Seismic refraction method lec22
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Transcript of Seismic refraction method lec22
Seismic Refraction Method
Overview (2)
Prepared byDr. Amin Khalil
Overview
Types and Properties of seismic waves
Seismic waves at an interface
Basic laws for seismic refraction
T-X graph (travel time distance curve)
Interpretation & Modeling
Travel time distance graph
T-x graph is made by picking the first onset of the first arrival seismic phases. The picked phase should be defined with great care. For refraction, which is an active source method, the first onset should generally be compressional, hence the polarity of the onset should be positive. We must take care because under certain circumstances the onset is masked due to noise and we may pick later arrivals that may be of –ve polarity.
Travel time curve
When the picked data is plotted, it will be time versus distances, that’s why we call it T-X or travel time distance curve.
Horizontal FlatInterface
• Horizontal interfaces provide a simple introduction to the construction of T-X diagrams.
• Close to the source, the first arrival is due to the direct ray travelling in layer 1.
• This plots as a straight line on the T-X diagram.
• The slope of the line is the reciprocal of the layer 1 velocity (assuming distance is on the X-axis).
• The intercept is zero.
• When the critical distance is exceeded, refraction occurs and some energy enters layer 2. A refracted ray then travels at V2 sending return rays back to the surface as it does so.
• At some point (the cross-over distance) the refracted ray (being the faster) will overtake the direct ray and the return rays will become the first arrivals, despite their longer travel distance.
• It is these that are now plotted on the T-X diagram
• The T-X diagram thus develops an upper branch due to the refracted ray.
• This is again a straight line, whose slope is the reciprocal of V2 .
• There is now an intercept time (T1) whose value is determined by the layer 1 thickness and the two velocities
• The intercept time is an example of a delay time sum, composed of the separate times taken by the signal to descend to the interface and then to return to the surface.
11 /VxT
1212
Vdf
Vcd
VacT
)cos( cihdfac
)tan( cihdebc
)tan(2 cihxdebcxcd
2)(12
)tan(2cos2
Vihx
iVhT c
c
22)(12
)tan(2cos2
Vx
Vih
iVhT c
c
22)(12
)cos()sin(
cos12
Vx
iVi
iVhT
c
c
c
Using Seismic Refraction to Map the Subsurface
Depth{
12
12
2 VVVVXcDepth
Interpretation using intercept time• The intercept time is given by
• Since, in this case, the ray path is symmetrical, the intercept time is the sum of two equal delay times
12
21
222VVVV
zT
15
3 layer case
• By a similar argument, a third layer introduces a third branch into the T-X diagram.
• The slope is the reciprocal of V3 and the intercept is a composite of the layer 1 and layer 2 delay times.
12
21
22
213
21
23
12 22VVVV
zVVVV
zT
Delay Time Method• Allows Calculation of Depth Beneath Each Geophone
• Requires refracted arrival at each geophone from opposite directions
• Requires offset shots
• Data redundancy is important
Delay Time Methodx
V1
V2
x
V1
V2
)cos()tan()tan(
)cos( 12221 c
BcBcA
c
AAB
iVh
Vih
Vih
VAB
iVhT
Delay Time Methodx
)cos()tan()tan(
)cos( 12221 c
PcPcB
c
BBP
iVh
Vih
Vih
VBP
iVhT
)cos()tan()tan(
)cos( 12221 c
PcPcA
c
AAP
iVh
Vih
Vih
VAP
iVhT
)cos()tan()tan(
)cos( 12221 c
BcBcA
c
AAB
iVh
Vih
Vih
VAB
iVhT
V1
V2
Delay Time Methodx
t T T TAP BP AB0
Definition:
V1
V2
(7)
ABBPAP TTTt 0
)cos(
)tan()tan()cos( 12221
0c
PcPcA
c
A
iVh
Vih
Vih
VAP
iVht
)cos(
)tan()tan()cos( 12221 c
PcPcB
c
B
iVh
Vih
Vih
VBP
iVh
)cos(
)tan()tan()cos( 12221 c
BcBcA
c
A
iVh
Vih
Vih
VAB
iVh
2120
)tan(2)cos(
2V
ihiV
hV
ABBPAPt cP
c
p
But from figure above, BPAPAB . Substituting, we get
2120
)tan(2)cos(
2V
ihiV
hV
BPAPBPAPt cP
c
p
or
210
)tan(2)cos(
2V
ihiV
ht cP
c
p
)cos(
)sin()cos(
1221
0c
c
cp
iVi
iVht
)cos(
)sin()cos(
221
1
21
20
c
c
cp
iVViV
iVVVht
)cos(
)sin()cos(
22121
1
2
10c
c
cp
iVVi
iVVVV
Vht
2
1sinVVicSubstituting from Snell’s Law,
)cos(
)sin()cos(
sin1
22121
10c
c
c
cp
iVVi
iVViVht
)cos(
)sin()cos(
sin1
22121
10c
c
c
cp
iVVi
iVViVht
Multiplying top and bottom by sin(ic)
)cos()sin(
)(sin)cos()sin(
1221
2
2110
cc
c
ccp
iiVVi
iiVVVht
)cos()sin(
)(cos221
2
10cc
cp
iiVViVht
)sin(
)cos(22
0c
cp
iViht
)sin(
)cos(22
0c
cp
iViht
2
1sinVVic
Substituting from Snell’s Law,
10
)cos(2V
iht cp (8)
We get
11
)cos(2
)cos(22
Ppoint at Delay timeVih
VihtD cpcpo
TP (9)