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Environmental and Exploration Geophysics II
Dipping Layer Refraction Problem,
Moveout and Coincident Source-Receiver Concepts
tom.h.wilson
[email protected]
Department of Geology and Geography
West Virginia University
Morgantown, WV
Tom Wilson, Department of Geology and Geography
The time distance (t-x) plot
Tom Wilson, Department of Geology and Geography
Determination of layer properties in the dipping layer
case requires shots in the down-dip and up-dip directions
Up-dip shot
Down-dip shot
Tom Wilson, Department of Geology and Geography
Repeat derivation for the up-dip direction
Tom Wilson, Department of Geology and Geography
The t-x plot gets a little more complicated and includes the combining the
responses in the up-dip and down-dip direction. Assuming there is no knowledge
of dip these directions are simply referred to as “forward” and “reverse.”
Tom Wilson, Department of Geology and Geography
Tom Wilson, Department of Geology and Geography
Note that the subscript d or u consistently refers to the
location of the source as downdip or updip, respectively.
Tom Wilson, Department of Geology and Geography
From an “intuitive” perspective - in which direction
will the refraction arrivals come in earlier?
Tom Wilson, Department of Geology and Geography
We can now determine c and 
Tom Wilson, Department of Geology and Geography
How do you determine V2?
sin  c 
V1
V2
V2 
V1
sin  c
1  1 V1
1 V1 

 c   sin ( )  sin ( ) 
2
Vu
Vd 
V1
sin  c 
V2
Tom Wilson, Department of Geology and Geography
Questions about problems 1-4?
Tom Wilson, Department of Geology and Geography
Some problems to consider: Problem set 4
1. A reversed seismic refraction survey indicates that a
layer with velocity V1 lies above another layer with velocity V2
and that V2>V1. We examine the travel times at a point located
midway (at C) between the shotpoints (at A and B). The travel
time of the refracted ray from end A to midpoint C is less than the
travel time of the refracted wave from end B to midpoint C. Show
that the apparent velocity determined from the slope of the travel
time curve for refracted waves produced from the source at A is
less that the apparent velocity for refracted waves produced from
the source at B. Toward which end of the layout does the
boundary between the V1 and V2 layers dip? i.e. where is downdip? Explain! (Robinson and Coruh, 1988)
Tom Wilson, Department of Geology and Geography
Here is some shot data collected in Marshall Co. WV
Enhanced display
We’d like to turn
this into geology.
Why do the
amplitudes drop
off below 200ms?
Tom Wilson, Department of Geology and Geography
How do we get here?
The short story
The effective source
receiver geometry for the
records shown at right
across the east margin of
the Rome Trough is
corrected so that the
source and receivers
share the same surface
location.
But - this is not the way
the data was collected.
Tom Wilson, Department of Geology and Geography
Note that the reflection point coverage spans half the
distance between the source and receiver
Tom Wilson, Department of Geology and Geography
The split spread provides symmetrical
coverage about the source
Tom Wilson, Department of Geology and Geography
Moveout and the moveout correction
t
Tom Wilson, Department of Geology and Geography
Redefine the reflection time equal to the 0-offset arrival
time (t0) plus the t (drop from t0 or “moveout”).
Tom Wilson, Department of Geology and Geography
Assume t2 is small relative to other terms and
can be ignored to approximate the moveout
t is the normal moveout correction
Tom Wilson, Department of Geology and Geography
Look at the reflection time distance
relationship in terms of t2 versus x2
Square both
sides of this
equation
Tom Wilson, Department of Geology and Geography
The hyperbola becomes a straight line
Tom Wilson, Department of Geology and Geography
In the t2-x2 form, the slope is 1/V2
Tom Wilson, Department of Geology and Geography
The moveout velocity
V is derived from the slope of the
reflection event as portrayed in
the t2-x2 plot. The derived
velocity is referred to as the
Normal Moveout Velocity, NMO
velocity, or, just VNMO.
Tom Wilson, Department of Geology and Geography
The VNMO is used as a correction velocity
2
x
 2  t2  2
V NMO
Tom Wilson, Department of Geology and Geography
If the velocity is accurately determined
the corrected time  equals t0
Fun with hyperbolas and ellipses
Tom Wilson, Department of Geology and Geography
If the correction velocity (VNMO) is too high then the
correction is too small and we still have a hyperbola
Tom Wilson, Department of Geology and Geography
2
If VNMO
 1
1 
 V then  2  2   1
 V VNMO 
2
And we have
Tom Wilson, Department of Geology and Geography
Tom Wilson, Department of Geology and Geography
NMO correction of the reflection events appearing in
the shot records across relatively horizontal strata
yields a more accurate image of subsurface geology.
Tom Wilson, Department of Geology and Geography
Tom Wilson, Department of Geology and Geography
These data sets are referred to as being single fold data.
Single fold implies only one trace per mid-point. Single
fold data are also sometimes referred to as 100% data
Tom Wilson, Department of Geology and Geography
• Continue your work on problem sets 3 and 4
• Hand in Exercises I-III and the Attenuation problem today
 Chapter 4, pages 165 to 199 and 206 to 229.
Tom Wilson, Department of Geology and Geography