dispersion features of different orders coexist. Tests on synthetic data and field data both demonstrate its effectiveness in separating the fundamental dispersion features within 3 iterations. In practice, we have applied this method to evaluate rock mechanics after hydraulic fracturing, which can be a troublesome task due to the possible transitions into soft formation and the acquisition noises caused by the fracking-induced unfavorable borehole condition. The results show that the method significantly improves the clarity of dispersion features and the attendant SFA map. From a perspective of dispersion, this method enables successful characterization of the shear slowness changes caused by two successive fracking operations. It provides a potential way in evaluating the hydraulic fracturing effects, which has demonstrated its effectiveness in near wellbore geological evaluation. New lights are cast on how to decompose the dispersion phenomena of borehole acoustics into their corresponding orders, via a hierarchical clustering method. Practical applications are provided to illustrate the potentials in squeezing more new values from the commonly available borehole acoustic waveforms.