geophysics · seismic resolution
Ricker Wavelet
click formula to derive ↑
Inputs
Hz
ms
ft/s
Description
Computes the Ricker (1953) zero-phase wavelet — the negative normalized second derivative of a Gaussian pulse, and the standard idealized source wavelet used throughout seismic resolution theory (Widess's tuning-thickness wedge model, dominant-wavelength/Fresnel-zone estimates elsewhere in this subcategory) — at a chosen evaluation time, and charts its full classic shape: one central positive peak flanked by two negative side lobes that decay to zero. Also computes and marks two different, non-competing answers to 'how thin a bed can this wavelet still resolve': Widess (1973)'s classic λ/4 rule of thumb, and Chung & Lawton (1995)'s numerically exact composite-amplitude peak for this specific wavelet shape — see this calc's limitations for how the two differ.
Variables
| Symbol | Unit | Description |
|---|---|---|
| r(t) | — | Wavelet Amplitude |
| T | ms | Dominant Period |
| h_W | ft | Widess (1973) — λ/4 Rule of Thumb |
| h_CL | ft | Chung & Lawton (1995) — Exact Ricker-Wavelet Peak |
| f | Hz | Dominant (peak spectral) frequency of the zero-phase wavelet — the same quantity used throughout this subcategory's wavelength/tuning/Fresnel calcs. |
| t | ms | Time, relative to the wavelet's central peak (t=0), at which to evaluate the amplitude — also the swept axis for the wavelet-shape chart below. |
| V | ft/s | Representative interval velocity — used only to convert the wavelet's own characteristic times into the two bed-thickness comparison outputs below (Widess vs. Chung & Lawton); has no effect on the wavelet shape, amplitude, or period above. |
Assumptions
- The source wavelet is exactly zero-phase and exactly this idealized closed form — real recorded/processed wavelets are broadband and only approximately Ricker-shaped
- A single dominant frequency f fully parameterizes the wavelet's time scale
Limitations
- Real seismic wavelets are rarely purely zero-phase or exactly Ricker-shaped in practice — this is the standard idealized/synthetic wavelet used for modeling and resolution theory, not a substitute for an actual extracted wavelet
- The displayed chart window is a fixed ±50 ms range, matching this calc's own t input range — it does not automatically rescale for very low (<~10 Hz) or very high (>~80 Hz) dominant frequencies, where the classic three-lobe shape may appear clipped or compressed
- h_Widess and h_ChungLawton answer two different questions, not one 'more correct' than the other: h_Widess is the classic, widely-taught quarter-wavelength approximation (Widess 1973), while h_ChungLawton is the numerically exact composite-amplitude peak for this specific zero-phase Ricker wavelet (Chung & Lawton 1995) — the two coincide only approximately, and Chung & Lawton's own value is consistently smaller (≈78% of Widess's) for a pure Ricker wavelet specifically. Neither should be read as superseding tuning_thickness's own published λ/4 result elsewhere in this subcategory — see that calc's own limitations for the separate, out-of-scope Kallweit & Wood (1982) broadband/highest-usable-frequency refinement, which this platform does not model (no highest-usable-frequency input exists anywhere on this platform) and is NOT the same relationship as either value shown here.
Use Cases
- → Visualizing what 'dominant frequency' means: See the actual wavelet shape a given dominant frequency implies before using that frequency in the wavelength, tuning-thickness, or Fresnel-zone calcs elsewhere in this subcategory.
- → Explaining side-lobe artifacts: Show why a strong reflector can produce a visible side-lobe 'ghost' event above/below the true reflection — the Ricker wavelet's own negative side lobes, not a processing artifact.
- → Synthetic seismogram / forward modeling sanity check: Confirm the wavelet shape and timing before convolving it with a reflectivity series in an external modeling exercise.
- → Choosing between the classic λ/4 rule and a more precise estimate: Compare Widess's simple, widely-taught quarter-wavelength thumb rule against Chung & Lawton's numerically exact peak for a pure Ricker wavelet, before deciding which figure to quote for a specific resolvability question.
Related Calculations
Region Notes
Global
The Ricker wavelet is a modeling idealization used worldwide in resolution theory and synthetic seismogram generation — it is not specific to any basin or play; always compare against an actual extracted/statistical wavelet from real data before relying on it for detailed interpretation.
References
Primary source
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