of Electromagnetic and Seismic Wavefields International Symposium on Geophysical Imaging with Localized Waves Sanya Hainin Island China July 2428 2011 Gregory A Newman Earth Sciences Division ID: 398897
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A New Approach to Joint Imaging of Electromagnetic and Seismic Wavefields International Symposium on Geophysical Imaging with Localized WavesSanya, Hainin Island ChinaJuly 24-28, 2011
Gregory A. NewmanEarth Sciences DivisionLawrence Berkeley National LaboratorySlide2
PRESENTATION OVERVIEW Controlled Source EM and Magnetotellric Data Acquisition Motivation for Joint Imaging Formulation of the Joint Inverse ProblemLarge Scale Modeling ConsiderationsNeed for High Performance Computing Joint MT/CSEM Imaging ResultsGulf of Mexico (synthetic example)Joint Imaging - EM & Seismic DataIssues & Proposed Methodology Laplace-Fourier Wave Field ConceptsSimilarities and Differences to the EM Wave FieldImaging Across Multiple Scale Lengths3D Elastic Wave Fields Preconditioners
and solvers for 3D Seismic Wave Field SimulationsConclusionsSlide3
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 geologySlide4
JOINT 3D INVERSE MODELINGj = a S {(djobs - djp)/ej}2 + b S {(Zjobs - Zj
p)/pj}2 + lh mh WT W mh + lv mv WT W mv
s.t
.
m
v
m
h
d
obs
and
d
p
are N observed and predicted CSEM data Zobs and Zp are M observed and predicted MT impedance datae & p = CSEM and MT data weights mh = horizontal conductivity parametersmv = vertical conductivity parameters W = Ñ2 operator; constructs a smooth model lh & lv = horizontal & vertical tradeoff parametersa & b = scaling factors for CSEM and MT data types
N
j=1
M
j=1
Minimize:Slide5
LARGE-SCALE 3D MODELINGCONSIDERATIONSRequire Large-Scale Modeling and Imaging Solutions10’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 methodsParallel ImplementationTwo levels of parallelizationModel 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 ProcessorsAbove procedure satisfactory except for very largest problemsTo treat such problems requires a higher level of efficiency
Optimal GridsSeparate inversion grid from the simulation/modeling grid Effect: A huge increase in computational efficiency ~ can be orders of magnitude Slide6
Optimal Grids
Ω
m
imaging grid
Ω
s
simulation grid
sail lines
10 km
10 km
100 km
100 kmSlide7
GRID SEPARATION EFFICIENCIESAdvantagesTaylor an optimal simulation grid Ωs for each transmitter-receiver setInversion grid Ωm covers basin-scale imaging volumes at fine resolutionSimulations grids much smaller, a subset of the imaging gridFaster solution times follow from smaller simulation gridsWhat’s RequiredA mapping of conductivity from Ωm to Ωs & Ωs to
ΩmConductivity on Ωs edged basedConductivity on Ωm cell basedAn appropriate mixing law for the conductivity mappings Slide8
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 LayoutSlide9
JOINT CSEM-MT IMAGING:The Benefits Slide10
Joint CSEM - MT ImagingMahogany Prospect Gulf of MexicoSlide11
Joint Imaging of EM and Seismic DataIssuesRock Physics Model links attributes to underlying hydrological parameterstoo simplisticdifficult or impossible to define robust/realistic modelDiffering Resolution in the DataEM data 10x lower resolution compared to seismicRTM & FWI of Seismic Datarequires very good starting velocity modelvelocity can be difficult or impossible to definehuge modeling cost due to very large data volumes (10,000’s of shots; 100,000’s traces per shot) Slide12
Joint Imaging of EM and Seismic DataA way forwardAbandon Rock Physics Model assume conductivity and velocity structurally correlatedemploy cross gradients: t = t = 0 => ; = 0 and/or =0 Equalize Resolution in the Datatreating seismic and EM data on equal termsLaplace-Fourier transform seismic data – Shin & Cha 2009 Slide13
Acoustic Wave EquationTime DomainFourier/Frequency Domain At first glance similar physics & similar resolution with EM fields skin depth: Laplace/Fourier Domain
Propagating WaveDamped Diffusive WaveSlide14
Seismic Imaging: Laplace-Fourier Domain BP Salt ModelStarting Velocity Model
Laplace ImageLaplace-Fourier ImageStandard FWI ImageNew FWI Image
337 shot gathers
151 detectors/shot
maximum offsets 15km
s
= 10.5 to 0.5
=0.5
s
= 10.5 to 0.5
f
= 6 to 0.5
=0.5
Taken from Shin & Cha, 2009Slide15
Laplace-Fourier Wavefield Modeling There are differences compared to EM fieldswavelength and skin depth are decoupledMeshing Issues to Consider grid points per wavelength:10 points – 2nd order accuracygrid points per skin depth: 6 points – 2nd order accuracyAccuracy Issueswavefield dynamic range extreme ~ 70 ordersiterative Krylov solvers require tiny solution tolerances tol=Slide16
LAPLACE-FOURIER IMAGING: Mahogany ProspectMisfit*
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
=2
π
)
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 seawaterSeismic 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 SystemSlide17
LAPLACE-FOURIER IMAGE:
Mahogany Prospect -18.5 km18.5 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 NorthSlide18
LAPLACE-FOURIER IMAGE: Mahogany Prospect1km 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 NorthSlide19
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
=
Ñ
2
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 Slide20
Recipe for Auxiliary Parameters
First carry out separate inversions for seismic and EM => choose smoothing parameters (cooling approach)
Next balance data
funtionals
for seismic and EM :
=> set
=> rescale accordingly
Test out values for
=> selected
=> trail values tested out over a few inversion iterations
balances
Consider total objective functional : Slide21
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; =0s =5,4,3,2,1 f = 0f = 0.25
seismic
12-16 km offsets
85 shots
121-161
detectors/shot
CSEM
16 km max. offsets
17 shots
161 detectors/shot
Computational Requirements: 4250 cores – Franklin NERSC
Processing Time: ~22 hoursSlide22
Elastic Wave Field Simulator First- order system for velocity –stress components Laplace-Fourier Domain
- velocity components, - stress components, - density, and - Lame coefficients.
Forces are defined via
Moment-Tensor components (R. Graves 1996) Slide23
Boundary and Initial ConditionsThe ordinary initial conditions for all components are zeros.The boundary conditions area) PML absorbing boundary conditions for velocityb) free surface boundary for normal stress component Slide24
Solution Realization Iterative Krylov Methods System transformed
: solve only for the velocity componentsD is complex non-symmetric15 diagonals for 2nd order scheme4th order scheme 51 diagonals
Coupled System
- matrices of FD first derivative
operators
Slide25
Solution Accuracy Slide26
Two Half Spaces Model Test Slide27
200x200x130 nodes Vertical cross section of velocity (p) y=4800 m. 3D salt body
SEG/EAEG SALT MODEL TESTSnap-shots of velocity field y-component y=4800 m s=(3+18.85i) sec-1Point source at r=(800,800,500), m ).Solution Time 1355 sec, 576 Iterations
Solution Tolerance 1e-7
y=4800 m
s=(3+18.85i) sec
-1
real
imaginarySlide28
Laplace-Fourier TransformationBenefitsWave 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.Imagingpossibilities to image at multiple scales and attributesA consistent Joint EM seismic imaging approach known to produce robust macro-models of velocityCritical to successful RTM and FWI of seismic reflection dataSlide29
ConclusionsDemonstrated Benefits Massively Parallel Joint Geophysical ImagingJoint CSEM & MTacoustic seismic (Laplace-Fourier Domain)HPC essentialFuture Developments in LF elastic wavefield imaging massively parallel (MP) LF elastic wavefield simulatorexploit simulator as a preconditionerfrequency domain wavefield modelingexam MP direct solvers gradient based 3D LF elastic imaging codeFuture Plans in Joint Imagingjoint EM and elastic wavefield 3D imaging capability Slide30
ACKNOWLEDGEMENTS My Colleagues: M. Commer, P. Petrov and E. Um Research Funding US Department of Energy Office of Science Geothermal Technologies Program
Slide31
Computational Details