geophysics · attributes
Instantaneous Frequency
f = Δφ / (360° × Δt)
click formula to derive ↑
Inputs
°
°
ms
Description
Computes instantaneous frequency as the discrete time-derivative of instantaneous phase (Taner, Koehler & Sheriff, 1979) from two adjacent phase samples — the rate at which the analytic trace's phase rotates, widely used as a thin-bed and attenuation (low-frequency shadow) indicator distinct from the dominant frequency of the wavelet as a whole.
Variables
| Symbol | Unit | Description |
|---|---|---|
| f | Hz | Instantaneous Frequency |
| φ1 | ° | Instantaneous phase (e.g. from the Instantaneous Amplitude & Phase calc) at the first of two adjacent time samples. |
| φ2 | ° | Instantaneous phase at the next time sample, one sample interval (Δt) after Sample 1. |
| Δt | ms | Time interval between the two phase samples — typically the seismic data's sample rate (commonly 1, 2, or 4 ms). |
Assumptions
- φ1 and φ2 are two temporally-adjacent instantaneous phase samples from the same analytic trace
- Δt is the actual sample interval between them, not an arbitrary time gap
- The true phase rotation between the two samples is less than half a cycle (180°) — see limitations
Limitations
- Large phase changes between samples (approaching or exceeding 180°) are ambiguous — this calc's unwrapping assumes the true rotation is the smaller of the two possible directions, which fails for very rapid phase rotation or undersampled data
- Instantaneous frequency is notoriously unstable near low-amplitude/phase-singularity zones in the underlying trace and can swing sharply negative or to unrealistically large values there — always cross-reference against instantaneous amplitude before trusting an outlier value
- This is a two-sample illustration of the underlying finite-difference math, not continuous full-trace or full-volume processing
Use Cases
- → QC a suspicious attribute sample: Hand-check a single suspicious instantaneous-frequency value from a seismic attribute volume against the underlying two-sample phase calculation.
- → Low-frequency shadow / attenuation indicator: Understand the mechanics behind using anomalously low instantaneous frequency beneath a reservoir as a hydrocarbon-related attenuation (DHI) indicator.
- → Teaching phase unwrapping: Demonstrate why raw phase differences must be unwrapped before being used to estimate instantaneous frequency.
Related Calculations
Region Notes
Gulf of Mexico
Low-frequency shadows beneath gas sands are a classically-cited instantaneous-frequency DHI in this basin — always confirm the anomaly persists across multiple adjacent traces before treating it as reservoir-related rather than noise.
Global
Instantaneous frequency estimates are most reliable in high-amplitude, high-signal-to-noise zones — treat isolated low-amplitude-zone readings with caution regardless of basin.
References
Primary source
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