NMOCor | R Documentation |
Remove the Normal Move-Out (NMO) from the trace given a constant velocity: this is a non-linear correction of the time axis that requires interpolation. Note that only the conventional NMO correction is currently implemented. The conventional NMO introduces a streching effect. A nonstretch NMO will be implemented in a near future.
## S4 method for signature 'GPR'
NMOCor(x, v = NULL)
x |
An object of the class |
v |
A length-one numeric vector defining the radar wave velocity in the ground |
Assuming a horizontal reflecting plane and homogeneous medium, the two-way
bistatic travel time of the reflected wave
for an antenna separation x
follows directly from the Pythagorean
theorem:
t_{TWT}(x,z) = \sqrt{\frac{x^2}{v^2} + \frac{4z^2}{v^2}}
where t_{TWT}(x)
is the two-way travel time at antenna
separation x
of the wave reflected at depth z
with propagation
velocity v
. This equation defines an hyperbola (keep z
constant,
increase the antenna separation x
and you obtain a hyperbola similar
to the reflection signals you obtain with common-mid point survey).
The idea behind NMO-correction is to correct the signal for the antenna
separation (offset) and therefore to transform the signal to the signal we
would have recorded with zero offset (x = 0
). We write the vertical
two-way traveltime at zero offset
t_0 = t_{TWT}(x = 0) = \frac{2z}{v}
Therefore, the NMO-correction \Delta_{NMO}
is
\Delta_{NMO} = t_{TWT}(x) - t_0
\Delta_{NMO} = t_0 (\sqrt{1 + \frac{x^2}{v^2 t_0^2}} - 1)
Tillard and Dubois (1995) Analysis of GPR data: wave propagation velocity determination. Journal of Applied Geophysics, 33:77-91
Shatilo and Aminzadeh (2000) Constant normal-moveout (CNMO) correction: a technique and test results. Geophysical Prospecting, 473-488
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