Weathered layer & statics from first-break refraction

Part 5 — Land acquisition

Learning objectives

Relate weathering-layer thickness and velocity to receiver static time
Explain uphole surveys and their role in ground-truthing the near-surface
Pick first-break refractions and invert for v₂ and h
Recognise tomographic inversion as the modern practice

The weathering (low-velocity) layer is a 5–30 m-thick skin of unconsolidated soil and rock at the surface. Every reflection recorded above it is delayed by 2 h cosθc / v₁ — tens of milliseconds, varying laterally with the thickness of the skin. If not corrected, the delays distort every reflector: hyperbolas tilt, amplitudes misalign, stacks de-focus. Correcting them is the statics problem, and the acquisition-phase step is to characterise the near-surface well enough that a statics model can be built.

Uphole surveys

At selected locations across the survey, the crew drills a shallow uphole (20–50 m), lowers a source into the hole, and fires at several depths while a surface geophone records. Travel time as a function of source depth gives v(z) directly: the slope of the travel-time curve is 1/v at each layer. Upholes give ground-truth at isolated points — usually 1 per 2–4 km² of survey area.

First-break refraction

On every recorded shot gather, the first arrival at each receiver is either the direct wave through the weathering (at small offsets) or a refracted head wave along the top of the bedrock (at larger offsets). The refracted first break has travel time

t(x) = x/v_2 + (2h\cos\theta_c)/v_1

with sinθc = v₁/v₂. The slope 1/v₂ gives the bedrock velocity directly; the intercept ti = 2h cosθc / v₁ gives the weathering thickness (given v₁ from upholes). Picking first breaks across every shot gather of the survey yields an enormous dataset for the inversion.

Tomographic inversion

Modern practice blends every first-break pick into a 3D near-surface velocity model using travel-time tomography. The model is parameterised on a fine grid; ray-tracing computes predicted first breaks; the grid values are iteratively updated until predictions match picks. Output: v(x, y, z) for the top 200–500 m of the earth, plus surface elevation, from which the static correction at each station is a path integral.

Residual statics

Even after first-break tomographic statics, small (few-ms) residuals remain, because the first-break picks are noisy and the near-surface model is smoothed. Residual statics are solved during processing from the reflections themselves (max-power stack, cross-correlation of traces to a pilot, etc.). But the acquisition-phase tomographic pass removes the bulk of the problem — without it, the reflections are too scrambled for any residual-statics solver to converge.

Rule of thumb: a 5 m lateral change in weathering thickness at v₁ = 700 m/s produces ≈ 10 ms of station-to-station static jitter. Ten milliseconds is enough to shift a 40 Hz wavelet by 40% of its period — a serious degradation. The whole near-surface effort exists to bring this jitter below 2 ms.

References

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.
Cordsen, A., Galbraith, M., Peirce, J. (2000). Planning Land 3-D Seismic Surveys. SEG Geophysical Developments 9.