Transcript RTM of Converted Waves

Reduced-Time
Migration of
Converted Waves
David Sheley
University of Utah
Outline
•
•
•
•
•
•
Motivation
Migration Theory
Error Analysis
Synthetic Data Results
Field Data Result
Conclusions & Future Work
PP vs PS Transmission Migration
Receiver Well
Source Well
0
Z
0
X
PP Reflection Migration
Source Well
P
P=?
P
Receiver Well
0
Z
0
X =?
Converted Wave Migration
0
P
P
PS
PS
Receiver Well
Source Well
Vp,Vs = ?
Z
0
X =?
Outline
•
•
•
•
•
•
Motivation
Migration Theory
Error Analysis
Synthetic Data Results
Field Data Result
Conclusions & Future Work
Conventional Migration
m(r) = S(zg, tsr + trg)
g
s
tsr
trg
r
g
PS Transmission Migration
g
m(r) = S(zg, dsr/Vp + drg/Vs)
s
drg/Vs
dsr/Vp
r
g
Problem
0
Receiver km/sec
7.0
Well
Source
Well
Depth (m)
20
6.0
40
5.0
60
0
Offset (m)
50
Reduced-Time Migration
• Data time shift
S’(g, t) = S(zg, t + t )
obs
sg
t
obs
sg =
Observed direct-P time
Data Shift
Original Data
Shifted Muted Data
0
0
P
S
PS
PS
SP
114
SP
114
20
Time (ms)
35
2
Time (s)
8
Reduced-Time Migration
• Data time shift
S’(zg, t) = S(zg, t + tsg )
obs
t
• Modify
obs
sg =
Observed direct-P time
the migration equation
m(r) = S(zg, tsr + trg - t + t )
g
calc
sg
m(r) = S’(zg, tsr + trg – t )
g
calc
sg
obs
sg
Outline
•
•
•
•
•
•
Motivation
Migration Theory
Error Analysis
Synthetic Data Results
Field Data Result
Conclusions & Future Work
Error Analysis -- CWM
Assumptions:
• Single trace
• Homogeneous media
• True velocity = c
• Migration velocity
c’ = c + dc
• Vp/Vs = psr
m(r) = S(zg, tsr + trg psr)
g
l
g
m(r) = S(zg, (dsr + drg psr)/c’ )
l
Error Analysis
Conventional Migration
(dsr + drg psr)/c’= (dsr + drg psr)/(c + dc)
l
l
2
~
~ (dsr + drg psr)(s – s dc)
l
e cm = - (dsr + drg psr) s dc
l
2
Error Analysis
Reduced-Time Migration
m(r) = S(g, tsr + trg - tsg + tsg )
g
calc
obs
Error Analysis
Reduced-Time Migration
tsr + trg - tsg + tsg
=
2
(dsr + drg psr - dsg)(s – s dc) + dsg s
calc
obs
l
l
ertm = - (dsr + drg psr - dsg) s dc
l
2
Error Functions
CWM vs. RTM
ecm = - (dsr + drg psr) s dc
l
2
ertm = - (dsr + drg psr - dsg) s dc
l
2
Imaging-Time Error
0
0
Offset (m)
500
16
ecm
12
250
0
8
ertm
4
250
0
Offset (m)
500
0
Outline
•
•
•
•
•
•
Motivation
Migration Theory
Error Analysis
Synthetic Data Results
Field Data Result
Conclusions & Future Work
Crosswell Model
V1 = 5000 m/s
V2 = 5500 m/s
Vp /Vs = 1.5
Source = 1500 Hz
ds = 2 m
dg = 2 m
Well Separation
= 100 m
0
V2
V1
114
0
Offset (m)
114
Synthetic Data
Original Data
Shifted Muted Data
0
0
P
S
PS
PS
SP
114
SP
114
20
Time (ms)
35
2
Time (s)
8
PS Transmission Migration
True Velocity
0
114
0
Offset (m)
114
Conventional PS Migration
+ 10 % Velocity
0
114
0
Offset (m)
114
Reduced-Time PS Migration
+ 10% Velocity
0
114
0
Offset (m)
114
Outline
•
•
•
•
•
•
Motivation
Migration Theory
Error Analysis
Synthetic Data Results
Field Data Result
Conclusions & Future Work
Data Problems
• Time Delay = 3 ms ?
• Well location
• Velocity Model
0
Kidd Creek
Receiver km/sec
7.0
Well
Source
Well
Depth (m)
20
6.0
40
5.0
60
0
Offset (m)
50
Depth (m)
Time
Shifted
CRG
0
20
40
60
0
Time (ms)
6
Conventional PS Migration
0
Depth (m)
20
40
60
0
Offset (m)
50
Reduced-Time PS Migration
0
Depth (m)
20
40
60
0
Offset (m)
50
RTM-PS CRG #8
0
Depth (m)
20
40
60
0
Offset (m)
50
Kidd Creek
0
20
40
60
0
Offset (m)
50 0
Offset (m)
50
Outline
•
•
•
•
•
•
Motivation
Migration Theory
Error Analysis
Synthetic Data Results
Field Data Result
Conclusions & Future Work
Discussion & Conclusions
• PS migration can image structure
invisible to reflection migration.
• Reduced-time migraton decreases the
error of an incorrect velocity model.
• Converted wave reduced-time
migration can successfully image a
transmitting boundary.
Future Work
• Model and migrate salt proximity
VSP data with converted wave RTM.
• Model and test PP RTM.
• Search for other applications of
RTM.
• Graduate.