Post on 19-Dec-2015
transcript
A New Approach to Joint Imaging of
Electromagnetic and Seismic Wavefields
International Symposium on Geophysical Imaging with
Localized Waves
Sanya, Hainin Island ChinaJuly 24-28, 2011
Gregory A. NewmanEarth Sciences Division
Lawrence Berkeley National Laboratory
PRESENTATION OVERVIEW Controlled Source EM and Magnetotellric Data Acquisition
– Motivation for Joint Imaging
Formulation of the Joint Inverse Problem– Large Scale Modeling Considerations– Need for High Performance Computing
Joint MT/CSEM Imaging Results– Gulf of Mexico (synthetic example)
Joint Imaging - EM & Seismic Data– Issues & Proposed Methodology – Laplace-Fourier Wave Field Concepts
» Similarities and Differences to the EM Wave Field» Imaging Across Multiple Scale Lengths» 3D Elastic Wave Fields » Preconditioners and solvers for 3D Seismic Wave Field Simulations
Conclusions
Marine CSEM & MT Surveying CSEMDeep-towed Electric Dipole transmitter
~ 100 AmpsWater Depth 1 to 7 km Alternating current 0.01 to 3 Hz ‘Flies’ 50 m above the sea floor Profiles 10’s of km in length Excites vertical & horizontal currents Depth of interrogation ~ 3 to 4 km Sensitive to thin resistive beds
MT Natural Source Fields
Less than 0.1 Hz Measured with CSEM detectors Sensitive to horizontal currents Depth of interrogation 10’s km Resolution is frequency dependent Sensitive to larger scale geology
Upstream Research
PIERS 2008
Continuous deep tow, 1.0 - 2.0 kts
seafloor
120kW currentsource
100 - 300 mElectric dipole
antenna
Fixed seafloor receivers
25-50 m
Marine EM Surveying
Log
10Fr
eque
ncy
(Hz)
345678
210
-1-2
Long Wave Radio
Ground Penetrating Radar
AM radio
Controlled Source EM
Magnetotellurics
NaturalNatural––sourcesourcemagnetotelluric signalsmagnetotelluric signals
Basic PrinciplePresence of increased subsurface resistivity enhances received EM fields
Increased resistivity
JOINT 3D INVERSE MODELING
= j a S (djobs - dj
p)/ej2 + b S (Zj
obs - Zj
p)/pj2
+ lh mh WT W mh + lv mv WT W mv
s.t. mv mh
dobs and dp are N observed and predicted CSEM data
Zobs and Zp are M observed and predicted MT impedance data
e & p = CSEM and MT data weights
mh = horizontal conductivity parameters
mv = vertical conductivity parameters
W = Ñ2 operator; constructs a smooth model
lh & lv = horizontal & vertical tradeoff parameters
a & b = scaling factors for CSEM and MT data types
N
j=1
M
j=1
Minimize:
LARGE-SCALE 3D MODELINGCONSIDERATIONS
Require Large-Scale Modeling and Imaging Solutions– 10’s of million’s field unknowns (fwd problem)
» Solved with finite difference approximations & iterative solvers – Imaging grids 400 nodes on a side
» Exploit gradient optimization schemes, adjoint state methods
Parallel Implementation– Two levels of parallelization
» Model Space (simulation and inversion mesh)» Data Space (each transmitter/MT frequency - receiver set fwd calculation independent)» Installed & tested on multiple distributed computing systems; 10 – 30,000 Processors
Above procedure satisfactory except for very largest problems– To treat such problems requires a higher level of efficiency
Optimal Grids– Separate inversion grid from the simulation/modeling grid – Effect: A huge increase in computational efficiency ~ can be orders of magnitude
Optimal Grids
Ωm imaging grid Ωs simulation grid sail lines
10 km
10 k
m
100 km
100
km
GRID SEPARATION EFFICIENCIES
Advantages– Taylor an optimal simulation grid Ωs for each transmitter-
receiver set– Inversion grid Ωm covers basin-scale imaging volumes at fine
resolution– Simulations grids much smaller, a subset of the imaging grid– Faster solution times follow from smaller simulation grids
What’s Required– A mapping of conductivity from Ωm to Ωs & Ωs to Ωm
» Conductivity on Ωs edged based» Conductivity on Ωm cell based
– An appropriate mixing law for the conductivity mappings
Joint CSEM - MT Imaging Mahogany Prospect, Gulf of Mexico
Study: 3D Imaging of oil bearing horizons with complex salt structures present Simulated Example: 100 m thick reservoir, 1 km depth, salt below reservoir Model: 0.01 S/m salt, 2 S/m seabed, 0.05 S/m reservoir, 3 S/m seawater MT Data: 7,436 data points, 143 stations & 13 frequencies 0.0005 to 0.125 Hz CSEM Data: 12,396 data points, 126 stations & 2 frequencies 0.25 and 0.75 Hz Starting Model: Background Model without reservoir or salt Processing Times: 5 to 9 hours, 7,785 tasks, NERSC Franklin Cray XT4 System
0x(km)
-5 -10 10 5
y=5 km cross section
Survey Layout
JOINT CSEM-MT IMAGING:The Benefits
Joint CSEM - MT ImagingMahogany Prospect Gulf of Mexico
Joint Imaging of EM and Seismic Data Issues
– Rock Physics Model » links attributes to underlying hydrological parameters» too simplistic» difficult or impossible to define robust/realistic model
– Differing Resolution in the Data» EM data 10x lower resolution compared to seismic
– RTM & FWI of Seismic Data» requires very good starting velocity model» velocity can be difficult or impossible to define» huge modeling cost due to very large data volumes
(10,000’s of shots; 100,000’s traces per shot)
Joint Imaging of EM and Seismic Data A way forward
– Abandon Rock Physics Model » assume conductivity and velocity structurally correlated» employ cross gradients: t = » t = 0 => ; = 0 and/or =0
– Equalize Resolution in the Data» treating seismic and EM data on equal terms» Laplace-Fourier transform seismic data – Shin & Cha 2009
dtetgsg st
0)()(ˆ
complexaresandsg )ˆ(
Acoustic Wave Equation
).(),,,(1
2
2
2
2
2
2
2
2
2tstzyxp
zyxtv
).(),,,(2
2
2
2
2
2
2
2
szyxp
zyxv
Time Domain Fourier/Frequency Domain
At first glance similar physics & similar resolution with EM fields skin depth:
Laplace/Fourier Domain
).(ˆ),,,(ˆ2
2
2
2
2
2
2
2
ssszyxpzyxv
s
Propagating Wave
Damped Diffusive Wave
rs
Seismic Imaging: Laplace-Fourier Domain
BP Salt Model Starting Velocity Model
Laplace Image
Laplace-Fourier Image
Standard FWI Image
New FWI Image
337 shot gathers151 detectors/shotmaximum offsets 15km
s = 10.5 to 0.5 =0.5
s = 10.5 to 0.5f = 6 to 0.5 =0.5
Taken from Shin & Cha, 2009
Laplace-Fourier Wavefield Modeling
There are differences compared to EM fields– wavelength and skin depth are decoupled
Meshing Issues to Consider– grid points per wavelength:10 points – 2nd order accuracy– grid points per skin depth: 6 points – 2nd order accuracy
Accuracy Issues– wavefield dynamic range
extreme ~ 70 orders– iterative Krylov solvers
require tiny solution
tolerances
0 5 10 15 20
10-60
10-50
10-40
10-30
10-20
10-10
Offset (km)
Ampl
itude
Analytic
10-30
10-50
10-70
10-90
10-110
10-130
tol=
LAPLACE-FOURIER IMAGING: Mahogany Prospect
Misfit
*
Survey line N 7500 km
Survey line N 5000 km
Survey line N 10000 km
Survey line N 2500 km
Survey line N -5000 km
-20 km 20 km
Survey line N 0 km
Survey line N -2500 km
287 sources, (σ=1, ω=2π)Source & Receiver & Spacing 1 km & 300 m Max. offsets 17 km 50 m below sea surface
West-East
Study: 3D Imaging of oil bearing horizons with complex salt structures present Simulated Example: 100 m thick reservoir, 1 km depth, salt below reservoir Model: 6 km/s salt, 3 km/s seabed, 2 km/s reservoir, 1.5 km/s seawater Seismic Data: 24,577 data points, 287 stations at 1 frequency (σ=1, ω=2π) Starting Model: Background Model without reservoir or salt Processing Times: 10.3 hours, 6,250 tasks, NERSC Franklin Cray XT4 System
LAPLACE-FOURIER IMAGE: Mahogany Prospect
-18.5 km 18.5 km
-0.9 km
13.5 km
-18.5 km 18.5 km
-0.9 km
13.5 km
0 km North 0 km North
2.5 km North 2.5 km North
5.0 km North 5.0 km North
7.5 km North 7.5 km North
10.0 km North 10.0 km North
12.0 km North 12.0 km North
LAPLACE-FOURIER IMAGE: Mahogany Prospect
1km below seabed
12.0 km North
-5.0 km North
-18.5 km 18.5 km West – East West – East -18.5 km 18.5 km
12.0 km North
-5.0 km North
Joint EM-Seismic ImagingProblem Formulation
and are N observed and predicted EM data
and are M observed and predicted Laplace-Fourier seismic data
and = EM and seismic data weights
= m conductivity parameters
= m acoustic velocity parameters
= Ñ2 operator; constructs a smooth model
and = conductivity & velocity tradeoff parameters
and = scaling factors for EM and seismic data types
are cross gradient structural constraints; is a penalty parameter
ii ttvv σσ
c
lljj
m
isem
M
lj
pl
obss
N
jj
pem
obsem dddd
1
1
2
1
2/ˆˆ/
WWWW TTTT
obsemd p
emdobssd obs
sd
σv
Wem s
t cm
Recipe for Auxiliary Parameters
First carry out separate inversions for seismic and EM => choose smoothing parameters (cooling approach))( sem
;sd
emdNext balance data funtionals for seismic and EM :
0;;1
emd
sd=> set
=> rescale accordinglyem
Test out values for => selected
;emd s
d
=> trail values tested out over a few inversion iterations
xg balances
Consider total objective functional : xgvmsmem
sd
emd
sd
emd
xg
Initial Imaging Resultsmarine example
conductivity image correlated with velocity; =1011
conductivity imageno correlation to velocity; =0
velocity imagecorrelated with conductivity; =1011
velocity imageno correlation to conductivity; =0
s =5,4,3,2,1 f = 0
f = 0.25
seismic 12-16 km offsets 85 shots 121-161 detectors/shot
CSEM16 km max. offsets 17 shots161 detectors/shot
Computational Requirements: 4250 cores – Franklin NERSCProcessing Time: ~22 hours
Elastic Wave Field Simulator First- order system for velocity –stress
components
Laplace-Fourier Domain - velocity components,
- stress components,
- density,
and - Lame coefficients.
, ,x y zv
, , , , ,xx xy xz yz yy zz
zyxf ,,
, , , ;
, , , ;
, , , ,
;
;
;
2 ;
2 ;
2 .
x x x x xx xy xz
y y y y xy yy yz
z z z z xz yz zz
xy y x x y
xz z x x z
yz z y y z
xx x x
yy y y
zz z z
s v div f
s v div f
s v div f
s v v
s v v
s v v
s div v v
s div v v
s div v v
Forces are defined via Moment-Tensor components (R. Graves 1996)
Μ
Boundary and Initial Conditions
The ordinary initial conditions for all components are zeros.
The boundary conditions are– a) PML absorbing boundary conditions for velocity– b) free surface boundary for normal stress component
Solution Realization Iterative Krylov Methods
System transformed : solve only for the velocity components
ˆ ˆ, .s
x x 11 12 13
y y 21 22 23
z z 31 32 33
v f D D D
D v = f D D D D
v f D D D
0 500 1000 1500
0
200
400
600
800
1000
1200
1400
1600
1800
nz = 14798
D is complex non-symmetric15 diagonals for 2nd order scheme4th order scheme 51 diagonals
,
.
s
s τ
v
τ = λμ D v
v b D τ f
Coupled System0 0
00
00; ;
0 0
00
0 0
2
00 0
00 0 ;
20 0
0
2
T
xx y z
y xy x
z xz x
yx y z
z yz y
zx y z
xy xyx
xz xzy
z
yz yz
DD D D
D DD D
D DD D
DD D D
D DD D
DD D D
b
b
b
τ vD D
b λμ
;
T
;τ vD D - matrices of FD first derivative operators
Solution Accuracy
Two Half Spaces Model Test
x, m
z, m
-2000 0 2000 4000 6000 8000 10000 12000
500
1000
1500
2000
2500
3000
3500
4000
4500
50001500
2000
2500
3000
3500
4000
200x200x130 nodes
Vertical cross section of velocity (p)
y=4800 m.
3D salt body
SEG/EAEG SALT MODEL TEST
Snap-shots of velocity field y-component
y=4800 m s=(3+18.85i) sec-1
Point source at r=(800,800,500), m ).Solution Time 1355 sec, 576 IterationsSolution Tolerance 1e-7
y=4800 m s=(3+18.85i) sec-1
real
imaginary
Laplace-Fourier Transformation
Benefits– Wave field simulations
» excellent choice for a preconditioner (frequency domain ) On a class of preconditioners for solving the Helmholtzs equation: Erlangga
et al., 2004, Applied Numer. Mathematics, 50 409-425.
– Imaging» possibilities to image at multiple scales and attributes
A consistent Joint EM seismic imaging approach
» known to produce robust macro-models of velocityCritical to successful RTM and FWI of seismic reflection data
Conclusions Demonstrated Benefits Massively Parallel Joint Geophysical Imaging
– Joint CSEM & MT– acoustic seismic (Laplace-Fourier Domain)– HPC essential
Future Developments in LF elastic wavefield imaging – massively parallel (MP) LF elastic wavefield simulator– exploit simulator as a preconditioner
» frequency domain wavefield modeling
– exam MP direct solvers – gradient based 3D LF elastic imaging code
Future Plans in Joint Imaging– joint EM and elastic wavefield 3D imaging capability
ACKNOWLEDGEMENTS
My Colleagues: M. Commer, P. Petrov and E. Um
Research Funding US Department of Energy
Office of Science Geothermal Technologies Program
Computational Details