Scale-Adaptive Continuous Wavelet Transform for Energy-Envelope Extraction and Instantaneous-Frequency Characterization in High-Resolution Sub-Bottom Profiling

In marine seismic surveys, the indistinguishability of subsurface boundaries caused by the superimposition of the acoustic signals reflected from it, particularly at specific frequency ranges characterized by strong spectral interference, reduces the resolution of the seismic record. We processed sub-bottom profiler data, acquired using a Bubble Pulser (nominal central frequency: ~400 Hz; effective bandwidth extending to ~1 kHz), (i) by extracting continuous wavelet transform (CWT) coefficients at the dominant energy scale to form the envelope and (ii) by applying Hilbert-based instantaneous frequency analysis to characterize medium-dependent spectral shifts. Envelope accuracy was benchmarked against four conventional filters using the sum of squared error (SSE) relative to a cubic-spline reference. CWT yielded the lowest SSE, outperforming low-pass 1 kHz and band-pass 400–1000 Hz; band-pass 400–650 Hz and low-pass 650 Hz were the least effective. Instantaneous-frequency trends differentiated rock, sand, and mud layers. Thus, compared to fixed-band filters, the scale-adaptive CWT envelope replicates raw energy more faithfully, while frequency attributes improve sediment classification. Low-pass filtering at 1000 Hz provides a more accurate representation of energy distribution than does bandpass filtering, particularly in the 400–650 Hz range. The integrated workflow—a robust, parameter-light alternative for high-resolution stratigraphic interpretation—enhances offshore engineering safety.