Amplitude Adjustments

Besides spherical spreading, there are other reasons for the observable decay in seismic amplitudes. One cause is the fact that velocity is not constant, but ordinarily increases with depth. Because of Snell's law, this increase means that the growth of the expanding wavefront is also not constant, but accelerating. For this and other reasons the observed decay of reflection amplitude normally exceeds that imposed strictly by spherical spreading.

Amplitude can also vary from trace to trace. These inconsistencies arise not only from genuine lateral inhomogeneities, but also from conditions in the field. Charge size and depth can vary along a line (and not always because we want them to cultural impediments often impose restrictions on charge size in particular). When low-power surface sources such as Vibroseis are used, a unit may fail, reducing the size of the source array. In marine work, air guns also occasionally fail, reducing the source volume somewhat. The result is a nonuniform suite of bangs. And on the receiving end, surface conditions can affect geophone plants.

The combined effect is a section where the traces are uneven, across and down. Deep, weak reflections may be hard to see. A known reflector may appear to come and go across the section. The solution involves normalizing the traces and then balancing them.

Trace Equalization

Trace equalization is an amplitude adjustment applied to the entire trace. It is directly applicable to the case of a weak shot or a poor geophone plant. We start with two traces that have been corrected only for spherical spreading ( Figure 1 ). Clearly, one trace has higher amplitudes than the other, so our task is to bring them both to the same level.

Figure 1

First, we specify a time window for each trace. Here, in the context of a near-trace section, the windows are likely to be the same, say, 0.0 to 4.0 seconds. Then, we add the (absolute) amplitude values of all the samples in the window for each trace. Division by the number of samples within the window yields the mean amplitude of the trace. (As we apply this process for all the traces of the section, we note the variability of the mean amplitudes.)

The next step is to determine a scaler, or multiplier, which brings the mean amplitudes up or down to a predetermined value. If, for instance, this desired value is 1000, and the calculated mean amplitudes are 1700 and 500, our scalers are 0.6 and 2.0 Each scaler is applied to the whole trace for which it is calculated ( Figure 1 ).

Equalization enhances the appearance of continuity, and provides partial compensation for the quirks in the field work that might otherwise degrade data quality.

Trace Balancing

Trace balancing is the adjustment of amplitudes within a trace, as opposed to among traces. Its effect is, again, the suppression of stronger arrivals, coupled with the enhancement of weaker ones, and its goal is the improvement of event continuity and visual standout. Two trace balancing processes are automatic gain control (agc) and time-variant scaling.

As with trace equalization, trace balancing requires the calculation of the mean amplitude in a given time window. In this step, however, there are numerous successive windows within each trace ( Figure 2 ), and the scalers apply only within those windows.

Figure 2

So, if our first calculated mean amplitude of Figure 2 is 5000, and the last is 500, and if we want them both scaled to 1000, our initial approach might be to multiply the amplitudes in the first window by 0.2, and those in the last by 2.0.

This process, however, would introduce discontinuous steps of amplitude at the junction of two windows. Two solutions to this are in common use. One solution, known as time-variant scaling, ( Figure 3 ) applies the

computed scaler at the center of each window, and interpolates between these scalers at the intermediate points.

Figure 3

Another approach, automatic gain control (agc), uses a sliding time window ( Figure 4 ), such that each window begins and ends one sample later than the one before.

Figure 4

Again, the scaling is applied to the amplitude of the sample at the center of the window. In this manner, we effect a smooth scaling that reacts to major amplitude variations while maintaining sensitivity to local fluctuations. We also ensure that a peculiarly large amplitude does not have undue influence throughout the entire trace.

Some Further Considerations

We now have to think about some problems we may encounter. The problem of ambient noise first arose in our discussion of the spherical spreading correction. We encounter it again when we have to determine the length of our trace normalization window. Particularly for weaker shots, ambient noise can dominate signal at later reflection times. In settling on a normalization window, then, we may choose to use the weakest shot in our data set.

We need also to determine a reasonable window length to be used in trace balancing. Ambient noise is not relevant here; rather, the prime determinant is the falsification of relative reflection strengths.

Consider the trace of Figure 5 .

Figure 5

It has a high amplitude reflection at 1.8 s, but is otherwise reasonably well-behaved. The center of the first time window we consider is at 1.6 s, at which time there is a reflection whose amplitude is, say, 625. Because the anomalous reflection is included in this window, the mean amplitude of the window is higher than it would otherwise be, perhaps 714. If the desired average is 1000, the required scaler for the window is 1.4, and the reflection at 1.6 s is brought up to 875.

Further down the trace, the sample at the center of a later window has an amplitude of 400. Within this window, there are no abnormal reflections, and the mean amplitude is also 400. So, the scaler of 2.5 does indeed bring the reflection up to an amplitude of 1000.

We see the problem: the large amplitude at 1.8 s causes a falsification of relative reflection strengths by suppressing those amplitudes within a half window length of it. We reduce this effect in several ways, acting separately or in concert.

First, we may weight the samples within each window ( Figure 6 ).

Figure 6

This reduces the contribution to the mean absolute amplitude of every sample not at the center of the window. Alternatively, we may reduce the window length ( Figure 7 ), thereby reducing the number of samples affected by the anomalous amplitude.

Figure 7

It varies with data area, but a sensible trace balancing window (provided a spherical spreading correction is applied first) is from 500 to 100 ms. Our guide must be the data: if the amplitudes are fairly uniform, there is less of a need to balance, and we get away from using longer windows.

A third method is to make the scaler some nonlinear function of the mean absolute amplitude. We might, for instance, scale to an amplitude of 500 if the mean absolute amplitude in a window is below 500; to 650 for mean amplitudes between 500 and 800; to 1000 for mean amplitudes between 800 and 1200; to 1350 for mean amplitudes between 1200 and 1500; and to 1500 for mean amplitudes above 1500.

A fourth method is to ignore, in the calculation of mean amplitude, any values which exceed the previous mean by some arbitrary ratio (perhaps 3:1). Thus, the scalers are derived from what we might call the "background" level of reflection activity; the background levels are balanced, but individual strong reflections maintain their relative strength.