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I am new to seismic data processing and I really have no understanding of the term 'phase'. So, could anybody give me a simple explaination of the term? Thank you

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I think wikipedia can more than adequately answer your question.

http://en.wikipedia.org/wiki/Phase_(waves)

However, in brief, the phase term describes the relationship between a waveform and a fixed reference point in time. For example the sinusoid $sin(\omega t)$ is zero at $t = 0$ whereas $sin(\omega t - \phi)$ is zero at $t = \phi$. $\phi$ could be referred to here as the phase offset.

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Phase is a property of sinusoidal waves and describes how far along the wave is in it's cycle. A simple wave may be described as

$$\sin(\theta)$$

Where $\theta$ is it's phase. It's usually measured in radians and at every multiple of 2$\pi$, the wave goes back to the beginning of its cycle and starts again.

If the wave is varying in time, it may be described as:

$$\sin( \omega t )$$

The wave will repeat its cycle every time $\omega t$ reaches $2\pi$, or every $2\pi/\omega$ seconds, which is the wave's period. The term, $\omega t$ is the wave's phase.

In seismology, the wave will travel through time and space. A wave in space and time will look like:

$$\sin( kx - \omega t )$$

Here, $k$ is the wave-vector describing the wavelength and direction of propagation of the wave in space.

$kx - \omega t$ is the wave's phase. Every time, $kx - \omega t$ reaches $2\pi$, the wave will repeat its cycle. The wave's wavelength is $2\pi/k$ and it's period is $2\pi/\omega$.

In a linear system, you can split any signal into a sum on sinusoidal signals at different frequencies, calculate how the individual sinusoidal signals propagate, then recombine them.

In many case it is easier to do calculations with sines and phase than it is to handle the propagation of the individual waves themselves.

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In seismic data processing the term phase is used/referred to differently in depending on the context. The answer from @tobassit is fundamentally correct but the way in which geoscientists and data processors refer to phase can cause some confusion.

Firstly, in terms of early stage seismic processing, where raw signal/receiver data is processed, the term "phase" is can be used to refer to the degree of phase rotation in the seismic wavelet in a processed dataset. During the seismic processing workflow a deconvolution and phase correction step is normally applied and the "phase" of the data will be set as either zero phase or mixed phase. Understanding the "phase" of a seismic dataset is critical in its subsequent use as it affects the relationship between peaks-troughs in the data and underlying the reflectivity series.

Secondly, in terms of post stack seismic data analysis, seismic traces are often represented by an Analytic Signal Model for the purposes of analysis and interpretation.

The analytical seismic trace is created by computing the Hilbert Transform of the real trace to produce quadrature trace (90 degree phase shifted version). This together with the original provides a complex trace from which number of useful quantities can be derived.

These are known as the complex trace attributes and include Instantaneous Phase (see link on wikipedia page above for the Analytic Signal) which is often referred to as 'phase' by seismic interpreters. The phase attribute is useful due to its directly relationship to subsurface structure independent of reflection strength.

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