Source signature measurement & QC

Processing assumes that every shot put the same wavelet into the ground. The crew checks that assumption shot by shot, with whatever each source allows it to measure. On an airgun array a near-field hydrophone about a metre from each gun records its output. Every hydrophone also hears the neighbouring guns, so the recordings are inverted for one notional source per gun, and the notional sources are summed with their surface ghosts to give the far-field signature of that shot (Ziolkowski et al., 1982). A vibrator estimates its ground force on every sweep from accelerometers on the baseplate and the reaction mass, weighted by their masses (Sallas, 1984). A dynamite shot has no signature record at all: the crew logs the time break and an uphole geophone near the hole, which catch a late or failed shot but not a change of wavelet.

Why per-shot signatures matter

The wavelet varies from shot to shot with gun timing, gun pressure, tow depth and sea state on water, and with coupling and charge size on land. Most of that variation is small jitter. A few shots carry a real fault: a gun that fails to fire, a gun that fires late, a string towed too deep. A faulty shot puts a wavelet into the data that processing does not expect, and every step that relies on a stationary wavelet (deconvolution, inversion, 4D differencing) degrades with it. QC therefore reduces each shot to a few numbers, such as the peak-to-peak amplitude of the primary, the primary-to-bubble ratio and the misfit to a reference signature, and flags the shots whose numbers stand apart from the rest of the sequence.

In the figure a six-gun tuned string fires 24 shots, and five of them carry a planted fault. Lower the threshold $k$ and watch which shots each of two rules flags in (b); then change the attribute, and load the line with more faults.

Median and MAD, not mean and standard deviation

The obvious rule, flag a shot more than $k$ standard deviations from the mean, fails exactly when it is needed. The faulty shots pull the mean toward themselves and inflate the standard deviation, so the gate widens around them; statisticians call this masking. In the figure’s opening state the five faults inflate the standard deviation of the peak-to-peak to 3.3 times the robust estimate, and mean $\\pm\\,k$ SD with $k = 3.5$ catches none of them. The median and the median absolute deviation barely notice a minority of outliers:

The factor 1.4826 makes $\\sigma\_{\\mathrm{MAD}}$ equal to the standard deviation for Gaussian data (Rousseeuw and Croux, 1993). A shot is flagged when $|x\_i - \\mathrm{median}(x)| > k\\,\\sigma\_{\\mathrm{MAD}}$, and in the opening state all five faults lie outside that band with no false alarm. The usual threshold is $k$ from 2.5 to 3 (Leys et al., 2013). Good shots scatter too: about 13% of Gaussian jitter lies beyond 1.5 standard deviations and about 1% beyond 2.5, and on the figure’s clean line of 48 shots $k = 1.5$ flags 7 good ones. The robust rule has a limit too. The MAD is itself inflated as the faulty fraction grows, so detection weakens well before half the sequence is faulty: on the figure’s 24-shot sequences $\\sigma\_{\\mathrm{MAD}}$ grows by a factor of 1.9 to 2.9 between 20% and 40% faulty, and at 40% with $k = 2.5$ the median rule catches anywhere from 1 to 8 of the 10 faults, depending on the sequence. At 50% the median breaks down entirely, and the shots must then be judged against a reference signature measured on a known-good array.

No single attribute sees every fault. A string towed too deep moves its ghost and lowers the peak-to-peak, but it scales the primary and the bubbles together, so its primary-to-bubble ratio hardly changes; a late or lost large gun spoils the bubble cancellation that tuning buys and moves the ratio a lot. In the opening sequence the peak-to-peak catches all five faults and the primary-to-bubble ratio only one. QC tracks several attributes, and flagged shots are left out of the averaged signature that processing uses.

What the field crew does with the flags

Flags start an investigation. A run of flags on one string points at that string: a gun that has stopped firing, a leaking air line, a depth controller that has failed. An isolated flag after a change in sea state may be a gun that has broached. On a vibrator, a flag sends the crew to the ground-force feedback and the phase lock. Marine shots are not re-shot one at a time: out-of-spec shots count against the contract’s tolerances, and a line segment with too many of them is re-shot or infilled. Flagging in real time keeps bad data out of the stack before the vessel or the crew has left the area.

References

• Ziolkowski, A. (1970). A method for calculating the output pressure waveform from an air gun. Geophysical Journal International, 21(2), 137-161.
• Ziolkowski, A., Parkes, G., Hatton, L., Haugland, T. (1982). The signature of an air gun array: computation from near-field measurements including interactions. Geophysics, 47(10), 1413-1421.
• Dragoset, W. H. (1990). Air-gun array specs: a tutorial. The Leading Edge, 9(1), 24-32.
• Sallas, J. J. (1984). Seismic vibrator control and the downgoing P-wave. Geophysics, 49(6), 732-740.
• Rousseeuw, P. J., Croux, C. (1993). Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88(424), 1273-1283.
• Leys, C., Ley, C., Klein, O., Bernard, P., Licata, L. (2013). Detecting outliers: do not use standard deviation around the mean, use absolute deviation around the median. Journal of Experimental Social Psychology, 49(4), 764-766.
• Pritchett, W. C. (1990). Acquiring Better Seismic Data. Chapman & Hall.