Why do we need frequency domain?
edited July 2018
Converting geophysical data from the space (or time) domain to the frequency domain (via Fast Fourier Transform) is common practice in geophysics, particularly when wanting to apply some sort of filter to that data.
We do this because it is more computationally efficient to filter data in the frequency domain compared to the space domain. For example, applying a filter such as a first vertical derivative to a grid of magnetic data in the space domain requires convolution using a two-dimensional filter. Depending on the type of filter, that process can be complex and therefore computationally expensive.
Transforming the data and the filter to the frequency domain allows us to simply multiply the two to get a filtered spectrum, which is then transformed back to a filtered grid in the space domain. This process is far more computationally efficient than convolution.
The following diagram describes the distinction between space and frequency domain filtering. It is taken from Reeves (2005), which you can access here:
I'd urge you to download the document and review Chapter 6, from which the diagram is taken.
Thank you very much Sir.
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