Description

This module builds a minimum-phase shaping operator from an input wavelet or gather, for use in wavelet-conditioning and signature-deconvolution workflows. It first converts the input into its minimum-phase equivalent (a spectral-factorization/Kolmogorov approach), optionally reshaping its amplitude spectrum first, then designs a matched (least-squares) filter that transforms the original input into that minimum-phase wavelet. The resulting operator can be used elsewhere to convert data recorded with the original (e.g. mixed- or zero-phase) wavelet into an equivalent minimum-phase representation. An optional spiking deconvolution pass can additionally be applied to the shaped output for quality control.

Input data

Input gather

The wavelet or gather (for example an extracted source signature, a well-tie wavelet, or a vibroseis pilot response) that the minimum-phase operator is derived from.

Parameters

Apply spectrum replacement

When enabled, the amplitude spectrum of the input is reshaped to a trapezoidal band (defined by the Low Roll-Off, Low Freq, High Freq and High Roll-Off parameters below) before the minimum-phase conversion. This is useful to suppress noisy, poorly-conditioned parts of the spectrum (very low and very high frequencies) that would otherwise destabilize the operator design. When disabled, the original spectrum is used unmodified.

Default: On.

Low Roll-Off

Low-frequency corner of the trapezoidal spectrum taper applied before conversion, below which the spectrum is rolled off toward zero. Used together with "Low Freq" to define the shape of the low-frequency slope of the passband.

Default: -48 Hz. Only used when "Apply spectrum replacement" is on.

Low Freq

Low-frequency edge of the flat passband of the trapezoidal spectrum taper. Frequencies above this value (up to High Freq) pass through unattenuated.

Default: 8 Hz. Minimum 0. Only used when "Apply spectrum replacement" is on; set to match the useful low-frequency content of your data/wavelet.

High Freq

High-frequency edge of the flat passband of the trapezoidal spectrum taper. Frequencies between Low Freq and this value pass through unattenuated.

Default: 80 Hz. Minimum 0. Only used when "Apply spectrum replacement" is on; set close to the highest reliable signal frequency in your data.

High Roll-Off

High-frequency corner beyond which the spectrum is rolled off toward zero, working together with "High Freq" to define the high-frequency slope of the passband.

Default: -48 Hz. Only used when "Apply spectrum replacement" is on.

Prewhitening

Amount of white noise added (as a fraction of the zero-lag energy) before the minimum-phase spectral factorization. This stabilizes the conversion against noisy or near-zero spectral values, at the cost of slightly smoothing the resulting operator's spectrum.

Default: 0.001 (0.1%). Minimum 0. Increase slightly if the resulting operator is unstable or excessively "spiky"; keep it small to preserve the true wavelet shape.

Operator window

Length of the matched-filter operator being designed to shape the input into its minimum-phase equivalent. It is automatically capped to the length of the input gather. A longer operator can match the target wavelet more precisely but requires more data to solve for reliably; a shorter operator is more stable but may leave some residual mismatch.

Default: 0.9 ms. Minimum 0.

Apply tapers

When enabled, a Hamming taper is applied to the leading edge of the minimum-phase wavelet and to the trailing edge of the designed operator, smoothing the edges so the operator does not end abruptly. This reduces ringing (Gibbs-type) artifacts when the operator is later convolved with data.

Default: On.

Apply zero tapers

When enabled (and tapers are applied), the very first sample of the designed operator is forced to zero. This can help avoid a spurious DC-like spike at the start of the operator.

Default: On. Only relevant when "Apply tapers" is on.

Taper filters window

Length of the Hamming taper applied at the edges when "Apply tapers" is on. A longer taper smooths the edges more gradually but shortens the effective, undistorted part of the operator.

Default: 0.10 ms. Only relevant when "Apply tapers" is on.

Matched filter parameters

Subtraction type

Numerical method used to solve for the matched-filter operator that converts the input into its minimum-phase equivalent. "SVD" (singular value decomposition) is the most robust choice for ill-conditioned or noisy problems; "Cholesky" and "Lsqr" are faster least-squares solvers suited to well-behaved data; "Levinson" and "Toepriz" use fast Toeplitz-system algorithms, which are efficient for longer operators but assume a stationary, well-conditioned autocorrelation.

Default: Cholesky. Switch to SVD if the solution looks unstable or the operator has an unexpectedly large amplitude.

Lambda

Damping (regularization) factor applied during the matched-filter solve, expressed as a fraction. Higher values make the solution more stable and conservative at the cost of a less exact match; lower values fit the target more precisely but are more sensitive to noise.

Default: 0.0001 (0.01%). Minimum 0.

Run spike decon on applied operator

When enabled, the designed operator is convolved with the input and the result is further processed with a spiking deconvolution, producing a QC gather that shows how close the shaped result comes to a spike (ideal minimum-phase, zero-length response). Useful for judging operator quality before using it elsewhere.

Default: On.

Spike decon parameters

All time operator detection

When enabled, the QC spiking deconvolution computes its autocorrelation using the full available time range rather than a shorter analysis window, which can give a more stable statistics estimate on short or low-fold data.

Default: Off. Only relevant when "Run spike decon on applied operator" is on.

Noise

Prewhitening level for the QC spiking deconvolution, expressed as a fraction of the zero-lag autocorrelation energy. Higher values give a more stable but less aggressive spike compression.

Default: 0.01 (1%). Only relevant when "Run spike decon on applied operator" is on.

Overlap taper window

Length of the taper used to blend the QC spiking-deconvolution result smoothly, avoiding a sharp edge at the analysis window boundary.

Default: 0.10 ms. Only relevant when "Run spike decon on applied operator" is on.

Output data

Output gather

The designed matched-filter (minimum-phase shaping) operator itself, ready to be applied to reshape other data that shares the same original wavelet.

QC

Quality-control gather showing the intermediate minimum-phase converted wavelet, or (if "Run spike decon on applied operator" is enabled) the result of applying the operator followed by a spiking deconvolution — useful for visually judging how close the final result is to an ideal spike.

References

Robinson, E. A., 1954 (reprinted 1967), Predictive decomposition of time series with application to seismic exploration: Geophysics, 32, 418-484.