Transcript No Slide Title

Environmental and Exploration Geophysics II
Velocity Analysis
tom.h.wilson
[email protected]
Department of Geology and Geography
West Virginia University
Morgantown, WV
Traces in a common
midpoint gather share the
common midpoint, but only
share a common depth
point when the reflector is
flat.
The moveout in the
common midpoint time
distance plot is hyperbolic
and symmetrical about the
midpoint (x=0).
NMO corrections to the arrivals in a commonmidpoint gather yield the same coincidence of
sources and receivers, but in this case all sources
and receivers relocate to the same midpoint.
The reliability of the output stack trace is critically
dependant on the accuracy of the correction velocity.
Average
Amplitude
Accurate correction ensures that the same part of
adjacent waveforms are summed together in phase.
If the correction velocity is in error then the reflection
response will be “smeared out” in the stack trace through
destructive interference between traces in the sum.
Recall - Benefits of CMP Sorting
and Stacking
As noted last week, signal
increases in proportion to
the fold of the data or
the number of traces (N)
summed to form the stack
traces. Random noise, on
the other hand, while not
eliminated, increases as
the N. Hence, the signal
amplitude increases as the
N relative to the noise
•How does the signal-to-
noise ratio in the stack
trace at left compare to
the signal-to-noise ratio
present in a single record
from this area?
Multiples are considered “coherent” noise or unwanted signal
n
n
VRMS 
n
2
V
 i ti
i 1
n
 ti
i 1
Vaverage 
V t
i 1
n
i i
t
i 1
i
VNMO is a "best fit" velocity
We made a point of noting and comparing the VRMS VAV and VNMO
because the VNMO is often taken to be the VRMS. However, each
of these 3 velocities has different geometrical significance.
•Multiples
•Refractions
•Air waves
•Ground Roll
•Streamer cable
motion
•Scattered waves
from off line
Underground Mine
Operations
Passive recordings
reveal coherent
background noise.
The hyperbolae are
associated with the
movement of an
auger along a panel
face of a longwall
mine.
Considerable
random ground
vibrations are also
present in this
recording.
Ground Roll
Air Waves
Refractions
Miller et al. 1995
Figure 1: Shot record showing
reflection event with
near offset arrival time
of approximately 80 ms.
The near-offset trace is
located 40 meters from
the source. Successive
traces are spaced at 3
meter intervals yielding
offsets ranging from 40
meters to 73 meters on
the outer trace.
Berger, 1992
Table 1 (right) lists
reflection arrival times for
three reflection events
observed in a common
midpoint gather. The
offsets range from 3 to 36
meters with a geophone
spacing of 3 meters.
Conduct velocity analysis of
these three reflection
events to determine their
NMO velocity. Using that
information, determine the
interval velocities of each
layer and their thickness.
Offset
(m)
Reflection
1
Reflection
2
Reflection
3
x
t1 (ms)
t2 (ms)
t3 (ms)
3
21.4
62.3
79.4
6
25
62.4
79.5
9
30.1
62.6
79.6
12
36.1
62.9
79.9
15
42.5
63.2
80.1
18
49.2
63.6
80.5
21
56.2
64.1
80.9
24
63.3
64.7
81.3
27
70.4
65.4
81.8
30
77.6
66.1
82.4
33
84.9
66.9
83
36
92.2
67.7
83.7
Berger, 1992
Source Receiver Offset (meters)
0
5
10
15
20
25
30
35
40
0
Arrival Time (ms)
20
40
60
80
100
Note hyperbolic moveout of
the three reflection events.
Recall 2
x
2
2
t  t0  2
Vrms
The variables t2 and x2
are linearly related.
t02 is the intercept &
1
is the slope
2
Vrms
X2
0
0
2000
Time
2
4000
6000
8000
10000
200
400
600
800
1000
1200
1400
Estimates of RMS
velocities can be
determined from the
slopes of regression
lines fitted to the t2-x2
responses.
Keep in mind that the
fitted velocity is
actually an NMO
velocity!
Start with definition of the RMS velocity
n
VRMS 
n
2
V
 i ti
i 1
n
 ti
i 1
The Vis are interval velocities and the tis are
the two-way interval transit times.
n
2
V
 i ti
2
i 1
VRMS

n
n
 ti
i 1
Let
t0 n
n 
   ti 
 i 1 
the two-way travel time of the nth reflector
hence
2
VRMS
t
n 0n
2
VRMS
t
n 0n
n
 Vi 2ti
i 1
 Vn2tn
n 1
 Vi 2ti
i 1
Since
2
VRMS
t
n 1 0 n 1
n 1
 Vi 2ti
i 1
2
2
2
VRMS
t

V
t

V
n n
RMSn 1t0 n 1
n 0n
2
2
Vn2tn  VRMS
t

V
RMSn 1t0 n 1
n 0n
Vn is the interval velocity of the nth layer
tn in this case represents the two-way
interval transit time through the nth layer
2
2
Vn2tn  VRMS
t

V
RMSn 1t0 n 1
n 0n
Vn2 
2
2
VRMS
t

V
RMSn 1t0 n 1
n 0n
tn
Hence, the interval velocities of individual layers can be
determined from the RMS velocities, the 2-way zero offset reflection arrival times and interval transit times.
The interval velocity that’s derived from the
RMS velocities of the reflections from the
top and base of a layer is referred to as the
Dix interval velocity.
However, keep in mind that we really don’t
know what the RMS velocity is.
An NMO velocity is estimated from the t2-x2
regression line for each reflection event and
that NMO velocity is assumed to “represent”
an RMS velocity.
Now let’s put these ideas into application
Homework assignment (see handout)
Seismic section (Figure 2 of your handout) showing
the arrival times of three reflection events.
A
B
A’
C
B’
C’
Think of these records as normal incidence seismograms
In the travel time plot, the reflectors are offset by an almost vertical normal
fault. Reflectors A, B, and C lie on the high side, and A’, B’, and C’ lie on the
low, or downthrown, side of the fault at right. Note that the interval transit
times, A to B and B to C on the upthrown block are greater than the interval
transit times A' to B' and B' to C' on the down-thrown block.
A
B
A’
C
B’
C’
With some Noise
Note that the fault plane is drawn through the diffraction apexes.
Recall that normal incidence records are the result of the stacking
process. Each record from any point on this line will be a sum of records
(after NMO correction) all of which shared a common midpoint but had
different source receiver offsets. A normal incidence or coincident
source-receiver section is also often referred to as a stack section.
s
e
c
o
n
d
s
Stack sections are compiled from a summation of the traces in a
CMP gather after the reflection arrival times have been corrected
for moveout. The section below corresponds to the CMP gather
located at 2500 feet along the profile (Figure 2) & the arrival
times have not been corrected for moveout.
A
B
C
Figure 3 of problem handout
The CMP Gather
2500’
A
B
A’
C
B’
C’
Figure 2 of problem handout
2,500 feet is the location of the midpoint for the traces in
the gather. The first trace at 2,750 feet lies 500 feet from
the source. The second trace lies at 2,950 feet.
2950’
Figure 3 of problem handout
Since the midpoint at 2,500 feet is shared by all traces in the
gather, the shots must be at equal distances to the left of the
midpoint. Where would the corresponding shot point be located?
2950’
Figure 3 of problem handout
What is the source receiver offset for the record located at 2950’?
2950’
Figure 3 of problem handout
The offset of the first receiver is 500’, the second 900’
the third at 1300’ and so on, increasing by 400’ from one
receiver to the next one out.
4100’
500’
Figure 3 of problem handout
The same relationships hold for the CMP gather shown in
Figure 4. The source-receiver offset for the first trace
in the gather is 500’, 900’ for the second and so on.
4100’
500’
A’
B’
C’
Figure 4 of problem handout
Develop a table for each CMP gather
measure and tabulate the arrival times
at each offset.
X
500
900
1300
1700
2100
2500
2900
3300
3700
4100
t1
t2
t3
Square the source-receiver offset distances and arrival times.
Fit regression lines to the resulting x2-t2 data points and determine
individual VNMO velocities.
Keep in mind that these are NMO velocities. You will use them as RMS
velocities to estimate the interval velocities of each layer, but keep in
mind the distinction between the VNMO and VRMS. The VRMS is a theoretical
value that we approximate using the VNMO velocity.
X2
5002
9002
13002
17002
21002
25002
29002
33002
37002
1.681 x 107
t12
t22
t32
•Compute Vints for the three intervals on the high
side of the fault (A, AB, and BC) and the low side
(A’, A’B’ and B’C’)
•Compute the thickness of each interval
•Discuss your results in a geologic context.
A
B
A’
C
B’
C’
Due Thurs, Nov. 2nd
Be sure and bring questions to class this Thursday.
You should be reading through the Pitfalls in Seismic Interpretation
Monograph handed out previously. We’ll pick up with the pitfalls
computer model studies next Tuesday.