Attenuates periodic/ringing events

Theory

Cepstrum(reverse order of Spec) Deconvolution is a wavelet-removal technique that works by transforming seismic data into the cepstrum where source periodicities (multiples, bubble pulses, reverberations) appear as isolated peaks. By applying a lifter (reverse order of fil) filter in the quefrency domain, these periodic components are removed, producing a cleaner, more reflectivity-like trace.

What is Cepstrum Deconvolution?

Cepstrum deconvolution is a method for removing the source wavelet from seismic data by converting the signal into the cepstrum domain — a special domain where reverberations, multiples, and periodic wavelet signatures appear as distinct peaks and can be isolated and removed.

It is especially good at:

• Removing short-period multiples
• Removing source bubble effects in marine data
• Removing ghosts
• Flattening reverberations
• Extracting the minimum-phase wavelet

Why Use Cepstrum Deconvolution?

Traditional deconvolution (spiking/predictive) struggles when:

• Wavelet is mixed-phase
• Reverberations are embedded inside the wavelet
• Multiples have regular periodicity
• Data have strong source bubble oscillations

Cepstrum deconvolution excels because:

• Convolution becomes addition in the cepstrum
• Periodic wavelet features show up as distinct spikes
• These can be suppressed using windows or filters

How Cepstrum Deconvolution Works?

A seismic trace is: x(t) = w(t) * r(t)

Step 1 — Fourier Transform: X(f) = W(f) . R(f)

Step 2 — Take Log Spectrum: ln X(f) = ln W(f) +  ln R(f)

This is the key: Convolution becomes addition.

Step 3 — Inverse FFT of log spectrum → Cepstrum

C(Ƭ) = F-1 {ln X(f)}

• Ƭ is called "quefrency"
• Peaks at particular t correspond to periodicities (multiples, bubble oscillations)

Step 4 — Apply a “lifter” (cepstral filter)

• Suppress long-period or short-period components
• Remove wavelet periodicity
• Keep reflectivity terms

Step 5 - Transform back

Ẍ(f) = exp {FFT(Cfiltered)}

Inverse FFT gives the cepstrum-deconvolved trace.

What Cepstrum Deconvolution Removes?

Short-path multiples - Bubble pulse or peg-leg multiples appear as repeating periodic events that are strong in cepstrum.

Ghost effects - Source/receiver ghost period appears as a cepstrum peak.

Source wavelet periodicity - Any oscillatory wavelet component (Vibroseis sweep edges, bubble oscillation).

Reverberations / ringing - Room acoustics / poor weathering layers.

Input data

Input DataItem

Input gather

connect/reference to the Output gather. This gather can be a pre or post stack gather.

Parameters

Time start - time of Primary

specify the start time of the primary energy/signal. This is the minimum quefrency (smallest cepstral time) to include in the primary cepstral window. This defines where the primary cepstrum begins. Too small value includes the lower frequencies and distort the wavelet. Too high value may attenuate the primaries.

Time end - time of primaty + Multiples

specify the end of the primary energy/signal along with multiple energy. This is the maximum quefrency included in the primary region. Beyond this value contains bubbles, short period multiples, reverberations, ringing, source and receiver ghosts etc. This is the key parameter in the cepstrum deconvolution. It sets where the primary/multiple ringing begins in the cepstrum. Anything beyond this value will be attenuated.

If value is too small - we may be attenuating the primaries, if the value is too big , we may not attenuating the multiples. Optimum values are recommended. For marine bubbles, anything between 20-40ms is a good starting point.

Noise

specify the percentage of white noise is added to the deconvolution to stabilize the output.

Settings

Auto-connection

By default, TRUE(Checked).It will automatically connects to the next module. To avoid auto-connect, the user should uncheck this option.

Bad data values option { Fix, Notify, Continue }

This is applicable whenever there is a bad value or NaN (Not a Number) in the data. By default, Notify. While testing, it is good to opt as Notify option. Once we understand the root cause of it,

the user can either choose the option Fix or Continue. In this way, the job won't stop/fail during the production.

Notify

It will notify the issue if there are any bad values or NaN. This will halt the workflow execution.

Fix

It will fix the bad values and continue executing the workflow.

Continue

This option will continue the execution of the workflow however if there are any bad values or NaN, it won't fix it.

Calculate difference

This option creates the difference display gather between input and output gathers. By default Unchecked. To create a difference, check the option.

Skip

By default, FALSE(Unchecked). This option helps to bypass the module from the workflow.

Output data

Output DataItem

Output gather

generates the deconvolved output gather.

Gather of difference

if opted, generates the difference gather after cepstrum deconvolution.

Information

There is no information available for this module.

Examples

Cepstrum deconvolution separates convolution into addition by taking log of the spectrum and inverse transforming it (the “cepstrum”). This allows us to detect and remove periodic wavelet components.

Actions

There are no action items available for this module so the user can ignore it.

Video lesson

YouTube video lesson, click here to open [VIDEO IN PROCESS...]

Related articles

Yilmaz. O., 1987, Seismic data processing: Society of Exploration Geophysicist

* * *   If you have any questions, please send an e-mail to: support@geomage.com  * * *

Input data

Input DataItem

The input data connection for this module. Connect this item to the output of the preceding module in the processing workflow to feed seismic trace data into the cepstrum deconvolution algorithm.

Input gather

The seismic gather to be deconvolved. This can be a pre-stack gather (e.g., a CMP, shot, or receiver gather) or a post-stack gather. Connect this to the Output gather of the previous module in the sequence. Each trace in the gather is processed independently through the cepstrum deconvolution algorithm to remove periodic wavelet components such as multiples, bubble pulses, and reverberations.

Parameters

Time start - time of Primary

Defines the start of the cepstral window used to isolate the primary signal. In the cepstrum domain, this is the minimum quefrency boundary — the point where the primary energy is considered to begin. Quefrency values below this threshold contain the very low-frequency (smooth) component of the log spectrum and are excluded from the primary window.

Default value: -100 ms. The negative sign indicates this is the pre-zero time window that captures the maximum-phase component of the wavelet. Setting this value too small (close to zero or positive) risks distorting the wavelet by excluding important low-quefrency components. Setting it too large (very negative) may inadvertently include low-frequency noise in the primary window. For most datasets, the default value of -100 ms is a good starting point.

Time end - time of primaty + Multiples

Defines the end of the cepstral primary window, and is the single most important parameter in cepstrum deconvolution. This value sets the quefrency boundary between the primary signal region and the periodic noise region. Any cepstral energy at quefrencies beyond this value — corresponding to short-period multiples, bubble pulses, reverberations, source/receiver ghosts, and ringing — will be attenuated by the lifter filter.

Default value: 400 ms. If this value is set too small, primary reflections may be attenuated along with the periodic noise, degrading the signal. If it is set too large, short-period multiples and reverberations will not be sufficiently removed. For marine data affected by bubble oscillations, values in the range of 20 to 40 ms are a recommended starting point. Use the cepstrum display to identify the quefrency of the dominant periodic event and set this value just below that peak.

Noise

Controls the amount of pre-whitening applied during the deconvolution step to stabilize the spectral division and prevent division by very small numbers (numerical instability). This is expressed as a fraction of the average spectral amplitude.

Default value: 0.01 (1%). A small noise value (e.g., 0.01) gives a stronger deconvolution effect but may amplify noise in frequency bands with low energy. A larger value (e.g., 0.1 or 10%) makes the output more stable but reduces the strength of the deconvolution. Increase this value if the output traces show unusual amplitude spikes or spectral ringing after processing.

References

Ulrych, T. J., 1971, Application of homomorphic deconvolution to seismology: Geophysics, 36, 650-660.