Transcript Reflection Traveltime Tomography Using Dynamic Smoothing

First Arrival Traveltime and
Waveform Inversion of
Refraction Data
Jianming Sheng and Gerard T. Schuster
University of Utah
October, 2002
Outline
• Motivation
• First arrival traveltime and
waveform inversion
• Numerical examples
• Summary
Motivation
Given: Traveltime and waveform
of CDP refraction data
Goal: High resolution tomogram
Problem: Can waveform tomography
provide better resolution than
ray-based tomography?
Ray-based Tomography vs.
Full Waveform Inversion
Ray-based
tomography
Efficient and robust
Full
waveform
tomography
No high-freq. limitation
Resolution limited by
high-freq. assumption
Slow convergence and
local minima problem
First-arrival Traveltime and
Waveform Inversion
Ray-based
traveltime
tomography
Efficient and robust
First-arrival
waveform
inversion
No high-freq. limitation
Initial model
Better convergence and
mild nonlinear
Outline
• Motivation
• First arrival traveltime and
waveform inversion
• Numerical examples
• Summary
First Arrival Traveltime and
Waveform Inversion
• Step 1: Preprocessing the raw data:
band-pass, 3D to 2D
transform, trace normalization
• Step 2: Picking first-arrival
traveltimes and muting out
other waves except first
arrivals
• Step 3:
First arrival traveltime
tomography
Minimizes traveltime residual



obs
Initial model


pre 2
• Step 4: First arrival
waveform inversion
Predicted
Observed
Misfit
function

s,g
obs
s,g
D
D
pre
s,g 2
Multigrid Tomography
• Traveltime tomography:
Dynamic smoothing scheme
(to attack local minima problem)
(Nemeth, T., Normark, E. and Qin, F., 1992)
Outline
• Motivation
• First arrival traveltime and
waveform inversion
• Numerical examples
• Summary
Numerical Examples
• Synthetic data I: Three-layer
• Synthetic data II: WesternGeco
(Blind test)
• Redmond mine survey data
Synthetic Model I
0
2500
20
1958
Suggested by
Source
Freq.
60
Hz
Konstantin Osypov
40
1416
Avg. Velocity 2400 m/s
873
Source Wavelength 40 m
60
0
100
Distance (m)
200
331
(m/s)
Synthetic Model I
0
2500
20
1958
1416
40 m
40
873
60
0
100
Distance (m)
200
331
(m/s)
Synthetic Data I
•
•
•
Synthetic data set was calculated
by 2-D FD acoustic wave equation
solver
Twenty-one shots and 51 traces
per shot were used.
Computational grid dimension was
401*121.
Synthetic Shot Gather
-80
Time (sec.)
0.0
Offset (m)
0.1
Air Wave
120
Traveltime Tomogram
0
2500
20
1958
1416
40
873
60
0
100
Distance (m)
200
331
(m/s)
Synthetic Model I
0
2500
20
1958
1416
40
873
60
0
100
Distance (m)
200
331
(m/s)
Traveltime Residual
2.0
1.0
0.0
1
Iterations
30
Waveform Tomogram
0
2500
20
1958
1416
40
873
60
0
100
Distance (m)
200
331
(m/s)
Synthetic Model I
0
2500
20
1958
1416
40
873
60
0
100
Distance (m)
200
331
(m/s)
Waveform Residual
12,000
8,000
4,000
0
1
Iterations
30
Numerical Examples
• Synthetic data I: Three-layer
• Synthetic data II: WesternGeco
(Blind test)
• Redmond mine survey data
True Velocity Model
0.0
Depth (km)
0.0
1.0
Horizontal distance (km)
26
1000 m/s
2050~2500 m/s
True Density Model
0.0
Depth (km)
0.0
1.0
Horizontal distance (km)
26
Recorded CSG # 150
Time (sec.)
-3000
0.0
2.0
Offset (m)
3000
Guessed Density Model
Density (kg/m3)
3400
 v 
  2100 

 1981.2 
0.5
1400
1000
Velocity (m/s)
5000
Source Wavelet
Amplitude
400
0
-600
0.0
Time (sec.)
0.25
Waveform Matching
Offset
(m)
-50
Amplitude
-25
0
25
50
0.0
Time (sec.)
0.2
Traveltime Tomogram
0.0
0.0
Horizontal distance (km)
26
m/s
2712
Depth (km)
2284
1856
1428
1.0
1000
Traveltime Tomogram
Depth (km)
5.0
0.0
Horizontal distance (km)
8.75
m/s
2409
0.1
2057
0.2
1705
0.3
1352
0.4
1000
Waveform Tomogram
Depth (km)
5.0
0.0
Horizontal distance (km)
8.75
m/s
2700
0.1
2275
0.2
1850
0.3
1425
0.4
1000
Migration section
Depth (km)
5.0
0.0
0.1
0.2
0.3
0.4
Horizontal distance (km)
8.75
Predicted CSG #150
Time (sec.)
-3000
0.0
2.0
Offset (m)
3000
Recorded CSG # 150
Time (sec.)
-3000
0.0
2.0
Offset (m)
3000
Numerical Examples
• Synthetic data I: Three-layer
• Synthetic data II: WesternGeco
(Blind test)
• Redmond mine survey data
Salt Diapir Data
•
Thirty-one shots and 120 traces
total 3188 traveltimes picked.
Shot interval: 20 m
geophone interval 5 m
•
Source frequency 40 Hz.
•
Record length 1 sec.
sample interval 0.5 millisecond .
CSG for Field Data
After Preprocessing
Time (sec.)
0
0.2
1
Geophone #
120
CSG for Field Data
After Muting
Time (sec.)
0
0.2
1
Geophone #
120
Wavelet Extracted
0
0.1
Traveltime Tomogram
5500
0
20 m
4500
3500
55 m
SALT
130
2500
Tunnel
1500
500
0
Distance (m)
590
(m/s)
Traveltime Residual
2.0
1.0
0.0
1
Iterations
30
Waveform Tomogram
5500
0
20 m
4500
3500
55 m
SALT
130
2500
Tunnel
1500
500
0
Distance (m)
590
(m/s)
Traveltime Tomogram
5500
0
20 m
4500
3500
55 m
SALT
130
2500
Tunnel
1500
500
0
Distance (m)
590
(m/s)
Waveform Residual
6,000
4,000
2,000
0
1
Iterations
30
Predicted CSG
Time (sec.)
0
0.2
1
Geophone #
120
CSG for Salt Data
After Muting
Time (sec.)
0
0.2
1
Geophone #
120
Logarithmic Amplitude Vs. Offset
Log10 Amplitude
2
0
Synthetic
-2
Observed
-4
0
Offset (m)
400
Problems
Seismic attenuation
Surface wave noise
Source wavelet inversion
& objective function
Outline
• Motivation
• First arrival traveltime and
waveform inversion
• Numerical examples
• Summary
Summary
• Synthetic results show that the
waveform tomogram is much more
resolved;
• The preliminary results for the field
data are not as good as expected, and
further work is needed.
Acknowledgment
I thank the sponsors of the 2002 University
of Utah Tomography and Modeling
/Migration (UTAM) Consortium for their
financial support . I thank Konstantin
Osypov for providing the data set.