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Seismic data is sorted by common midpoint and then corrected for normal moveout

Travel-time vs offset distance to show flat layer, NMO, and over-/under-corrected NMO

In reflection seismology, the definition of Normal Move Out (NMO) is the difference in reflection travel times from a common midpoint (CMP) on a horizontal reflecting surface due to variations in the source-geophone distance. ^[1] The relationship between arrival time and offset is hyperbolic and it is the principal criterion that a geophysicist uses to decide whether an event is a reflection or not.^[2] Normal Move Out (NMO) is distinguished from dip move-out (DMO), the systematic change in arrival time due to a dipping layer.

The normal moveout depends on a complex combination of factors including the velocity above the reflector, offset, dip of the reflector and the source-receiver azimuth in relation to the dip of the reflector^[3]. For a flat, horizontal reflector, the traveltime equation is^[4]:

$T_{x}^{2}=T_{0}^{2}+{\frac {x^{2}}{V^{2}}}$

where ' $T_{x}$ is two-way travel-time from source to receiver; x is distance from source to receiver (offset); V is velocity of the medium above the reflecting interface; $T_{0}$ is two-way travel-time at zero offset, when the source and receiver are in the same place.

The normal move-out $T_{NMO}$ is determined by the difference between the travel time at the receiver distance $T_{x}$ and the travel time at the source (offset is 0) $T_{0}$ ^[5]:

$T_{NMO}=T_{x}-T_{0}={\sqrt {T_{0}^{2}+{\frac {x^{2}}{V^{2}}}}}-T_{0}$

where x is distance from source to receiver (offset); V is velocity of the medium above the reflecting interface.

The NMO equation demonstrates that normal move-out travel-time decreases with increasing depth to the reflecting surface and/or increasing velocity. Normal move-out also increases with increasing source-receiver distances. NMO has the strongest effect at small $T_{0}$ and far offsets, therefore shallow events are influenced more by NMO effect and removal of NMO effect. In NMO correction, shallow events are more sensitive to velocity errors.

Non-hyperbolic move-out is most likely caused by: (in descending order)^[6]:
1. statics variation of the weathering layer;
2. lateral velocity variation below the weathering layer;
3. anisotropy;
4. fourth order move-out due to thin horizontal layering.

NMO correction

In reflection seismic surveying, the goal is to produce a seismic profile where all reflections on each receiver trace are presented as if the trace was recorded at x=0. To accomplish this goal, an NMO correction needs to be applied to all reflecting times. NMO correction can be used as a seismic processing tool to powerfully distinguish between reflections and other events such as refractions, diffractions and multiples. If an accurate NMO correction has been applied, reflections will appear as straight horizontal lines (see diagram "travel-time vs offset distance"), refractions will now appear as inverse curves and diffraction and multiple arrivals will retain some curvature.^[7] These unwanted arrivals can now be removed with a properly designed filter.

From refraction time-distance data, it is possible to determine the velocity from the surface to reflecting interface. This velocity is the NMO velocity and can be used to remove the effect of offset on the traveltimes $T_{NMO}$ (as shown in the equation above). If the NMO velocity is the same as the velocity of the medium, the reflection will be a horizontal line (as shown in the figure). If the NMO velocity is greater than the velocity of the medium, the NMO correction will be too small and the reflection will be under-corrected (as shown in the figure). If the NMO velocity is less than the velocity of the medium, the NMO correction will be too large and the reflection will be over-corrected (as shown in the figure).

NMO correction will reduce the amplitude spectra of frequency ^[8]. When NMO is removed in the data, reflections are flat in the CMP gather, meaning that the travel-time is $T_{0}$ at all offsets. The removal of NMO introduces a wavelet stretch in time domain data, so the frequencies bandwidth is compressed in frequency domain data , particularly at far offsets. The reduction in frequency bandwidth at far offset shows in the data after Fourier Transform (FFT). The severely stretched portions will lower the stack frequency bandwidth and thus degrades resolution. It is undesirable to leave severely stretched reflections in the data. One of the current strategies is called stretch mute which will mute the severely stretched portions.

NMO correction in Seismic Unix

Over-Corrected Data with NMO Velocity 200 m/s. Reflections are not flat and weaker after stacking.

Under-Corrected Data with NMO Velocity 5000 m/s. Reflections are not flat and weaker after stacking.

Here is an example of NMO corrections using Seismic Unix. The purpose of this example is to study the effects of different choices of velocities on normal moved-out seismic data and to determine the best single-velocity model with which to correct NMO seismic data. A constant NMO velocity of 1500 m/s is applied, then create one stacked trace of the data by adding all CMP traces together to create one stack trace. If 1500 m/s is the correct NMO velocity, the reflections will be flattened and have a strong spike on stack trace. If 1500 m/s is wrong, reflections will not be flat and will be weak after stacking.

There are 6 steps in this Seismic Unix script to test various constant NMO velocities:
STEP 1: data is sorted and windowed by common midpoint (CMP) and offset;
STEP 2: data is moved-out;
STEP 3: stack the CMP data;
STEP 4: data is filtered;
STEP 5: data is gained;
STEP 6: data is displayed.

#!/bin/sh
set -x
# To test NMO velocities 1000-1500 m/s with an increment of 100 m/s

counter=0
vel_start=1000
vel_last=1500
vel_inc=100
first_cmp=225
last_cmp=3675

for ((vel=$vel_start; vel<=$vel_last; vel=$vel+$vel_inc)) 

do

	echo $vel
	susort  <CMP_filename.su  cdp offset \
		| \
	suwind key=cdp min=$first_cmp max=$last_cmp \
		| \
	sunmo  vnmo=$vel \
		| \
	sustack \
		| \
        sufilter  f=80,120,300,500 \
		| \
	sugain agc=1 wagc=0.1 \
		| \
	suximage clip=1 \
	xbox=$[$counter*200] ybox=0 wbox=200 hbox=600 \
	title="$vel m/s" & \				
	counter=$[$counter+1]
done

The results include the raw data and the data after NMO correction. The NMO velocities are 200 m/s, 1500 m/s and 5000 m/s, respectively. In raw data, the reflections are downward curved. With the NMO velocity of 1500 m/s, the reflections are flattened and appear the strongest after stacking. With NMO velocities of 200 m/s and 5000 m/s, respectively, the data appears weaker, and they are over-corrected and under-corrected, respectively. Thus, the velocity of 1500 m/s is the best choice of NMO velocity for the this data.

References

^ Burger, H. R., Sheehan, A. F., Jones, C. H. (2006). Introduction to Applied Geophysics: Exploring the Shallow Subsurface (1st ed.). W. W. Norton & Company. p. 160. ISBN 0-393-92637-0.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press. p. 86. ISBN 0-521-46826-4.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Yilmaz, Öz (2001). Seismic data analysis. Society of Exploration Geophysicists. p. 274. ISBN 1-56080-094-1.
^ Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 301. ISBN 1-59370-015-6.
^ Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 301. ISBN 1-59370-015-6.
^ Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 309. ISBN 1-59370-015-6.
^ Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press. p. 146. ISBN 0-521-46826-4.{{cite book}}: CS1 maint: multiple names: authors list (link)
^ Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 301. ISBN 1-59370-015-6.

Category:Seismology

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[1] Burger, H. R., Sheehan, A. F., Jones, C. H. (2006). Introduction to Applied Geophysics: Exploring the Shallow Subsurface (1st ed.). W. W. Norton & Company. p. 160. ISBN 0-393-92637-0.{{cite book}}: CS1 maint: multiple names: authors list (link)

[2] Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press. p. 86. ISBN 0-521-46826-4.{{cite book}}: CS1 maint: multiple names: authors list (link)

[3] Yilmaz, Öz (2001). Seismic data analysis. Society of Exploration Geophysicists. p. 274. ISBN 1-56080-094-1.

[4] Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 301. ISBN 1-59370-015-6.

[5] Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 301. ISBN 1-59370-015-6.

[6] Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 309. ISBN 1-59370-015-6.

[7] Sheriff, R. E., Geldart, L. P. (1995). Exploration Seismology (2nd ed.). Cambridge University Press. p. 146. ISBN 0-521-46826-4.{{cite book}}: CS1 maint: multiple names: authors list (link)

[8] Liner, Christopher (2004). Elements of 3D Seismology. Tulsa, Ok: Pennwell Books. p. 301. ISBN 1-59370-015-6.

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