Subsurface Sensing and Super-Resolution Imaging: Application of Computational

Electromagnetics and Acoustics

Qing Huo LiuDepartment of Electrical and Computer Engineering

Duke UniversityDurham, NC 27708, USAwww.ee.duke.edu/~qhliu

September 14, 2016Parma, Italy

Announcing a new journal jointly created by IEEE AP, MTT, and EMC Societies

IEEE J. Multiscale and Multiphysics Computational Techniques (JMMCT)

Professor Qing Huo Liu, Editor in Chiefwww.ee.duke.edu/~qhliu

Manuscripts submitted for JMMCT typically should have the following two components:

1. Electromagnetic waves and fields +

2. Multiscale and/or MultiphysicsBut novel CEM methods will be also considered

Manuscript Central: https://mc.manuscriptcentral.com/jmmct-ieee

First JMMCT papers have been published since April 2016 at IEEE Xplorehttp://ieeexplore.ieee.org/xpl/RecentIssue.jsp?punumber=7274859

Outline

• Introduction: Multiscale and Multiphysics Computation for Subsurface

• Large-Scale Forward Methods for Imaging• Multiscale and Multiphysics Forward

Modeling• Inverse Problem and Super-Resolution

Imaging• Summary

3

Resource Exploration by EM and Seismic (Acoustic) Waves

Google Images

Marine Seismic (EM) Land Seismic (EM)

Wave scattering from complex media4

Hydraulic Fracturing in Oil Reservoir:Multiscale Problem

Hydraulic fracturing is widely used to increase permeability*

* http://greenplug.nu/5

Multiscale, Multiphysics Problems• Imaging for oil exploration/production is

multiscale in electromagnetic and seismic survey

• Multiphysics: Seismic and EM waves coupled with fluid flow in porous media

Sensors Vertical wellHorizontal well

Oil & water zones

• Surface surveyo Seismic, EM, gravity

• Borehole loggingo Acoustic, EM, nuclear

• Surface-to-Borehole and cross-well

6

EM Waves and Elastic WavesEM Waves from an antenna• Transverse waves• Speed of light (~0.3 Bm/s)

Elastic Waves in a Solid• Longitudinal (P) waves &

Transverse (S) waves• Speeds of sound: vp & vs

(~1 km/s)

• Fluid is a special case with only P waves

EH

k

c us1

up k

vpvsus2

7

Major Differences Between Acoustic and EM Waves in Subsurface

Acoustic waves (~50 Hz)• Low acoustic attenuation

(viscosity)

EM waves (~1 Hz)• High EM attenuation

(conductivity)

• Wave phenomena: sharp reflections, diffractions

• Diffusion phenomena: smoothed diffusive fields

• High frequency waves can have deep penetration

• Only low frequency field can have deep penetration

• High resolution• “Far”-field measurements

• Low resolution• Near-field measurements

• Not sensitive to water/oil interface

• Sensitive to water/oil interface

8

Multiscale, Multiphysics Inversion

• Seismic inversion: high structure resolution, but low contrast between oil & water

• EM inversion: High contrast between oil & water, but low spatial resolution

• Fluid flow can be tightly coupled with EM fields for reservoir/fluid imaging

9

Outline

• Introduction: Multiscale and Multiphysics Computation for Subsurface

• Large-Scale Forward Methods for Imaging• Multiscale and Multiphysics Forward

Modeling• Inverse Problem and Super-Resolution

Imaging• Summary

10

Pseudospectral and Spectral Methods for Seismic ImagingChallenge of Large Scale Elastodynamic Simulations

Sensors Vertical wellHorizontal well

Seismic survey

Phononic crystals, acoustic metamaterials（google image)

Global seismic simulation/inversion11

Large Scale Elastic Wave Computation• Elastodynamic equations - 3D velocity-stress equation: Vector

wave problem

The model is usually much larger than wavelength Phononic crystals：～(20λ)3

Seismic survey in oilfield：～(1000λ)3

Global seismology：～(10000λ)3

Reducing sampling density is the key in large scale computation

1 ( ) ( )Tt t λ µ

ρ∂ = ∇⋅ + ∂ = ∇ ⋅ + ∇ +∇ +v σ f σ v I v v g

ρ：Mass densityλ：P wave moduleμ：Shear wave module

Anisotropic medium：(λ,μ) become cijkl（21 independent parameters）

12

Seismic Imaging:Finite Difference and Pseudospectral (PS) Methods

• Acoustic Wave Equations for Absorptive Media

• Pseudospectral Method

• Finite Difference Method: FD for derivatives

13

Finite Differences vs. Pseudospectral Method

• FDTD Method Easy to implement and robust– Requires a dense grid (~20 PPWs)

• Pseudospectral (PS) Method Highly accurate: 2 PPW is adequate (Nyquist). A factor of 10n more efficient than FDTD for the n-

dimensional problem Assumption of periodicity

Periodic

• This wraparound effect corrupts late-time solutions14

How to Remove Wrap-Around Effect due to FFT?

• Traditional methods to eliminate wraparound effect:– Extend the computational domain– Use absorptive media (sponge) around the

computational domain– Neither method is satisfactory.

• The PSTD (Pseudospectral Time Domain) method: PML (perfectly matched layer) with the PS Method– The PSTD method uses PML to eliminate the

wraparound effect (Liu, 1996)– No wraparound; no reflections

Periodic

PML 15

2D Marmousi II RTM with PSTD

17 km x 3.5 km

Marmousi II Vp model

2D Marmousi II RTM

• Grid size Δx = Δz = 12m, so discretized model grids is 1417 x 292.

• The seismic source is 𝑓𝑓0 = 20 Hz Ricker wavelet. The minimum space sampling density is

• 100 sources, with a shot interval of 142 m.• The velocity model in RTM is a smooth layered

medium

(J. Xie et al., JCA, 2016)

Sampling Density= 𝒗𝒗𝒎𝒎𝒎𝒎𝒎𝒎𝟐𝟐.𝟕𝟕𝟕𝟕𝒇𝒇𝟎𝟎𝚫𝚫𝚫𝚫

= 𝟏𝟏𝟎𝟎𝟎𝟎𝟎𝟎𝟐𝟐.𝟕𝟕𝟕𝟕×𝟐𝟐𝟎𝟎×𝟏𝟏𝟐𝟐

=1.515 PPW

Image of Pre-stack RTM using PSTD

Good resolution even under the sub-Nyquistsampling of only 1.515 PPW

Ground truth

GPR (Ground Penetrating Radar)

NUFFT Imaging of 3D Objects

y

x

3D Configuration (W. Scott, Georgia Tech)

3D Imaging Results (GT plywood)

Raw Data

GPR Landmine Detection

•22

Spectral Element Method (SEM)• Suitable for large scale problems in EM and

seismology: L>>λ• High-order basis functions improve the accuracy

and efficiency with a small sampling density– SEM: 3-4 PPW– This is in contrast with traditional finite difference

and finite element methods: ~20 PPW are needed

23

Advantages of SEM• Spectral convergence; low sampling density• No Runge phenomenon• Diagonal mass matrix

• MPB: 84,000 s• SEM: 4684 s (18X faster)

• 3.4 PPW to reach 0.1% error• Comparison with traditional methods

24

Outline

• Introduction: Multiscale and Multiphysics Computation for Subsurface

• Large-Scale Forward Methods for Imaging• Multiscale and Multiphysics Forward

Modeling• Inverse Problem and Super-Resolution

Imaging• Summary

25

Multiscale Discontinuous Galerkin Time-Domain (DGTD) Method

• Fine structures – FETD; Coarse structures: SETD• Intermediate regions: FDTD• Interface between different subdomains: Riemann solver• Time integration: Hybrid implicit/explicit method

J. Chen & QH Liu, Proc. of the IEEE, 2013. 26

Hybridization with Nonlinear SPICE Circuit Solver: Antenna Direct Modulation

Diode 2Diode 1

Modulated input

Output at receiver

Measured (Keller et al., 2008) 27

Oilfield Application: Secondary Recovery by Water Flood with Magnetic Contrast Agent

• One injection well at center; magnetic contrast agent injected with water

• Four producing well at four corners• Tx at injection well. Rx at producing wells

TxInjection

Rx

Rx

Rx

Rx

Multiphysics: Coupling of EM with Fluid Flow

28

Permeability distribution after injection. Slug height = 20 m, Freq = 10 Hz

Secondary magnetic field at Well 1: x=142.5m, y =142. 5m, z = -10:1:30 m

x (m)

y (m

)

T =13 Day

20 40 60 80 100 120 140

20

40

60

80

100

120

140

1

1.2

1.4

1.6

1.8

2

-10 0 10 20 3036.96

36.98

37

37.02

37.04

z (m)

∆ H

z ( %

)

Day 13

29

Outline

• Introduction: Multiscale and Multiphysics Computation for Subsurface

• Large-Scale Forward Methods for Imaging• Multiscale and Multiphysics Forward

Modeling• Inverse Problem and Super-Resolution

Imaging• Summary

31

Diffraction Limit in Imaging• In the far-field zone, signals do not resolve

two objects separated less than half a wavelength

d ≥ λ/2

•Rayleigh diffraction limit: Two objects cannot be resolved if d ≤ λ/2 32

Diffraction Limitd = λ/2d = λ d = λ/4

•33

Inverse Scattering Method: FWI with Multiple Scattering Physics

• The forward problem is solved by a fast volume integral equation solver, the BCGS-FFT method – A problem with 20 million cells can be solved on a PC

• The nonlinear inverse problem is solved by– Distorted Born iterative method (DBIM)

• Ill-posedness can be overcome by regularization and frequency diversity

• Multiple-scattering physics can be used to improve resolution

Inverse Solver: Distorted Born Iterative Method with BCGS-FFT Method

• The nonlinear inverse scattering problem

• Parameterization1) In terms of contrast2) In terms of geometrical parameters

• Nonlinearity and convergence rate

• Solve equivalent linear equation system

• Iteration stops when the data misfit is small enough

† †2

2 2 2δγ δ

+ =

n n nn+1

nS D S

M M M fI xf x f

35

MWI in Free Space: Super-Resolution Imaging from 2D Measured Data

(Measured Data from K. Belkebir, Institut Fresnel, France)36

Results without Considering Multiple Scattering Physics

Born approximation: Diffraction limit- No multiple scattering physics included

2 GHz

37

Nonlinear Inverse Results for Dielectric Constant

2 GHz 2 GHz to 3 GHz

2 cm

Super-resolution is already achieved at 3 GHz ! The inverse method can resolve 1/5 wavelength.

38

3 GHz to 4 GHz 5 GHz to 6 GHz

7 GHz to 8 GHz 9 GHz to 10 GHz

Higher Frequencies

39

3-D Inverse Scattering from Fresnel Database (2009)(Inverse Problems, vol. 25, no. 2, 2009)

A mysterious object enclosed in a cube of size100 mm x 100 mm x 100 mm

r=1.796 m 9x9 Source Locations

27 Receiver Locations

100 mm Over 30,000 complex DOFs in inversion 40

Remarkable reconstruction in 3D - Super-resolution

Reconstruction of the Mysterious Target

41

1. Develop fast forward and inverse methods for nanoparticle contrast agents

• Permittivity and conductivity contrast agents• Magnetic permeability contrast agents • Develop inverse solvers to infer the distributions of

contrast agents in 4D

2. Apply these methods for understanding physics, interpretation, scaled experiments, and field testing

Nanoparticles as Contrast Agent for Subsurface Imaging

42

New Advance: Magnetodielectric Media

Contrast agents may be used to enhance the EM signal: magnetic (µr) contrast as well as conductivity contrast• Contrasts in εr and µr must be reconstructed

simultaneously

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

2, , ,

, ,inv

inv

sca ET b TD

Hb TD

k g d

j g d

χ

ωµ χ

′ ′ ′ ′= +∇∇⋅

′ ′ ′ ′− ∇×

∫∫

E r r r r r E r r r

r r r H r r r

( ) ( ) ( ) ( ) ( )

( ) ( ) ( )

2, , ,

, ,inv

inv

sca HT b TD

Eb TD

k g d

j g d

χ

ωε χ

′ ′ ′ ′= +∇∇⋅

′ ′ ′ ′∇×

∫∫

H r r r r r H r r r

+ r r r E r r r

43

Centers of two unknown objects: (-65m, 65m, 65m ),(65m, -65m, -65m )

16 coil transmitters in each well, location range (z): -600 m ~ 600 m

100 receivers in each well, location range (z): -1000 m ~ 1000 m

Background medium

Two unknown objects 1 180, 0.1 / , 1r S mε σ µ= = =

2 280, 1 / , 2r S mε σ µ= = =

z

y

x

o

70m

70m

Simultaneous Reconstruction of Conductivity and Permeability at 5 Hz

44

Reconstructed conductivity

Simultaneous Reconstruction of Conductivity and Permeability at 5 Hz

Reconstructed relative permeability

z

xVMD

Axis of symmetry

4 m

16 m

Homogeneous Background :

Frequency: 10 Hz

8cm

10cm Steel Case

Borehole

PML

Receivers

20m

10 m

z=-120~120m

5 m

5m

mFracture1 m

Electric Properties of Fracture

Cross Well

5 Layer Model in

NMM

EM Through-Casing Fracture Imaging

Very Challenging FEM Mesh •46

Very Challenging FEM Mesh

•47

Numerical Mode Matching (NMM) Method for N Layers

1. Fields in each layer are expanded in term of eigenmodes

2. Coefficients are expressed by local and global reflection matrices

3. Recursive relations for reflection matrices

• NMM for EPT tool (2.5D), 1989• NMM for Induction (2D), Chew,

Nie, Liu, Anderson, 1990.• 2.5D NMM for off-axis induction

tool (Liu, 1993)• 3D NMM for electrode-type tools,

Fan and Liu, 2000.

NMM: > 200 times faster than FEM 48

New Progress in NMM Method

• Extended to anisotropic media• Perfectly matched layer (PML) for

truncation of computational boundary• High order basis functions• Completely solved the axis singularity for

triaxial induction tools• Through-casing resistivity and fractures

49

Comsol Mesh (2D FEM)

NMM COMSOL

No. of elements 161 (1D, Line) 1,367,451

Time for mesh 0.01 sec 42 min

Memory (GB) 0.3 16.0

CPU time (seconds) 10.2 280.0

CasingFracture

Very challenging for 3D FEM for tilted fractures

Comparison Between Comsol and NMM

•50

Lab experiment setup

Carbon steel casing

Conductive fracture

Through Casing Fracture Mapping: Lab Experiments, Theory, and Inversion

0 1 2 3 4-200

-150

-100

-50

0

50

100

150

logg

ing

dept

h (m

m)

Normalized | Hzsct | or | Vsct | (mV)

TR1 = 70.9 mm

TR2 = 90.9 mm

TR3 = 110.9 mm

TR4 = 130.9 mm

TR4 = 150.9 mm

Theory (solid line) and measurements (‘x’)

•51

Fracture Mapping through Carbon Steel Casing

x(mm)

y(m

m)

Fracture Result

-200 -100 0 100 200

-200

-150

-100

-50

0

50

100

150

200

100 200 300

0.1

0.2

0.3

0.4

0.5

Measurements

| Hzsc

t | (A

/m)

Measured dataSimulation Results

Fracture mapping with carbon steel casing Measurements and simulation

Fracture is well reconstructedx(mm)

y(m

m)

-150 -100 -50 0 50 100 150

-150

-100

-50

0

50

100

150

S/m

2000

4000

6000

8000

10000

12000

14000

16000

Conductivity reconstruction in tap water in open hole environment.

OD = 16.4 cm

Tap water: σ = 0.0293 S/m

0 100 200 300 4000

5

10

15

20

25

30

Measurements

Am

p ( H

zzs )

(V/m

)

Measured dataSimulation results

Salty water: σ = 1.01 S/m

OD = 16.4 cm

•52

[With M. Zhuang @ XMU]

Earthquake at Taiwan Strait

Summary

• Multiscale forward modeling requires a mix of methodologies to work together: consistency, stability, and efficiency

• Multiscale inverse problems: very challenging in resolving multiple scales

• Multiphysics forward and inverse problem: Huge number of parameters

53