Signature Deconvolution

Key Takeaways

• Airgun bubble pulse removal is the most critical application of signature deconvolution in marine seismic exploration, because the bubble pulse train from a single airgun has a dominant period (the time between successive bubble oscillations) that falls in the exploration seismic frequency band (40-200 Hz for typical airgun sizes and depths), causing the bubble pulse reflections to overlap with and interfere with the primary reflections from subsurface interfaces: for a 150 cubic inch airgun at 6 meters depth, the primary bubble period is approximately 90-120 milliseconds, meaning that the first bubble pulse arrives 90-120 ms after the primary pulse and produces a second set of reflections from the same geological interfaces that overlap with primary reflections from interfaces 90-120 ms deeper (roughly 100-150 meters deeper at 2,000 m/s interval velocity); in practice, airgun arrays are designed to reduce the bubble pulse amplitude relative to the primary pulse by deploying multiple airguns of different volumes that are tuned (designed to have bubble periods in destructive interference with each other), converting the extended bubble train to a more compact primary pulse with suppressed bubbles — but the residual bubble energy in the array output still requires removal by signature deconvolution to achieve the temporal resolution needed for exploration imaging; the combination of array design (hardware bubble suppression) and signature deconvolution (software bubble removal) achieves the near-zero-phase, compact wavelets used in exploration seismic processing that maximize temporal resolution while minimizing wavelet side lobes that would interfere with thin-bed detection.
• Deterministic versus statistical deconvolution approaches to wavelet removal represent two fundamentally different philosophies with different data requirements and limitations: deterministic deconvolution (which includes signature deconvolution) uses an explicitly measured or modeled source wavelet to design the inverse filter applied to the data, requiring a measurement of the actual source output but making no assumptions about the statistical properties of the subsurface reflectivity; statistical deconvolution (spiking deconvolution, predictive deconvolution, Wiener deconvolution) estimates the source wavelet statistically from the autocorrelation of the seismic trace under the assumption that the earth's reflectivity series is white (spectrally flat) and that the wavelet is minimum phase, without requiring an explicit measurement of the source signature; the advantage of deterministic signature deconvolution is that it is not constrained by the minimum phase or white reflectivity assumptions and can correctly handle non-minimum-phase, zero-phase, or mixed-phase wavelets that violate the statistical deconvolution assumptions; the disadvantage is that it requires an accurate measurement of the source signature, which may be unavailable (in historical data), inaccurate (if the near-field measurement does not correctly represent the far-field wavelet), or variable (if the source signature changes during the survey due to gun timing variations, air pressure fluctuations, or depth variations of the airgun array); in practice, modern marine seismic processing uses a combination of near-field signature measurements for initial deterministic deconvolution and post-stack statistical deconvolution to remove any residual wavelet effects that the deterministic step did not fully address.
• The ghost reflection is an additional wavelet complication in marine seismic acquisition that signature deconvolution must also address: the ghost is the reflection of the downgoing pressure wave from the sea surface (which acts as a near-perfect free surface reflector with reflection coefficient of -1) back downward, arriving at the hydrophone cable a short time after the direct downgoing wave; the time delay between the direct wave and the ghost depends on the depth of the source and the depth of the receiver cable below the sea surface (typically the ghost delay for a source at 7 meters depth is approximately 9 milliseconds, and the ghost adds a notch in the amplitude spectrum at the frequency where the direct wave and the ghost are in perfect destructive interference — the notch frequency being approximately 1/(2*ghost delay) = approximately 56 Hz for a 9 ms delay); the ghost notch removes energy from the seismic data at the notch frequency (and its harmonics), reducing the effective bandwidth and temporal resolution; deghosting (the removal of the ghost reflection through combined source-side and receiver-side deghosting algorithms) is part of the signature deconvolution workflow in modern broadband marine seismic processing, often achieved by processing data recorded by dual-depth cable configurations (where separate cables at different depths have ghost notches at different frequencies, allowing the combined data to fill in the ghost notch of each individual cable by selecting the frequency range where each cable has adequate signal above the ghost notch).
• Land seismic source signatures (Vibroseis sweep, explosive source) require different approaches to signature characterization and removal compared to marine airgun signatures: Vibroseis sweep correlation is the first step in processing vibroseis data, cross-correlating the recorded trace (which contains the convolution of the earth's reflectivity with the entire sweep duration of 6-20 seconds) with the pilot sweep (the theoretical or measured sweep signal that was sent to the vibrator trucks) to compress the long sweep to a short zero-phase autocorrelation wavelet that approximates a compact, symmetric wavelet with minimal side lobes; the correlation process converts the vibroseis correlated trace to an equivalent dataset comparable to that obtained with an impulsive source, enabling the same downstream processing sequence (CMP stacking, migration, inversion) as used for impulsive sources; deviations of the actual vibrator output from the theoretical sweep (due to mechanical limitations of the vibrator baseplates, ground coupling variations, and harmonic distortion) produce a correlated wavelet that departs from the ideal zero-phase autocorrelation, requiring ground force estimation (measuring the actual force delivered to the ground) and correlation with the ground force rather than the theoretical sweep to reduce these systematic errors; explosive source wavelets (from dynamite or other chemical explosives) are approximately impulsive and minimum-phase but vary between shots depending on the charge size, depth, and geological coupling at the shot location, requiring statistical estimation of the wavelet for spiking or predictive deconvolution rather than a single measured signature.
• Broadband seismic processing has revived interest in signature deconvolution as the enabling step that allows seismic data recorded with extended low-frequency content (down to 2-3 Hz from new airgun designs and recording systems capable of measuring low-frequency pressure variations) to be processed to a broader usable frequency band than conventional data: the low-frequency content of broadband data is particularly valuable for seismic inversion (converting seismic amplitudes to acoustic impedance, which requires low-frequency information to constrain the long-wavelength impedance trend that short-wavelength reflection data alone cannot provide) and for full waveform inversion (which uses all frequencies of the recorded wavefield for velocity model building, but is most effective when started with low-frequency data that provides robust convergence of the iterative inversion before higher-frequency data is introduced); the broadband signature deconvolution workflow must correctly handle the full frequency range from 2 Hz to 150 Hz (or higher), including the ghost notch removal across this range, requiring the deghosting and signature deconvolution algorithms to be evaluated for correctness across this extended bandwidth rather than just the conventional 10-80 Hz band that earlier processing was designed for; the commercial introduction of broadband marine seismic surveys by WesternGeco (Broadband Solution), CGG (BroadSeis), PGS (GeoStreamer), and TGS beginning around 2010 drove the development of the full broadband processing workflows, including signature deconvolution capable of handling the extended bandwidth, that are now standard in high-quality exploration seismic.