Vibroseis: sweeps and distortion

Part 1 — Sources

Learning objectives

Design a linear vibroseis sweep by choosing f1, f2, and T
Recognise the Klauder wavelet as the output of pilot cross-correlation
Understand why total energy and peak force are independent trade-offs
Identify harmonic distortion in the correlator output as a source-nonlinearity signature

Vibroseis trucks push the ground with a baseplate driven by a hydraulic servo. The driving signal is a sweep — a chirp that scans through frequencies for several seconds. Linear sweeps ramp frequency at a constant rate; nonlinear sweeps (boost low-f, taper high-f) are tuned for specific targets.

Sweep design trade-offs

f1 (start frequency): low f1 recovers deep targets but is hard for the baseplate and couples poorly in the near-surface.
f2 (end frequency): high f2 is needed for near-surface resolution but attenuates fast (§0.10).
Sweep duration T: longer T puts more total energy into the ground (T is equivalent to fold — see §0.8). Typical T = 8–16 s for land 3D.
Taper length: the first and last ~5% of the sweep are cosine-tapered to avoid spectral leakage. Without the taper you get ringing in the Klauder wavelet.

Peak force vs total energy

Two knobs that are independent. Peak force is limited by baseplate hydraulics (typical 60-80 kN for a big truck). Total energy = peak force × sweep duration × duty cycle. Increase T and you add energy without changing peak force. Add more vibrators in the source array (a "VP" = vibrator point with 3-4 trucks) and you add peak force at the cost of correlated noise and site impact.

Harmonic distortion

Nonlinearities in the ground (or in the hydraulics) generate harmonics of the driving frequency. After correlation these show up as curved wavelets at negative times ("harmonic ghosts"). Real vibroseis processing uses ground-force feedback — the pilot used for correlation is the actual force on the ground, measured by a transducer, not the intended pilot. This suppresses distortion in the correlator.

References

Crawford, J. M., Doty, W. E. N., Lee, M. R. (1960). Continuous signal seismograph. Geophysics, 25(1), 95–105.
Sallas, J. J., Weber, R. M. (1982). Comments on the digital-filter equivalent of a vibrator. Geophysics, 47(11), 1577–1582.
Pritchett, W. C. (1990). Acquiring Better Seismic Data. Chapman & Hall.
Yilmaz, Ö. (2001). Seismic Data Analysis: Processing, Inversion, and Interpretation of Seismic Data (2 vols.). SEG Investigations in Geophysics 10.