Subsurface Sensing and Super-Resolution Imaging ... · Imaging: Application of Computational...
Transcript of Subsurface Sensing and Super-Resolution Imaging ... · Imaging: Application of Computational...
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
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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
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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
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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
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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
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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
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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)
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Seismic Imaging:Finite Difference and Pseudospectral (PS) Methods
• Acoustic Wave Equations for Absorptive Media
• Pseudospectral Method
• Finite Difference Method: FD for derivatives
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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
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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
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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
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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
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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
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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
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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
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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
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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.
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3 GHz to 4 GHz 5 GHz to 6 GHz
7 GHz to 8 GHz 9 GHz to 10 GHz
Higher Frequencies
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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
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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
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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
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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
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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
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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
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