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Adaptive subtraction is a processing technique used on seismic data. It can be applied either pre-stack or post-stack.
A common use for Adaptive Subtraction would be in multiple removal processes. Multiples are duplicate echos caused by a variety of different things but they are all "noise" that needs to be removed in processing so that the final seismic section only shows "primary" reflections.
In processing, a common methodology to remove the multiple energy, or false echoes, is to generate a model of the multiples and then subtract the model from the actual recorded seismic.
This cannot be a simple subtraction because the models that are built will have different amplitudes, frequency range and phase compared to the actual recorded energy. In order to do an effective subtraction recorded energy - multiple model energy = primary energy only the actual data and the model need to be synchronized in amplitude, time, phase and frequency. This is what adaptive subtraction does. It adapts the model to match the recorded seismic to make the subtraction effective.
There are many steps involved in adapting the model, sometime you will hear the term "match filter" which is a way of applying a "filter" to one set of values to make it more similar to another set of values. In this case the filter would be use to match the model to the recording. Match filtering is one component of adaptive subtraction.