Spatial Aliasing - Wrap Around F-K Spectra
Aliasing and frequency wrap is a consequence of violation of Nyquist-Shannon sampling theorem which states that a continuous signal must be discretely sampled at least twice the frequency of the highest frequency in the signal.Hence we need to briefly go into the mathematics of the same.

Let x(t) be a continuous signal, y(n) is discrete signal where y(n)= x(nT). Please note that x(t) will have a continuous time Fourier transform (CTFT) while y(n) will have a Discrete Time Fourier Transform (DTFT)

We can construct a mathematical model of sampling using the continuous Dirac delta function p(t) :
$ p(t)= \sum_{k=-\infty}^{k= \infty}\delta(t-KT) \forall t \in Real $

Let  w(t) =x(t)p(t).We can show that CTFT of continuous function w(t) is DTFT of y(n). Writing the frequency domain representation of w(t)

$W(\omega) = 1/2\pi \  X(\omega) * P(\omega) = \int_{-\infty}^{\infty} X(\Omega) P(\Omega -\omega)d\Omega \ \ \  $ , where * is convolution 

now CTFT of p(t)  can be written as 

$P(\omega) = 2\pi /T \sum_{-\infty}^{\infty} \delta(\omega -k\ 2\pi /T) $

thus $W(\omega) = 1/2\pi \int_{-\infty}^{\infty} X(\Omega)2\pi /T \sum_{-\infty}^{\infty} \delta(\omega -k\ 2\pi /T) d\Omega \\
=   1/T \sum_{-\infty}^{\infty} \int_{-\infty}^{\infty} X(\Omega)  \delta(\omega -k\ 2\pi /T) d\Omega \\
=1/T \sum_{-\infty}^{\infty}X(\omega -k\ 2\pi /T) \   \ \ \ \ \ \ \ \     ...using\  \ shifting\  property  $ , 

Thus we can say that $Y(\omega) = 1/T \sum_{-\infty}^{\infty} X((\omega -2\pi k)/T) $

So we can say that DTFT of y(n): $Y(\omega) $, is a shifted and repeated version of CTFT x(t) i.e. $X(\omega)$. The DTFT is the sum of the CTFT and its copies shifted by multiples of 2π/T.This is shown in the figure bleow. The frequency axis is normalized to −π/T &lt; ω &lt; π/T. 



If X(ω) = 0 outside the range −π/T &lt; ω &lt; π/T, i.e. x(t) has no frequency greater than nyquist, then the copies will not overlap the range −π &lt; ω &lt; π and there is no problem as seen in figure above.

However if X has non-zero frequency components higher than π/T (fs/2 or nyquist). There will be overlap causing a wrap around in f-k domain. Refer below:



Notice that in the sampled signal, the frequencies in the vicinity of π are distorted by the overlapping of frequency components above and below π/T in the original signal causing wrap in F-k domain. Now in often spatial sampling is low as in case of Seismic or MRI due to constrains on number of detectors hence there is a aliasing in wavenumber. This spatial aliasing appears as wrap around in Frequency wavenumber Spectra.      

Source of Images :R. G. Lyons: Understanding Digital Signal Processing (2nd Edition)

Reference : EECS, University of California Berkeley