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 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:

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 = Ñ Ñ » t = 0 => Ñ Ñ ; Ñ = 0 and/or Ñ =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

).(),,,(12

2

2

2

2

2

2

2

2 tstzyxpzyxtv

=

).(),,,(2

2

2

2

2

2

2

2

szyxpzyxv

=

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)

Am

plitu

de

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/

ll

beaj

WWWW TTTT

obsemd p

emdobssd obs

sde

σv

Weml sl

a bt cm

Recipe for Auxiliary Parameters

First carry out separate inversions for seismic and EM => choose smoothing parameters (cooling approach))( sem ll

;sdj

emdjNext balance data funtionals for seismic and EM :

0;;1 === jjab em

d

sd=> set

=> rescale accordinglyeml

Test out values for => selected

;emdaj s

dbj

=> trail values tested out over a few inversion iterations

xgj balances

Consider total objective functional : xgvmsmem

sd

emd jjljlbjajj =

sd

emd bjaj

xgj

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, l 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

l

l

l

= =

= =

= =

=

=

=

=

=

=

Forces are defined via Moment-Tensor components (R. Graves 1996)

Μ

Ñ

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 DD 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 System 0 000

00; ;

0 0000 0

2

00 000 0 ;2

0 00

2

Txx y z

y xy x

z xz x

yx y z

z yz y

zx y z

xy xyx

xz xzy

zyz yz

DD D DD DD DD DD D

DD D DD DD D

DD D D

b

b

b

l l l

l l l

l l l

= =

= =

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 velocity

Critical 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