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Metodos_Sismicos.pdf
Sismologia.pdf
Refraction_Seismic_Method.pdf
GEOL 335.3
Refraction Seismic Method
Intercept times and apparent velocities;
Critical and crossover distances;
Hidden layers;
Determination of the refractor velocity and depth;
The case of dipping refractor:
Hagedoorn plus-minus method;
Generalized Reciprocal Method ('refraction 
migration'); 
Travel-time continuation.
Reading:
� Reynolds, Chapter 5
� Telford et al., Sections 4.7.9, 4.9
� Sheriff and Geldart, Chapter 4.
GEOL 335.3
Two-layer problem
One reflection and one refraction
x
critical
S
i
c
i V
1
V
2
>V
1
Direct
HeadwaveRefracted
Re
fle
ct
ed
x
t
x
crossover
Dire
ct
Reflected: H
ead
pre-critical
post-c
ritical
t= t 0�
x
V 2
= t 0�x p2
t=
x
V 1
= x p1
t
0
At pre-critical 
offsets,
record direct 
wave and 
reflection 
In post-critical domain,
record direct wave, 
refraction, and reflection 
h
1
GEOL 335.3
Travel-time relations
Two-horizontal-layer problem
For a head wave:
For a reflection:
this is also sin i
intercept time, t
0
GEOL 335.3
Multiple-layer case
(Horizontal layering)
p is the same 
critical ray 
parameter;
t
0
 is 
accumulating 
across the 
layers:
GEOL 335.3
Dipping Refractor Case
shooting down dip
S
i
c
V
1
V
2
>V
1
h
d
R
x
α (dip)
i
c
h
uA
B
R'
xsinα
x(cosa-sinα tani
c
)
xsinα/cosi
c
sini
c
would change to '-' for up-dip shooting
GEOL 335.3
Refraction Interpretation
Reversed travel times
One needs reversed recording (in opposite directions) for 
resolution of dips.
The reciprocal times, T
R
, must be the the same for 
reversed shots.
Dipping refractor is indicated by:
Different apparent velocities (=1/p, TTC slopes) in the two 
directions;
� determine V
2
 and α (refractor velocity and dip).
Different intercept times.
� determine h
d
 and h
u
 (interface depths).
S
x
t
R
T
R
2zd cosi c
V 1
2zu cosic
V 1
slope= p1=
1
V 1
pu=
sin ic��
V 1
pd=
sin ic��
V 1
GEOL 335.3
Determination of Refractor 
Velocity and Dip
Apparent velocity is V
app
 = 1/p, where p is the ray 
parameter (i.e., slope of the travel-time curve).
Apparent velocities are measured directly from the 
observed TTCs;
V
app
 = V
refractor
 only in the case of a horizontal layering.
For a dipping refractor: 
� Down dip: (slower than V
1
);
� Up-dip: (faster).
From the two reversed apparent velocities, i
c
 and α 
are determined:
V d=
V 1
sin ic��
V u=
V 1
sin ic��
ic=
1
2
sin�1
V 1
V d
�sin�1
V 1
V u
,
ic��= sin
�1 V 1
V u.
ic��= sin
�1 V 1
V d
,
�=
1
2
sin�1
V 1
V d
� sin�1
V 1
V u
.
From i
c
, the refractor velocity is: V 2=
V 1
sin ic
.
GEOL 335.3
Determination of Refractor Depth
From the intercept times, t
d
 and t
u
, refractor depth is 
determined:
hd=
V 1 t d
2 cos ic
,
hu=
V 1 t u
2 cos ic
.
S
i
c
V
1
V
2
>V
1
h
d
R
x
α (dip)
i
c
h
uA
B
GEOL 335.3
Apparent Velocity
Relation to wavefronts
Apparent velocity, V
app,
 is the velocity at which the 
wavefront sweeps across the geophone spread.
Because the wavefront also propagates upward, 
V
app, 
≥ V
true
:
A C
θ
B
wavefront
Pr
o
pa
ga
tio
n
di
re
ct
io
n
Apparent propagation direction
AC= BC
sin � V app=
V
sin �
.
2 extreme cases:
� θ = 0: V
app
 = ∞;
� θ = 90°: V
app
 = V
true
.
�
GEOL 335.3
Delay time
Consider a nearly horizontal, shallow interface with strong 
velocity contrast (a typical case for weathering layer).
In this case, we can separate the times associated with the 
source and receiver vicinities: t
SR
 = t
SX
 + t
XR
.
Relate the time t
SX
 to a time along the refractor, t
BX
: 
t
SX
 = t
SA
 – t
BA 
+
 
t
BX
 = t
S Delay
+x/V
2
.
S
i
c
V
1
V
2
>V
1
h
s
x
B
A X
Rh/cosi
c
htani
c
t S Delay=
SA
V 1
�
BA
V 2
=
h s
V 1 cos ic
�
h s tan ic
V 2
=
h s
V 1 cos ic
1 � sin2 ic =
h scosic
V 1.
Note that V
2
=V
1
/sini
c
Thus, source and receiver delay times are:
t S , R Delay=
h s , r cosic
V 1.
t SR= t S Delay�t R Delay�
SR
V 2.
and
h
r
GEOL 335.3
Plus-Minus Method
(Weathering correction; Hagedoorn)
Assume that we have recorded two headwaves in opposite 
directions, and have estimated the velocity of overburden, 
V
1.
How can we map the refracting interface?
S
1
V
1
D(x) S2
S
1
x
t
S
2
T
R
tS1 D
tS2 D
D
Solution:
� Profile S
1
 → S
2
:
� Profile S
2
 → S
1
:
Form PLUS travel-time:
t S1 D=
x
V 2
�t S1�t D ;
t S2 D=
SR � x
V 2
�t S2�t D.
t PLUS= t S1 D�t S2 D=
SR
V 2
�t S1�t S2�2t D= t S1 S2�2t D.
t D=
1
2
t PLUS � t S1 S2 .Hence:
To determine i
c
 (and depth), still need to find V
2
.
GEOL 335.3
Plus-Minus Method
(Continued)
S
1
V
1
D(x) S2
S
1
x
t
S
2
T
R
tS1 D
tS2 D
D
To determine V
2
:
Form MINUS travel-time:
t MINUS= t S1 D � t S2 D=
2x
V 2
�
SR
V 2
�t s1 � t s2 .
slope t MINUS x =
2
V 2
.Hence:
The slope is usually estimated by using the Least 
Squares method.
Drawback of this method – averaging over the pre-critical 
region.
this is a constant!
GEOL 335.3
Generalized Reciprocal 
Method (GRM)
S
1
V
1
D S2
S
1
x
t
S
2
T
R
tS1 D
tS2 D
D
The velocity analysis function:
Introduces offsets ('XY') in travel-time readings in the 
forward and reverse shots;
so that the imaging is targeted on a compact interface region.
Proceeds as the plus-minus method;
Determines the 'optimal' XY:
1) Corresponding to the most linear time-depth function;
2) Corresponding to the most detail of the refractor.
XY
XY
t D=
1
2
t S1 D�t S2 D � t S1 S2 �
XY
V 2
.
t V=
1
2
t S1 D � t S2 D�t S1 S2 , should be linear, slope = 1/V2;
The time-depth function:
this is related to the desired image: h D=
t D V 1 V 2
V 2
2
� V 1
2
GEOL 335.3
Phantoming
Refraction imaging methods work within the region 
sampled by head waves, that is, beyond critical 
distances from the shots;
In order to extend this coverage to the shot points, 
phantoming can be used:
Head wave arrivals are extended using time-shifted 
picks from other shots;
However, this can be done only when horizontal 
structural variations are small.
x
t
Phantom arrivals
GEOL 335.3
Hidden-Layer Problem
Velocity contrasts may not manifest themselves in 
refraction (first-arrival) travel times.
Three typical cases:
Low-velocity layers;
Relatively thin layers on top of a strong 
velocity contrast;
Short travel-time branch may be missed with sparse 
geophone coverage.
Seismic.pdf
B
a
sic
 C
o
n
cepts
 of
 S
eism
ics
P
rof
.
 
 D
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.
 M
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nfred
 K
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A
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 v
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 E
rdb
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w
ellen
R
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n
s
-
 u
nd
 R
efraktio
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sseism
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TR
A
V
EL
 TIM
E
C
U
R
V
ES
First
 A
rriv
als
R
efraktio
n
sseism
isch
e
 A
u
sw
ertu
ng
R
efraktio
n
sseism
ik
:
B
eispiel
H
igh
-resolutio
n
 reflectio
n
 sectio
n
 sh
o
w
ing
 faulted
 dipping
 stru
ctu
re
 of
 copp
er
 o
re
sedim
ents
 (y
ello
w)
 at
 interface
 of
 sh
ale
 and
 co
nglo
m
erate
 sedim
ents
.
 C
opp
er
m
in
eralizatio
n
 o
rigin
ated
 in
 lo
w
er
 b
asaltic
 flo
w
s
 (blu
e)
.
 M
in
eralizatio
n
 lay
er
 lies
 in
 th
e
d
epth
 rang
e
 of
 1000
 to
 2500
 feet
 b
elo
w
 g
rad
e
.
 S
eism
ic
 S
o
u
rce:
 B
iso
n
 EW
G
-5;
g
eoph
o
n
e
 sp
acing
:
 20
 feet
.