Trace editing & amplitude recovery

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: flag it so the stack leaves it out of the fold count, since left in, its zeros are averaged in and dim every event. If it recurs at one channel, the geophone or recording amplifier is broken, a field issue to report.
• Reversed polarity. One receiver wired backwards. Spot by comparing to neighbours; multiply by −1.
• Clipped (saturated). Amplitude hits a hard ceiling. Mute the clipped portion or reject the whole trace if severe.
• Spiky. Single-sample or short-burst spikes overwhelm the wavelet. Apply a time-domain de-spiking filter (a median in a short window), or kill the trace if the spikes are chronic.
• Noisy. Random noise across the whole band, from wind, traffic or a poorly planted geophone. No filter separates it from the signal, and one noisy trace can dominate a mean stack: kill it.
• 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.

Reading that list is the easy part; recognizing the defects on a real record is the skill, and it only comes from looking. The shot record below hides one channel of each kind among 24. Step through it, keep, kill, flip or repair each channel, and let the stack judge your edits: it is compared with the stack of the same record without its defects. A reversed channel is the subtle one, since its lobes sit half a cycle off from those of its neighbours.

Left in, the six broken channels put the stack of shot 1 32 % away from its defect-free reference, and the right edits bring it to 2 %. The reversed channel alone costs each event 2/N of its amplitude, where N is the live fold at its time: about a tenth for the three deeper events, where 21 channels are live, and about 15 % for the first, at 0.50 s, where the mutes leave 13. The dead one does its harm only through the fold: killed, it leaves the count and the average is right again, which is why switching the fold off undoes the kill. Repair suits defects that are narrow in time or in frequency, such as spikes and hum; random noise is neither, and has to be killed.

2. The physics behind amplitude decay

A spherical wavefront expanding from a point source spreads its energy over a sphere. For a reflection recorded at two-way time $t$ in a constant-velocity earth, the wave has travelled a path of length $r = Vt$. Energy per unit area drops as $1/r^{2}$, so amplitude drops as $1/r$. For a layered earth, Newman (1973) showed that the geometric spreading scales approximately as

where $V\_1$ is the velocity at the surface and $V\_{\\mathrm{rms}}$ the RMS velocity down to time $t$. In practice we apply a simpler power-law correction $t^{g}$, with $g$ between 1 and 2 chosen to flatten the observed amplitude envelope: $g = 1$ undoes constant-velocity spreading, and about 2 suits a velocity that rises with depth. This is spherical-divergence correction, also called geometric-spreading gain, or simply $t^{g}$ gain. In the figure below, raise $g$ until the envelope is flat, then find what no gain can do.

With no gain, marker 2 comes back at 0.14 of its true size against marker 1, and the recorded envelope falls with slope −1.55 on log-log axes. That slope is the exponent: at $g = 1.5$ the envelope turns flat and the two markers return to their true ratio. Push $g$ to 3 and marker 2 is 7.5 times too strong, while the noise, which never decayed, rises to 4.9 times the shallow signal. The S/N from 3.4 to 3.9 s stays at 7 dB throughout, because a gain that depends only on time multiplies signal and noise alike. AGC flattens the envelope too, but with a 500 ms window it returns the bright spot, marker 2, at 0.73 of its true size against the dim marker 1, because it scales every window to the same level.

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

For typical sediments $Q$ ranges from about 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. Switch on absorption in figure 2.2.2 and the envelope bends away from every straight line: no $t^{g}$ can follow a loss that grows exponentially with time.

Q compensation reverses this in the frequency domain by multiplying each frequency by $e^{+\\pi f t/Q}$. 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.
• Keep deterministic gain for AVO; never AGC. AVO needs true relative amplitudes, because the whole point is measuring amplitude against angle. Spherical-divergence and Q corrections are deterministic, so they are part of true-amplitude processing; data-dependent gains such as AGC or trace balancing must be kept out of the data used for 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. That is fine for display, but it destroys the amplitude relationships AVO needs: in figure 2.2.2 a 500 ms AGC returns the bright spot at 0.73 of its true size against a dim reflector. Use it for picking and QC, not for production amplitude products.

5. Picking g in practice

Plot the RMS envelope in long windows (hundreds of ms) against time; it should fit roughly $C/t^{g}$. Fit $g$ as the slope on a log-log plot, as the dotted line in figure 2.2.2 does; typical values are 1.2 to 1.8 for land and 1.0 to 1.5 for marine. Fit only the times where signal dominates: where noise takes over, the envelope flattens and the fitted $g$ comes out low. Apply the fitted $g$ and 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

The drill above packs one defect of each kind into a single record, 6 of its 24 channels, far more than a real shot carries. In production, if more than about 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.

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.