Trace editing & amplitude recovery

Part 2 — Pre-Processing Foundations

Learning objectives

Identify bad traces (dead, reversed, noisy) and choose the appropriate edit — kill, flip, or interpolate
Explain geometric (spherical) divergence and apply a t^g gain to compensate
Describe the role of Q compensation and when it is (and is not) worth applying
Recognize over-gaining and under-gaining on an amplitude envelope

The raw traces coming out of acquisition have two problems before you even start processing: a handful are broken, and the rest have amplitudes that decay with travel time for purely physical reasons. The fix is two operations: trace editing to deal with the broken ones, and amplitude recovery to compensate the physics.

1. Trace editing — the easy part first

Before any amplitude work, scan every shot for traces that are obviously bad. The common categories:

Dead trace. All zeros. Kill it (set to zero). If systematically recurring at a specific channel, the geophone or recording amplifier is broken — a field issue to report.
Reversed polarity. One receiver wired backwards. Spot by comparing to neighbors; multiply by −1.
Clipped (saturated). Amplitude hits a hard ceiling. Mute the clipped portion or reject the whole trace if severe.
Noisy / spiky. Single-sample or short-burst spikes overwhelm the wavelet. Apply a time-domain de-spiking filter (median in a short window) or kill if chronic.
Monochromatic hum. 50 or 60 Hz power-line pickup. Notch filter, or let the subsequent noise-attenuation step do it.

Trace editing is mostly keyboard-driven tedium — open a shot gather, eyeball it, click bad traces, save. Automated tools flag candidates; the processor confirms. An experienced processor can edit a hundred shots an hour.

2. The physics behind amplitude decay

A spherical wavefront expanding from a point source spreads its energy over a sphere of radius r = v·t/2 (one-way) or v·t (two-way). Energy per unit area drops as 1/r², so amplitude drops as 1/r. For a layered earth with interval velocity v(t), the geometric spreading scales approximately as

A(t) \;\propto\; \frac{1}{t \cdot v(t)^{2}}

— but in practice we apply a simpler power-law correction t^g with g between 1 and 2, chosen to flatten the observed amplitude envelope. This is spherical-divergence correction, also called geometric-spreading gain, also called simply t^g gain.

The raw trace on the left has three reflectors with equal true reflectivity, but amplitude decays with t^1.5. The deepest event looks nearly invisible. Slide the gain exponent — at g = 0 no correction is applied; at g = 1.5 the amplitudes become equal; at g = 2 the deep event now dominates (over-gained). The badge at the top reflects your current regime.

3. Anelastic attenuation: Q

Beyond geometric spreading, real rocks also absorb energy. The quality factor Q parameterizes this absorption: the amplitude of a plane wave after travel time t is

A(f, t) = A_0(f)\,\exp\!\left(-\frac{\pi f t}{Q}\right)

For typical sediments Q ranges from 30 (loose wet sand, strong absorption) to 200 (tight carbonates, mild absorption). The key feature is that higher frequencies attenuate faster — so the wavelet broadens with depth and the deep section loses bandwidth.

Q compensation reverses this in the frequency domain by multiplying each frequency by exp(+πft/Q). The operator is unstable at high frequencies (exponential amplification of noise), so it is always stabilized with a white-noise floor. In practice: applied cautiously on processed stacks for resolution enhancement, less often on pre-stack data where it can make noise attenuation harder.

4. When to gain and when not to

Always apply t^g gain before display. A raw trace looks dead at depth; gain is what makes the section readable.
Remove gain before AVO analysis. AVO needs true amplitudes because the whole point is measuring amplitude vs angle. Gain is applied for display then inverted before the amplitude extraction.
Q compensation is optional. On shallow high-SNR targets it may not be needed. On deep targets it is the difference between “you can see the reservoir” and “you cannot.”
Automatic gain control (AGC) is a different animal. AGC normalizes amplitudes to a constant RMS within a sliding window — great for display, but it destroys the amplitude relationships AVO needs. Use for picking and QC, not for production amplitude products.

5. Picking g in practice

Plot the RMS envelope of a long window (hundreds of ms) as a function of time; it should fit roughly C/t^g. Fit g on a log-log plot; typical values are 1.2–1.8 for land and 1.0–1.5 for marine. Apply the fitted g. Inspect before and after — a well-gained trace looks roughly equal-amplitude from shallow to deep with perhaps slight damping at the ends.

6. When trace-edit hides a bigger problem

If more than ~5 % of traces need editing, something is wrong acquisition-side. Check the receiver pattern — dead traces often cluster on a particular cable, spread line, or receiver-depth. A bad cable in a towed streamer or a bad sub-array on land rarely goes away on its own. Flag it to acquisition QC and the next shot line.

**The one sentence to remember**

Spherical-divergence gain recovers the geometric amplitude loss so deep events are visible; trace editing removes the recordings where no processing could save them; Q compensation is the optional bandwidth recovery that makes deep targets legible.

Where this goes next

Section §2.3 tackles statics — the fixed time shifts produced by weathered near-surface layers that distort every reflection. Refraction statics (first-break picking) and tomographic statics are the two main tools.

References

Yilmaz, Ö. (2001). Seismic Data Analysis (2 vols.). SEG.
Claerbout, J. F. (1976). Fundamentals of Geophysical Data Processing. McGraw-Hill.
Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge UP.