Wavenumber-frequency diagram¶
A spectral plot of temporal frequency against spatial wavenumber whose energy ridges reveal propagation direction, phase velocity, group velocity, and dispersion.
Core Idea¶
A wavenumber–frequency diagram is a joint spatial-temporal spectrum. Energy ridges show wave modes and direction; omega divided by k gives phase velocity, while the ridge slope gives group velocity, provided sampling and transform conventions are explicit. Wave modes appear as ridges or branches. Wave modes appear as ridges or branches.
Scope of Application¶
The representation applies to spatially sampled wave fields whose temporal evolution supports joint spectral analysis. Use it for distributed wave measurements in atmospheric, seismic, ocean, and acoustic analysis, with aliasing and window effects reported.
- Atmospheric waves. Separates propagating equatorial and planetary modes.
- Seismic arrays. Estimates direction and apparent velocity.
- Ocean waves. Compares observed energy with dispersion branches.
- Acoustics. Diagnoses modes in distributed sensor data.
- Velocity filtering. Selects spectral regions corresponding to propagation ranges.
Clarity¶
The diagram distinguishes wavelength, temporal period, propagation direction, phase velocity, and group velocity—quantities often collapsed into ‘wave speed.’ It also separates a theoretical dispersion curve from the observed energy that supports or departs from it. The closest near miss sets the boundary: A dispersion-relation plot is the closest near miss: it may show theoretical omega(k) curves without displaying observed spectral energy.
Manages Complexity¶
A space–time field contains many overlapping waves. Joint spectral transformation reorganizes them by k and frequency, so coherent branches, directions, velocities, and aliases can be inspected without tracing every oscillation in the original coordinates. The central spectral separation–space–time localization tradeoff is this: Fourier resolution separates modes while obscuring when and where transient energy occurred. A second phase velocity–group velocity tension matters because Ratio and slope coincide only for nondispersive relations. The resolution–alias avoidance tension adds that Broader aperture and duration sharpen spectral estimates, while sample spacing limits unambiguous range.
Abstract Reasoning¶
Use three linked moves: specify spatial and temporal sampling, units, orientation, and transform signs; window and transform the field while quantifying spectral resolution and aliases; locate coherent energy ridges rather than isolated high-power pixels. As a collapse test, the case exits when spatial sampling is absent, aliasing makes k uninterpretable, or plotted quantities are not temporal frequency and spatial wavenumber. A fourth check is to compare ridge ratio and slope with candidate phase and group velocities. A final check is to test mode and medium interpretations against theoretical dispersion and independent observations.
Knowledge Transfer¶
The representation transfers literally across wave disciplines when a space–time field and transform conventions exist. A generic chart of ‘scale versus rate’ is only analogous; physical velocity and dispersion inferences require wave phase, wavenumber, and frequency. No canonical parent prime is currently asserted; broader structural comparisons remain related-prime analogies until separately adjudicated in the DAG. The diagram is built from spatial and temporal frequency components. Ridge shape records how frequency depends on wavenumber.
Relationships to Other Abstractions¶
Current abstraction Wavenumber-frequency diagram Domain-specific
Parents (1) — more general patterns this builds on
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Wavenumber-frequency diagram is a kind of Scientific Diagram Domain-specific
Wavenumber-frequency diagram satisfies the defining boundary of Scientific Diagram: A scientific diagram is a convention-governed visual representation that maps observations, model variables, or derived quantities into spatial coordinates, symbols, curves, regions, or relations so that scientific structure can be compared, calculated, diagnosed, or inferred.
Hierarchy path (1) — routes to 1 parentless root
- Wavenumber-frequency diagram → Scientific Diagram → Representation → Abstraction
Neighborhood in Abstraction Space¶
Wavenumber-frequency diagram sits in a moderately populated region (44th percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.
Family — Domain-Specific Measurement Parameters (36 abstractions)
Nearest neighbors
- Energy (signal processing) — 0.90
- Doppler spectroscopy — 0.88
- Infrasonic passive differential spectroscopy — 0.87
- Spectral Density — 0.86
- Scattering — 0.86
Computed from structural-signature embeddings · 2026-10-08