open source simulations and inversions in geophysics
Lindsey Heagy with
Rowan Cockett, Seogi Kang, Doug Oldenburg, Gudni Rosenkaer, Dom Fournier, et al
Geophysical Inversion Facility
University of British Columbia
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● Context: an applied EM problem
○ An example: steel casing
● Big picture: simulations and inversions in geophysics
○ What are the pieces?
● Framework & Toolbox
○ How do we implement this?
● Building in the open
○ What can I do with it?
○ Collaborative development
● Interactive geophysics
○ Teaching with numerical simulations
outline
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em?
Electrical conductivity can be diagnostic for…
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em + steel casing
This is a problem. Want to
characterize this
(SEG Abstract: Heagy et al, 2015)
Physical Properties
● highly conductive
● significant (variable) magnetic
permeability
Geometry
● cylindrical
● thin compared to length
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● Fields
magnetic flux density
current density
● Physical Properties
● Fluxes
Constitutive Relations
Maxwell’s Equations (quasi-static)
electric field
magnetic field
electrical conductivity
magnetic permeability
Time
Frequency
math!
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primary magnetic
flux density
Interpolate
secondary source
current density
Casing
3D Geology
Data
Simulate
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grounded electric
Physics:
Maxwell’s Equations
Physical Properties
electrical conductivity
magnetic permeability
anisotropy...
Meshes
2D Cylindrical
Sources
inductive loop
primary-secondary
Data &
Sensitivities
…
and Time
Frequency
3D
custom
pieces: simulation
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inverse problems
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Magnetics Gravity
DC resistivity Magnetotellurics Seismic
Geophysics!
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simulations and inversions
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simulations and inversions
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building for researchers
● Flexibility to experiment
● Integration of information
○ Geologic
○ Multiple physics
● Reproducible and transparent
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● Modular: building blocks
○ organized in a framework
○ pieces available to manipulation
● Declarative: express intent
○ write what you mean
○ looks like the math
● Extensible: new research
○ quantitative communication
○ built in feedback loops
● Open: for the future
○ reproducible
○ opportunities for collaboration
building for researchers
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building for researchers
● Modular: building blocks
○ organized in a framework
○ pieces available to manipulation
● Declarative: express intent
○ write what you mean
○ looks like the math
● Extensible: new research
○ quantitative communication
○ built in feedback loops
● Open: for the future
○ reproducible
○ opportunities for collaboration
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framework
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Implemented in Python!
framework
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forward simulation
Survey: Data collection and geometry Problem: Physics
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finite volume
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create a mesh
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● Fields
● Fluxes
● Physical Properties
discretize
electric field
magnetic field
magnetic flux density
current density
electrical conductivity
magnetic permeability
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solve
continuous
discrete
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framework
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Data Misfit Regularization
Inverse Problem
inversion elements
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inversion as optimization
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For second order optimization
techniques, need data:
And sensitivities:
sensitivities
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forward simulation
&
sensitivities
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Forward
Inverse
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?
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Model & Physical Properties: What should we invert for?
(SEG Abstract: Kang et al, 2015)
Derivatives using chain rule:
or :
● Active reservoir layer
● Parametric representation
● ...
inversion model physical properties
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?
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grounded electric inductive loop
point dipole
(electric or magnetic)
fields from a primary problem
natural source
Sources: How do we excite the Earth?
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?
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Solve 2nd order system
Solve E-B, H-J ?
or
and compute derivative
Physics: How do we solve Maxwell’s equations
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?
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compute fields everywhere:
what we solved for from source
derivative
Fields: How do we calculate the EM fields and fluxes?
from source
from physics
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?
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...
Data:
Receivers: What, and where, do we measure?
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Plug in the pieces
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Sensitivities
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How do we know it works?
Testing!
● Taylor series
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for example: casing & sensitivities
What is the sensitivity with respect to the…
● conductivity of the
○ Block?
○ Layer?
○ Background?
● Depth and thickness of the layer?
● Location and widths of the block?
Heagy et al. 2016 - in review
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for example: casing & sensitivities
What is the sensitivity with respect to the…
● conductivity of the
○ Block?
○ Layer?
○ Background?
● Depth and thickness of the layer?
● Location and widths of the block?
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for example: casing & sensitivities
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for example: casing & sensitivities
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data
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sensitivities
● Need background model
● Collect data away from the
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sensitivities
● Need background model
● Collect data away from the
source (up to ~1 km away)
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summary
● Modular, composable pieces
○ Compartmentalize concerns
○ All pieces available to
manipulation → extensible
● Testing!
○ Test pieces
○ Test composite
http://www.flickr.com/photos/13403905@N03/2080281038/
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Building in the open
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Heagy et al. 2016 - in review
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Heagy et al. 2016 - in review
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Magnetics Gravity
DC resistivity Magnetotellurics Seismic
Geophysics!
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DC Resistivity
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Potential Fields: Gravity & Magnetics
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Airborne Time Domain EM Inversion
Figure above shows plan views of (a) the true conductivity model and (b) the
recovered model, and section views of (c) the true and (d) the recovered
conductivity models. Figure to the left shows observed and predicted data. Core
cell size: 50×50×20 m, The number of cell: 50×50×48 = 120,000; Reference
model: Half-space model with conductivity value, 0.005 S/m; Inexact
Gauss-Newton: 13 iterations; Cpu time: 48hrs; Maximum memory usage: 51.2GB;
Cpu:Intel(R)Xeon(R) CPU 2.80 GHz; Ram: 64 GB
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SimPEG MT: Magnetotellurics
Rosenkjær et al 2015
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Fluid Flow in the Vadose Zone: Richards Equation
Cockett & Haber (2016)
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Exploring Model Spaces
Saltwater intrusions
Kang et al (2015)
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● Creating a toolbox and framework for geophysics
● Focusing on flexibility and speed for the researcher
● Starting to build a community
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BIRS
2016
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strategies for open, collaborative development
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communicating: slack
testing: TravisCI
organizing: version control
docs: sphinx, rtfd
licensing: MIT