Parameter Extraction for Seafloor- Borehole-Controlled Source Electromagnetic Data Based on VMD-Hilbert Transform

The seafloor-borehole-controlled source electromagnetic method (SB-CSEM) advances submarine mineral detection through seabed-deployed transmitters and borehole receivers, effectively suppressing seawater-induced signal attenuation. To address persistent challenges in weak high-frequency signal detection, we develop a variational mode decomposition-Hilbert transform (VMD-HT) algorithm integrating edge effect suppression via autoregressive forward–backward extrapolation and adaptive VMD (AVMD) for spectral separation, with subsequent analytic-signal extraction through the HT. Precision parameter extraction is achieved via frequency-shift demodulation and robust phase unwrapping, providing a systematic framework for low-signal-to-noise ratio (SNR) electromagnetic signal recovery. Parameter optimization establishes <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> = 500 as the optimal penalty factor for signals below 50-dB SNR, coupled with dynamic mode selection to prevent spectral leakage. Numerical validation demonstrates the method’s significant advantages over conventional fast Fourier transform (FFT) and wavelet techniques, achieving Pearson correlation coefficients approaching unity while maintaining low amplitude and phase estimation relative errors of 0.03 and 0.11 at 40-dB SNR. VMD outperforms empirical mode decomposition (EMD) in processing SB-CSEM signals, and its integration with HT surpasses VMD-FFT performance. Field tests using Indian Ocean datasets demonstrate enhanced stability in rapid frequency-variation environments, outperforming traditional approaches in practical seabed exploration scenarios.