NMOcorrect: Normal Move-Out correction

In emanuelhuber/RGPR: Ground-penetrating radar (GPR) data visualisation, processing and delineation

Normal Move-Out correction

Description

Remove the Normal Move-Out (NMO) from the trace given a 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. The Normal Move-out is defined as the difference between the two-way time at a given offset and the two-way zero-offset time.

Usage

NMOcorrect(
  x,
  thrs = NULL,
  v = NULL,
  method = c("linear", "nearest", "pchip", "cubic", "spline")
)

## S4 method for signature 'GPR'
NMOcorrect(
  x,
  thrs = NULL,
  v = NULL,
  method = c("linear", "nearest", "pchip", "cubic", "spline")
)

Arguments

x	An object of the class GPR
thrs	[numeric(1)|NULL] Definite the threshold for muting (i.e., suppressing) the values where the NMO-stretching is above the threshold. Setting thrs = NULL, the full data will be used.
v	A length-one numeric vector defining the radar wave velocity in the ground
method	[character(1)] Interpolation method to be applied: one of pchip, linear, nearest, spline, cubic (see also interp1).

Details

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)

References

• 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

emanuelhuber/RGPR documentation built on May 13, 2024, 9:31 p.m.