geophysics · attributes
Instantaneous Amplitude & Phase
A(t) = √(x² + x'²) | φ(t) = atan2(x', x)
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Inputs
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Description
Implements the analytic-signal (complex trace) formulation of Taner, Koehler & Sheriff (1979) at a single time sample: given the real trace value and its Hilbert-transform (quadrature) companion at the same instant, computes the instantaneous envelope amplitude and phase that underlie modern seismic amplitude and phase attribute volumes.
Variables
| Symbol | Unit | Description |
|---|---|---|
| A | — | Instantaneous Amplitude (Envelope) |
| φ | ° | Instantaneous Phase |
| x | — | The real seismic trace amplitude sample at the instant of interest, in whatever relative/normalized amplitude scale the trace is carried in. |
| x' | — | The Hilbert-transform (90°-phase-shifted) companion sample at the same instant, computed by seismic processing software — together with x, forms the analytic (complex) trace. |
Assumptions
- x and x' are a genuine Hilbert-transform pair at the same instant — x' was correctly computed from the real trace, not an arbitrary independent value
- Both values are already scaled/normalized consistently with the source seismic volume
Limitations
- This is a single-sample illustration of the underlying complex-trace math, not full-trace or full-volume attribute extraction — real interpretation workflows compute these attributes continuously across an entire trace/volume in dedicated processing software
- Instantaneous phase is highly sensitive to noise at low amplitude (small x and x') — interpret phase values and displays cautiously in low-signal zones
- Amplitude values are only meaningful relative to the same seismic volume's own scaling — not comparable in absolute terms across different surveys or processing sequences
Use Cases
- → QC a suspicious attribute sample: Hand-check a single suspicious sample from an amplitude or phase attribute display against the underlying complex-trace calculation.
- → Teaching the complex-trace foundation: Demonstrate how envelope (amplitude) and phase attribute volumes are mathematically derived from the same analytic trace.
- → Bright-spot vs. continuity attribute context: Understand why amplitude (envelope) attributes highlight fluid/lithology contrasts while phase attributes highlight geometric continuity, from the same underlying signal.
Related Calculations
Region Notes
Gulf of Mexico
Envelope (instantaneous amplitude) attribute volumes are a standard bright-spot/DHI screening tool in this basin's classic gas-sand plays.
North Sea
Instantaneous phase volumes are widely used here to trace subtle fault and channel-margin continuity through zones where amplitude alone is inconclusive.
Global
Always confirm the sign/polarity convention (SEG normal vs. reversed) of the source volume before interpreting phase values — a reversed-polarity volume shifts all phase readings by 180°.
References
Primary source
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