# Relative trace balancing

Series Investigations in Geophysics Öz Yilmaz http://dx.doi.org/10.1190/1.9781560801580 ISBN 978-1-56080-094-1 SEG Online Store Figure 1.4-12  (a) A field record, (b) after geometric spreading correction which shows differences in amplitude levels of the near- and far-offset channels caused by differences in gain settings during recording. (c) Following the application of trace balancing, these differences in amplitudes are removed. Displayed at the bottom are the autocorrelograms. Note in (a) the effect of different gain settings on the amplitude level of the autocorrelogram from trace to trace.

All of the gain applications described in this section modify the trace amplitudes by function g(t) in a time-varying manner (equations 4 and 5). In true amplitude processing, it is necessary to display the data without applying a time-varying data-dependent gain function. However, some amplitude scaling is always necessary for display, since plotters require input data amplitudes to fall in a specific range. Trace balancing (trace equalization) schemes are used for this type of scaling. The balance factor is defined as the ratio of the desired rms to the rms amplitude that is computed from a specified time window. A separate balance factor is computed for and applied to each trace, individually. Alternatively, a single balance factor based on a selected trace within a group of traces can be applied to the entire group. This is called relative trace balancing. Note that trace balancing amounts to scaling the trace by using a single factor that is time-invariant (equivalent to a single-window rms AGC). Figure 1.4-12 shows rms trace balancing of field data to correct for the differences in gain settings between the recording channels. Trace balancing commonly is applied immediately after deconvolution, and on final stacks using large gates.

 $k_{Nyq}={\frac {1}{2\Delta x}},$ (4)

 ${\frac {\Delta x}{\Delta t}}={\frac {f}{k}}.$ (5)