![]() The Hilbert transform is a linear operator that produces a 90° phase shift in a signal, and it is a good first step in our exploration of phase. We do not often examine phase spectrum because it is difficult to interpret, but we can manipulate Fourier phase to change the structure of our signal without affecting its amplitude spectrum. However, every signal also has a phase spectrum, and the phase encodes the signal's structure - the distribution of the signal energy through time. Most of the time when dealing with Fourier transforms, we concentrate on magnitude, which tells us about the distribution of signal energy through frequency. Complex numbers are essentially 2D vectors, meaning they have two components: magnitude and phase angle. Taking the transform of any real signal will result in a set of complex coefficients. The data we are using are the Penobscot 3D survey from the Open Seismic Repository, which is openly licensed CC-BY-SA by the Canada Nova Scotia Offshore Petroleum Board, and dGB Earth Sciences. The code to produce them, some of which is included here, is available in the SEG tutorials GitHub repository. The plots included in this tutorial were created using GNU Octave. We will also check how close to zero phase our test data set is. We will look at how to manipulate the phase of a seismic trace by manipulating the phase of its Fourier transform and will use that idea to generate the well-known instantaneous-phase poststack attribute. In this tutorial, we will focus on aspects of phase relevant to the interpreter. Several publications have discussed the concepts and ambiguities. It doesn't help that the word phase is used to mean a variety of things, depending on whether we refer to the propagating wavelet, the observed wavelet, poststack seismic attributes, or an entire seismic data set. The concept of phase permeates seismic data processing and signal processing in general, but it can be awkward to understand, and manipulating it directly can lead to surprising results. This tutorial originally appeared as a featured article in The Leading Edge in October 2014 - see issue.
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