Extraction of reflected waves from acoustic logging data using variation mode decomposition and curvelet transform

Remote reflection waves, essential for acquiring high-resolution images of geological structures beyond boreholes, often suffer contamination from strong direct mode waves propagating along the borehole. Consequently, the extraction of weak reflected waves becomes pivotal for optimizing migration image quality. This paper introduces a novel approach to extracting reflected waves by sequentially operating in the spatial frequency and curvelet domains. Using variation mode decomposition (VMD), single-channel spatial domain signals within the common offset gather are iteratively decomposed into high-wavenumber and low-wavenumber intrinsic mode functions (IMFs). The low-wavenumber IMF is then subtracted from the overall waveform to attenuate direct mode waves. Subsequently, the curvelet transform is employed to segregate upgoing and downgoing reflected waves within the filtered curvelet domain. As a result, direct mode waves are substantially suppressed, while the integrity of reflected waves is fully preserved. The efficacy of this approach is validated through processing synthetic and field data, underscoring its potential as a robust extraction technique.