Source taxonomy: impulsive vs extended

Seismic sources come in two families. Impulsive sources release their energy in a few milliseconds: dynamite, air-gun arrays and weight drops. Extended sources, vibroseis trucks on land and marine vibrators offshore, release comparable energy over a sweep lasting several seconds, at a far lower peak. Downstream the physics is the same; what differs is the peak the source must reach, the length of the record, and one extra processing step before a reflection can be seen.

In the figure an impulse and a sweep carry the same energy. Record four reflections with the sweep, two of them only 12 ms apart, correlate the record with the pilot, then change the sweep’s band and length and watch what sets the width of the wavelet you get back.

What the correlation does

At the opening sweep, 10 to 40 Hz over 8 s, the sweep’s peak in (a) is 26 dB below the impulse’s, and the raw record in (b) cannot be read: every reflection is a copy of the 8 s chirp, and the copies overlap. The remedy is to record the pilot, the sweep sent into the ground, and cross-correlate every trace with it. The autocorrelation of the pilot is the Klauder wavelet $K(\\tau)$: zero phase, with the amplitude spectrum $|S(f)|^2$, the square of the sweep’s, so it spans the same band. After correlation each reflection collapses to a Klauder wavelet at its own two-way time, which is why an extended source can stand in for an impulsive one.

The figure opens with the 8 s sweep squeezed about 190 times, into a Klauder wavelet whose envelope is 42 ms wide, and the two reflectors at 0.80 s still merged. Two widths matter. The envelope follows the bandwidth, about $1.2/(f\_2 - f\_1)$ wide. What splits a close pair is the central peak inside it, 13 ms across at half its height here, and that is set by the upper frequency: raise $f\_2$ past about 65 to 70 Hz and the pair comes apart, whatever $f\_1$ and $T$ (exercise 1). The sweep length $T$ leaves the wavelet almost unchanged; it sets how much energy a force-limited vibrator puts into the ground, and with it the signal-to-noise ratio after correlation (exercise 2). The octave count $\\log\_2(f\_2/f\_1)$ sets the ringing: squeeze the sweep into one octave and the first side lobe is only 1.5 dB below the peak (exercise 3), which is one reason modern sweeps reach down to a few hertz.

When to pick each

• Dynamite: the most impulsive source available. Used on land where permits allow, fired in drilled holes below the weathered layer, which couples the charge to firm rock and moves the ghost notch lower in frequency (Section 1.2). Banned or restricted in many regions.
• Air-gun array: the standard marine impulsive source. A single gun rings with a bubble pulse; arrays of guns of different volumes are tuned so the bubbles cancel while the first peaks add (Section 1.4). Its high peak pressure makes environmental impact the main concern.
• Vibroseis: the standard land extended source. Safer than dynamite and repeatable, with the force on the ground measured and controlled; often the only source allowed in towns and near infrastructure. Sweep design is Section 1.3.
• Marine vibrator: emerging; its peak sound pressure is 10 to 20 dB below an air-gun array of comparable energy (Section 1.7).

References

• Pritchett, W. C. (1990). Acquiring Better Seismic Data. Chapman & Hall.
• Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press.
• Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.