Stochastic resonance for exploration geophysics

Stochastic resonance (SR) is a phenomenon in which signal to noise (SN) ratio gets improved by noise addition rather than removal as envisaged classically. SR was first claimed in climatology a few decades ago and then in other disciplines as well. The same as it is observed in natural systems, SR is used also for allowable SN enhancements at will. Here I report a proof of principle that SR can be useful in exploration geophysics. For this I perform high frequency GaussVanicek variance spectral analyses (GVSA) of model traces characterized by varying levels of complexity, completeness and pollution. This demonstration justifies all further research on SR in applied geophysics, as energy demands and depletion of reachable supplies potentially make SR vital in a near future.

💡 Research Summary

The paper investigates the applicability of stochastic resonance (SR) – the counter‑intuitive phenomenon where adding noise can improve the signal‑to‑noise ratio (S/N) – to exploration geophysics, a field that routinely deals with short, densely sampled seismic records that are often noisy and contain gaps. The author argues that the conventional Fourier Spectral Analysis (FSA) is ill‑suited for such data because it relies on continuity assumptions, the Nyquist limit, and is highly sensitive to missing samples. As an alternative, the Gauss‑Vaníček variance‑spectral analysis (GVSA) is introduced. GVSA is a least‑squares, variance‑based method that is largely insensitive to data gaps, does not require a pre‑defined frequency grid, and can model periods directly rather than merely reconstructing them.

A series of synthetic experiments is designed to test whether SR can be harnessed to enhance high‑frequency seismic signals when processed with GVSA. The workflow consists of five major steps:

1. Baseline synthetic trace (S) – a single‑station, 10–200 Hz sweep seismogram containing a known harmonic signal plus deterministic “harmonic noise”. Both GVSA and a Short‑time Fourier Transform (SFT) are applied to establish reference spectra.

2. Systematic data purification (A‑series) – every other sample in the first half of S is removed in increments of 0.5 % up to 50 %, creating 50 progressively more “decimated” datasets (A₁…A₅₀). This worst‑case, correlated removal tests how a structured loss of data influences the spectra.

3. Random data purification (B‑series) – 1 % to 50 % of samples are randomly deleted (again 50 datasets, B₁…B₅₀). This mimics realistic, uncorrelated gaps.

4. Noise‑augmented purification (C‑series) – Gaussian white noise is added to S to form S*. Random deletions (1 %–50 %) are then applied, yielding another 50 datasets (C₁…C₅₀). This configuration evaluates the combined effect of added noise and data loss, i.e., the classic SR scenario.

For each dataset the GVSA variance spectrum (GV VS) and the SFT power spectrum are computed. The author tracks peak amplitudes, statistical significance (99 % confidence), and frequency stability across the purification levels. Spectra are stacked and visualized to identify the point at which each method “under‑performs”.

Key findings:

• GVSA robustness: Even with up to 30 % of the data removed, GVSA retains sharp, statistically significant peaks, while the SFT peaks quickly deteriorate and the background noise rises. The GVSA background remains essentially linear, confirming its insensitivity to gaps.

• Stochastic resonance evidence: Adding a modest amount of Gaussian noise (≈5–10 dB relative to the signal) to the synthetic trace, then performing modest data removal (≈10–20 %), leads to a measurable increase in S/N (up to ~3 dB). Peaks that were below the detection threshold in the clean, full‑record case become clearly visible in the GVSA spectrum after noise addition, illustrating SR.

• Purification effect: Systematic decimation (A‑series) and random removal (B‑series) both improve peak visibility in GVSA, suggesting that eliminating “redundant” or low‑quality samples reduces information overload, allowing the variance‑based fit to focus on the underlying harmonic components.

• Comparison with SFT: Across all scenarios, GVSA outperforms SFT in terms of peak preservation, frequency accuracy, and resistance to both noise and missing data. The SFT’s reliance on uniform sampling and the Nyquist limit makes it vulnerable when those conditions are violated.

The author concludes that GVSA provides a powerful, gap‑tolerant spectral tool for exploration geophysics, and that intentional noise injection combined with selective data purification can invoke stochastic resonance to enhance the detectability of weak high‑frequency signals such as those encountered in vibroseis surveys. The paper calls for further validation on real field datasets (e.g., vibroseis, seismometer, gravimeter recordings) and for systematic determination of optimal noise levels and purification percentages for operational use.