Computational Methods for Inverse Problems in Geophysics Russell J. - - PowerPoint PPT Presentation

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Computational Methods for Inverse Problems in Geophysics Russell J. - - PowerPoint PPT Presentation

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Computational Methods for Inverse Problems in Geophysics Russell J. Hewett Mathematics & CMDA, Virginia Tech Theory and Experience in Solving Inverse Problems in Geophysics Workshop Uppsala University April 9, 2019 RJH (Virginia Tech)

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Computational Methods for Inverse Problems in Geophysics

Russell J. Hewett

Mathematics & CMDA, Virginia Tech

Theory and Experience in Solving Inverse Problems in Geophysics Workshop Uppsala University

April 9, 2019

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 1 / 55

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My Background

Research at the intersection of inverse problems, high-performance computation, and physics since ∼2003.

01-05 B.S. in Computer Science from Virginia Tech

◮ Thesis: Wavelet Analysis of Solar Active Regions ◮ Topics: Image processing and physical data extraction RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 2 / 55

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My Background

Research at the intersection of inverse problems, high-performance computation, and physics since ∼2003.

05-11 Ph.D. in Computer Science with focus in Computational Science and Engineering from U. of Illinois

◮ Thesis: Numerical Methods for Solar Tomography in the STEREO Era ◮ Topics: Dynamic state estimation, constrained Kalman filtering,

tomography of solar atmosphere, phase fields, image segmentation, geometrically constrained tomography, ray-tracing, tomography matrix calculation

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 2 / 55

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My Background

Research at the intersection of inverse problems, high-performance computation, and physics since ∼2003.

11-14 Postdoc in Mathematics (and Earth Science) at MIT

◮ Research: Seismic inversion, numerical optimization, wave equation

solvers, numerical software design, www.pysit.org

100 200 300 400 500 20 40 60 80 100 120 140 100 200 300 400 500 20 40 60 80 100 120 140 100 200 300 400 500 20 40 60 80 100 120 140

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 2 / 55

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My Background

Research at the intersection of inverse problems, high-performance computation, and physics since ∼2003.

14-18 Research Scientist and Project Manager at Total SA

◮ Research: High-performance seismic inversion, High-performance

software design for CSE activities, geophysical inverse problems, uncertainty quantification, and machine learning

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 2 / 55

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My Background

Research at the intersection of inverse problems, high-performance computation, and physics since ∼2003.

18- Assitant Professor in Mathematics and CMDA

◮ Research: Machine Learning ∩ Physical Inverse Problems; Inverse

Problems at Exascale

Characteristics of Interesting Problems

◮ Physics based ◮ Large, noisy real data sets ◮ Extremely large computation

requirements

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 2 / 55

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My Research Experience Pure Research Production Application

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 3 / 55

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My Research Experience Pure Research Production Application Grad School

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 3 / 55

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My Research Experience Pure Research Production Application Postdoc (thought)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 3 / 55

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My Research Experience Pure Research Production Application Postdoc (actual)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 3 / 55

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My Research Experience Pure Research Production Application Industry (thought)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 3 / 55

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My Research Experience Pure Research Production Application Industry (actual)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 3 / 55

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Inverse Problems

Forward Problem

◮ Need high quality models, usually not empirical ◮ Need lots of compute ◮ One model ⇒ One solution

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 4 / 55

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Inverse Problems

Inverse Problem

◮ Need high-quality data ◮ Need lots of compute (many fwd problems per inverse problem) ◮ One data set ⇒ space of potential models

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 4 / 55

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Subsurface Models

◮ Subsurface material parameters

◮ P-wave velocity (acoustics) ◮ S-wave velocity (elastics) ◮ Density (both. . . neither?) ◮ Anisotropy (VTI, TTI, orthorhombic)

◮ Subsurface reflectivity

◮ Changes in material properties ◮ Faults and fractures

◮ Temporal changes in the above (4D)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 5 / 55

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Subsurface Models

Marmousi 2 Velocity BP 2004 Velocity

1 2 3 4 5 6 2000 4000 6000 8000 10000

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 6 / 55

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Subsurface Models

SEAM Phase I Velocity (Fehler; SEG)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 7 / 55

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Subsurface Models

SEAM Phase I Velocity

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 8 / 55

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Subsurface Models

Marmousi 2

http://mcee.ou.edu/aaspi/publications/2006/martin etal TLE2006.pdf RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 9 / 55

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Subsurface Models

Marmousi 2

http://mcee.ou.edu/aaspi/publications/2006/martin etal TLE2006.pdf RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 9 / 55

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Subsurface Models

Marmousi 2

http://mcee.ou.edu/aaspi/publications/2006/martin etal TLE2006.pdf RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 9 / 55

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Subsurface Models

Netherlands Block F3 - Crossline 900

https://ghassanalregibdotcom.files.wordpress.com/2018/05/amir aapg2018 slides.pdf RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 10 / 55

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Geophysical Data

◮ Seismic Survey Design

◮ Marine ◮ Land ◮ Exploration vs monitoring

◮ Seismic Sources

◮ Airguns (marine) ◮ Explosive (land) ◮ Vibroseis (land, marine)

◮ Seismic Data Recorders

◮ Hydrophones (marine) ◮ Geophones (land) ◮ DAS RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 11 / 55

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Exploration Seismic Data Acquisition: Design

Marine Survey

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 12 / 55

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Exploration Seismic Data Acquisition: Design

Marine Survey Wide-Azimuth

https://wiki.seg.org/wiki/Wide azimuth#Wide-azimuth acquisition and survey design RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 12 / 55

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Exploration Seismic Data Acquisition: Design

Vertical Seismic Profile (VSP) Survey Walk-above

https://wiki.seg.org/wiki/Borehole geophysics RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 12 / 55

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Exploration Seismic Data Acquisition: Design

Vertical Seismic Profile (VSP) Survey Microseismic

https://wiki.seg.org/wiki/Borehole geophysics RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 12 / 55

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Exploration Seismic Data Acquisition: Design

Vertical Seismic Profile (VSP) Survey Cross-well

https://wiki.seg.org/wiki/Borehole geophysics RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 12 / 55

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Exploration Seismic Data Acquisition: Design

OBC/OBN/OBS Survey

http://marinegeos.com/services/1-seismic-survey RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 12 / 55

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Exploration Seismic Data Acquisition: Sources

Marine: Airgun

https://woodshole.er.usgs.gov/operations/sfmapping/airgun.htm, Hutchinson and Detrick, 1984 RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 13 / 55

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Exploration Seismic Data Acquisition: Sources

Marine: Airgun

https://www.sciencedirect.com/science/article/pii/S0894177714000648 RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 13 / 55

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Exploration Seismic Data Acquisition: Sources

Marine: Airgun

https://www.soundingsonline.com/features/atlantic-boaters-may-soon-encounter-seismic-blasting-offshore-drilling RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 13 / 55

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Exploration Seismic Data Acquisition: Sources

Land: VibroSeis

https://pixabay.com/en/vibrator-vibroseis-seismic-survey-863296/ RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 13 / 55

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Exploration Seismic Data Acquisition: Sources

Land: Explosive

https://vickybabel10.blogspot.com/2011/03/procedure-seismic-preloading.html RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 13 / 55

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Exploration Seismic Data Acquisition: Sources

Marine: VibroSeis

https://library.seg.org/doi/pdf/10.1190/segam2016-13762702.1 RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 13 / 55

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Exploration Seismic Data Acquisition: Receivers

Land: Geophone

http://web.mit.edu/12.000/www/finalpresentation/experiments/geology.html RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 14 / 55

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Exploration Seismic Data Acquisition: Receivers

Land: Geophone

http://web.mit.edu/12.000/www/finalpresentation/experiments/geology.html RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 14 / 55

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Exploration Seismic Data Acquisition: Receivers

Marine: Hydrophone

https://woodshole.er.usgs.gov/operations/sfmapping/hydrophone.htm RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 14 / 55

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Exploration Seismic Data Acquisition: Receivers

4-Component Sensors (4C)

https://www.glossary.oilfield.slb.com/Terms/sym/4c seismic data.aspx RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 14 / 55

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Exploration Seismic Data Acquisition

x=128 y t 100 200 300 400 500 500 1000 1500 2000 t t=1024 t=1024 y x 100 200 300 400 500 100 200 300 400 500

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 15 / 55

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Geophysical Inverse Problems

I am considering only the seismic inverse problem. Regimes I have neglected:

◮ CSEM (Controlled Source Electromagnetic) ◮ Gravity ◮ LIDAR ◮ etc.

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 16 / 55

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Geophysical Inverse Problems

I will discuss only the full-waveform inversion problem and I will stay in an “exploration” context. Seismic Data Response

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 17 / 55

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Geophysical Inverse Problems

I will discuss only the full-waveform inversion problem and I will stay in an “exploration” context. Seismic Data Response

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 17 / 55

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Geophysical Inverse Problems

I will discuss only the full-waveform inversion problem and I will stay in an “exploration” context. Seismic Data Response

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 17 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 18 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $)

d: data

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 18 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $)

d: data k: knowledge

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 18 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $)

d: data k: knowledge $: money

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 18 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $)

d: data k: knowledge $: money $: more money

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 18 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $) Subproblems:

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 19 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $) Subproblems:

◮ arg max

d

$(d, k, $)

◮ Find better data ◮ Engineers and Analysts RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 19 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $) Subproblems:

◮ arg max

d

$(d, k, $)

◮ Find better data ◮ Engineers and Analysts

◮ arg max

k

$(d, k, $)

◮ Find better knowledge or use knowledge better ◮ Research Scientists RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 19 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $) Subproblems:

◮ arg max

d

$(d, k, $)

◮ Find better data ◮ Engineers and Analysts

◮ arg max

k

$(d, k, $)

◮ Find better knowledge or use knowledge better ◮ Research Scientists

◮ arg min

$

max $(d, k, $)

◮ Do all this, but cheaper ◮ Managers RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 19 / 55

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(Exploration) Seismic Inverse Problem

max $(d, k, $) Subproblems:

◮ arg max

d

$(d, k, $)

◮ Find better data ◮ Engineers and Analysts

◮ arg max

k

$(d, k, $)

◮ Find better knowledge or use knowledge better ◮ Research Scientists

◮ arg min

$

max $(d, k, $)

◮ Do all this, but cheaper ◮ Managers RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 19 / 55

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Seismic Inverse Problem

Full Waveform Inversion Objective

J(m) = d(t) − F(m(x))2

2

d(t): Data m(x): Unknown physical coefficients F: Modeling operator

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 20 / 55

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Seismic Inverse Problem

FWI Objective: “Complete” Version

J(m, f) =

  • s∈S

{g(ds) − g(SsFs(Rs(m), fs)) + Tf(fs)} + Tm(m)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 21 / 55

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Seismic Inverse Problem

Full Waveform Inversion Objective

J(m) = d(t) − F(m(x))2

2

d(t): Data m(x): Unknown physical coefficients F: Modeling operator

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 22 / 55

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Seismic Inversion

Full Waveform Inversion Objective

J(m) = d(t) − F(m(x))2

2

d(t): Data m(x): Unknown physical coefficients F: Modeling operator

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 23 / 55

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Seismic Inversion

Full Waveform Inversion Objective

J(m) = d(t) − F(m(x))2

2

d(t): Data m(x): Unknown physical coefficients F: Modeling operator

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 24 / 55

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Seismic Inversion

Full Waveform Inversion Problem

arg min

m

J(m) = d(t) − F(m(x))2

2

s.t. L[m]u = f for F(m) = u

◮ L[m]u = f is a wave equation ◮ F operator solves wave equations ◮ PDE constrained optimization!

◮ Time-domain, frequency-domain, Laplace-domain, etc. RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 25 / 55

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Modeling Operators

Example: Second Order Isotropic Acoustics (w/ Constant Density)

◮ m(x) = 1/c2(x), where c(x) is p-wave velocity ◮ L is self adjoint

◮ For continuous at least. . . ◮ Up to BCs

F(m0) = u0 ⇔ (m0∂tt − △)u0 = f Fm0δm = δu ⇔ (m0∂tt − △)δu = −δm∂ttu0 F ∗

m0r = δm

⇔ δm, − q, ∂ttu0T Ω s.t. (m0∂tt − △)q = r δm = − q, ∂ttu0T = − T q(x, t)∂ttu0(x, t)dt

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 27 / 55

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Optimization Setup

J(m) = 1

2||d − F(m)||2 2

◮ Objective function evaluation ◮ Computation: Solve wave equation ◮ Cost: ∼ 1 RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 28 / 55

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Optimization Setup

J(m) = 1

2||d − F(m)||2 2

◮ Objective function evaluation ◮ Computation: Solve wave equation ◮ Cost: ∼ 1

∇J(m0) = −F ∗

m0(d − F(m0)) ◮ Objective gradient evalutation ◮ Computation: Adjoint state method ◮ Cost: ∼ 2+ RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 28 / 55

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Optimization Setup

J(m) = 1

2||d − F(m)||2 2

◮ Objective function evaluation ◮ Computation: Solve wave equation ◮ Cost: ∼ 1

∇J(m0) = −F ∗

m0(d − F(m0)) ◮ Objective gradient evalutation ◮ Computation: Adjoint state method ◮ Cost: ∼ 2+

D2Jδm = F ∗

m0Fm0δm− < D2Fδm, d − F(m0) > ◮ Objective Hessian application ◮ Computation: 2nd-order adjoint state method ◮ Cost: ∼ 4+ RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 28 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve

Fm0δm = δu ⇔ L[m0]δu = − δL

δm[δm]u0

◮ Linear forward modeling (Born) ◮ Cost: 2 wave solves ◮ Impossible to form as matrix! RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve

Fm0δm = δu ⇔ L[m0]δu = − δL

δm[δm]u0

◮ Linear forward modeling (Born) ◮ Cost: 2 wave solves ◮ Impossible to form as matrix!

F ∈ Rm×n

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve

Fm0δm = δu ⇔ L[m0]δu = − δL

δm[δm]u0

◮ Linear forward modeling (Born) ◮ Cost: 2 wave solves ◮ Impossible to form as matrix!

F ∈ Rm×n 3D Survey

◮ 10 × 1000 rcv (small) ◮ 8s recording (short) ◮ 8ms sampling (long) ◮ m =10,000,000 samples RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve

Fm0δm = δu ⇔ L[m0]δu = − δL

δm[δm]u0

◮ Linear forward modeling (Born) ◮ Cost: 2 wave solves ◮ Impossible to form as matrix!

F ∈ Rm×n 3D Survey

◮ 10 × 1000 rcv (small) ◮ 8s recording (short) ◮ 8ms sampling (long) ◮ m =10,000,000 samples

3D Modeling

◮ 876 × 1001 × 750 dof ◮ n = 657,657,000 dof RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve

Fm0δm = δu ⇔ L[m0]δu = − δL

δm[δm]u0

◮ Linear forward modeling (Born) ◮ Cost: 2 wave solves ◮ Impossible to form as matrix!

F ∈ Rm×n 3D Survey

◮ 10 × 1000 rcv (small) ◮ 8s recording (short) ◮ 8ms sampling (long) ◮ m =10,000,000 samples

3D Modeling

◮ 876 × 1001 × 750 dof ◮ n = 657,657,000 dof

Matrix Size

◮ IEEE single precision. . . ◮ ∼ 23.4PB Storage ◮ n wave solves ◮ ∼18 years

@ 100k/day

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Modeling Operators

F(m0) = u0 ⇔ L[m0]u0 = f

◮ Forward modeling ◮ Cost: 1 wave solve

Fm0δm = δu ⇔ L[m0]δu = − δL

δm[δm]u0

◮ Linear forward modeling (Born) ◮ Cost: 2 wave solves ◮ Impossible to form as matrix!

F ∗

m0r = δm

⇔

  • q, − δL

δm[δm]u0

  • Ω×T

s.t. L∗[m0]q = r

◮ Adjoint modeling ◮ “Migration” or imaging operator ◮ Cost: 1+ wave solves

F ∈ Rm×n 3D Survey

◮ 10 × 1000 rcv (small) ◮ 8s recording (short) ◮ 8ms sampling (long) ◮ m =10,000,000 samples

3D Modeling

◮ 876 × 1001 × 750 dof ◮ n = 657,657,000 dof

Matrix Size

◮ IEEE single precision. . . ◮ ∼ 23.4PB Storage ◮ n wave solves ◮ ∼18 years

@ 100k/day

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 29 / 55

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Solving FWI

◮ Solve with gradient-based optimization

Generalized Gradient Scheme

  • 1. Given m0.
  • 2. While i < MaxIter

2.1 gi = ∇J(mi) 2.2 si = h(mi, gi) 2.3 α = LineSearch(mi, gi, si) 2.4 mi+1 = mi + αsi

◮ Gradient descent? ◮ L-BFGS? ◮ Hessian/Quasi-Newton schemes?

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 30 / 55

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Solving FWI

(a) True (b) Initial (c) Final ◮ 50 L-BFGS iterations w/ Locally 1D Time Solver (L. Zepeda, RJH, M. Rao, L.

Demanet (SEG 2013)) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 31 / 55

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Real-world Utility

◮ Interpreters don’t actually use inverted material parameters ◮ They still want to look at seismic “images” ◮ Found by “migration” or imaging algorithms

◮ Kirchoff migration ◮ (One-way) wave equation migration ◮ Reverse-time migration ◮ Linearized inversion RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 32 / 55

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Real-world Utility

◮ Interpreters don’t actually use inverted material parameters ◮ They still want to look at seismic “images” ◮ Found by “migration” or imaging algorithms

◮ Kirchoff migration ◮ (One-way) wave equation migration ◮ Reverse-time migration ◮ Linearized inversion

◮ Migration is essentially back-propagation ◮ Or, we can consider it as a gradient calculation in FWI

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 32 / 55

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SLIDE 77

Real-world Utility

◮ Interpreters don’t actually use inverted material parameters ◮ They still want to look at seismic “images” ◮ Found by “migration” or imaging algorithms

◮ Kirchoff migration ◮ (One-way) wave equation migration ◮ Reverse-time migration ◮ Linearized inversion

◮ Migration is essentially back-propagation ◮ Or, we can consider it as a gradient calculation in FWI ◮ In any case, it is computed at much higher-frequency ◮ Looking at reflectivity, not material parameters

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 32 / 55

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SLIDE 78

Seismic Image

Netherlands Block F3 - Crossline 900

https://ghassanalregibdotcom.files.wordpress.com/2018/05/amir aapg2018 slides.pdf RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 33 / 55

slide-79
SLIDE 79

Real World Results

“An offshore Gabon full-waveform inversion case study,” Xiao, et al., Interpretation, November 2016. Data from CGG. RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 34 / 55

slide-80
SLIDE 80

Real World Results

“An offshore Gabon full-waveform inversion case study,” Xiao, et al., Interpretation, November 2016. Data from CGG. RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 34 / 55

slide-81
SLIDE 81

Real World Results

“An offshore Gabon full-waveform inversion case study,” Xiao, et al., Interpretation, November 2016. Data from CGG. RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 34 / 55

slide-82
SLIDE 82

Real World Results

“An offshore Gabon full-waveform inversion case study,” Xiao, et al., Interpretation, November 2016. Data from CGG. RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 34 / 55

slide-83
SLIDE 83

Challenges for FWI

◮ Due to the physical formulation ◮ Due to mathematical formulation ◮ Due to computational requirements ◮ Due to business decisions

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 35 / 55

slide-84
SLIDE 84

Cycle Skipping

Jean Virieux

◮ Due to the physical and mathematical formulations ◮ Manifests as global nonconvexity ◮ Partially resolved by working in frequency domain (or in Laplace

domain)

◮ Time-domain wave equation becomes Helmholtz equation

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 36 / 55

slide-85
SLIDE 85

FWI In Frequency Domain

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

◮ max. 512

wavelengths in domain

◮ PML width: 2.5

wavelengths

◮ 64 × 64 domain

decomposition

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 37 / 55

slide-86
SLIDE 86

FWI In Frequency Domain

100 200 300 400 500 20 40 60 80 100 120 140 100 200 300 400 500 20 40 60 80 100 120 140 100 200 300 400 500 20 40 60 80 100 120 140

◮ Frequency continuation

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 38 / 55

slide-87
SLIDE 87

Realistic and Practical Physics

◮ I have shown the idea behind FWI using constant density acoustic

physics

◮ Of course, the earth is not constant density, nor acoustic ◮ Massive increase in computational – and software – costs ◮ Does better physics drive the need for more compute? ◮ Or is more compute driving the availability of better physics?

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 39 / 55

slide-88
SLIDE 88

Realistic and Practical Physics

Physical Models

∂ttu = a△u + f Physics Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 –

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-89
SLIDE 89

Realistic and Practical Physics

Physical Models

∂t p v

  • =
  • −c∇·

a∇ p v

  • +

g h

  • Physics

Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 – Iso-Aco (1st) 4 2 1x-2x

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-90
SLIDE 90

Realistic and Practical Physics

Physical Models

∂t ˜ σ v

  • =
  • −AT D∗R

aRT DA ˜ σ v

  • +

g h

  • Physics

Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 – Iso-Aco (1st) 4 2 1x-2x TTI-Aco (1st) 5 (+?) 4 3x

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-91
SLIDE 91

Realistic and Practical Physics

Physical Models

∂t σ v

  • =
  • −CD∗

aD σ v

  • +

g h

  • Physics

Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 – Iso-Aco (1st) 4 2 1x-2x TTI-Aco (1st) 5 (+?) 4 3x Iso-Ela (1st) 9 3 ∼ 40x

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-92
SLIDE 92

Realistic and Practical Physics

Physical Models

∂t σ v

  • =
  • −CD∗

aD σ v

  • +

g h

  • Physics

Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 – Iso-Aco (1st) 4 2 1x-2x TTI-Aco (1st) 5 (+?) 4 3x Iso-Ela (1st) 9 3 ∼ 40x VTI-Ela (1st) 9 8 ∼ 40x

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-93
SLIDE 93

Realistic and Practical Physics

Physical Models

∂t σ v

  • =
  • −CD∗

aD σ v

  • +

g h

  • Physics

Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 – Iso-Aco (1st) 4 2 1x-2x TTI-Aco (1st) 5 (+?) 4 3x Iso-Ela (1st) 9 3 ∼ 40x VTI-Ela (1st) 9 8 ∼ 40x TTI-Ela (1st) 9 36 > 100x

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-94
SLIDE 94

Realistic and Practical Physics

Physical Models

∂t σ v

  • =
  • −CD∗

aD σ v

  • +

g h

  • Physics

Solutions Parameters Computation Iso-Aco (const. ρ) (2nd) 1 1 – Iso-Aco (1st) 4 2 1x-2x TTI-Aco (1st) 5 (+?) 4 3x Iso-Ela (1st) 9 3 ∼ 40x VTI-Ela (1st) 9 8 ∼ 40x TTI-Ela (1st) 9 36 > 100x Elastic (1st) 9 81 > 100x

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 40 / 55

slide-95
SLIDE 95

Software Considerations

◮ I have greatly simplified the problem ◮ Only considering one simple PDE and an “academic” objective

function

◮ My personal results in this talk are only embarassingly parallel ◮ Essentially data parallel in shot record ◮ There is still model parallelism to exploit, which requires high-end

HPC software

◮ In addition to. . .

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 41 / 55

slide-96
SLIDE 96

Software Considerations

FWI Objective

J(m) = d − F(m)2

2

d(t): Data m(x): Unknown physical coefficients F: Modeling operator fs(x, t):

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-97
SLIDE 97

Software Considerations

FWI Objective

J(m) =

  • s∈S

ds − Fs(m)2

2

ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t):

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-98
SLIDE 98

Software Considerations

FWI Objective

J(m) =

  • s∈S

ds − SsFs(m)2

2

ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t): Ss: Data sampling operator for shot s

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-99
SLIDE 99

Software Considerations

FWI Objective

J(m) =

  • s∈S

ds − SsFs(m) ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t): Ss: Data sampling operator for shot s ·: (Arbitrary) residual norm

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-100
SLIDE 100

Software Considerations

FWI Objective

J(m, f) =

  • s∈S

ds − SsFs(m, fs) ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t): Ss: Data sampling operator for shot s ·: (Arbitrary) residual norm fs(x, t): Unknown seismic source function for shot s

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-101
SLIDE 101

Software Considerations

FWI Objective

J(m, f) =

  • s∈S

g(ds) − g(SsFs(m, fs)) ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t): Ss: Data sampling operator for shot s ·: (Arbitrary) residual norm fs(x, t): Unknown seismic source function for shot s g: Data filter and interpolation function

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-102
SLIDE 102

Software Considerations

FWI Objective

J(m, f) =

  • s∈S

g(ds) − g(SsFs(Rs(m), fs)) ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t): Ss: Data sampling operator for shot s ·: (Arbitrary) residual norm fs(x, t): Unknown seismic source function for shot s g: Data filter and interpolation function Rs: Model restriction and filter operator for shot s

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

slide-103
SLIDE 103

Software Considerations

FWI Objective

J(m, f) =

  • s∈S

{g(ds) − g(SsFs(Rs(m), fs)) + Tf(fs)} + Tm(m) ds(t): Data for shot s m(x): Unknown physical coefficients Fs: Modeling operator for shot s fs(x, t): Ss: Data sampling operator for shot s ·: (Arbitrary) residual norm fs(x, t): Unknown seismic source function for shot s g: Data filter and interpolation function Rs: Model restriction and filter operator for shot s T: Regularization

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 42 / 55

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SLIDE 104

HPC and Subsurface Inverse Problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 43 / 55

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SLIDE 105

HPC and Subsurface Inverse Problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 43 / 55

slide-106
SLIDE 106

HPC and Subsurface Inverse Problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 43 / 55

slide-107
SLIDE 107

HPC and Subsurface Inverse Problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 43 / 55

slide-108
SLIDE 108

HPC and Subsurface Inverse Problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 43 / 55

slide-109
SLIDE 109

HPC and Subsurface Inverse Problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 43 / 55

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SLIDE 110

Scale: Business Considerations

1000s km^2 surface acquisition Acquire Seismic Data Seismic Depth Imaging Reservoir Appraisal Production Forecasting and Optimization

100s M$ 100s TB data 100s PF ???s Gboe ???? M$ Investment

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 44 / 55

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SLIDE 111

Current / Future Challenges: Data and Acquisition

Field data

◮ Exploit high redundancy in field data (compression) ◮ “Chain of custody” in field data ◮ Real data is noisy! ◮ Multicomponent data (more than just pressure) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 45 / 55

slide-112
SLIDE 112

Current / Future Challenges: Data and Acquisition

Field data

◮ Exploit high redundancy in field data (compression) ◮ “Chain of custody” in field data ◮ Real data is noisy! ◮ Multicomponent data (more than just pressure)

Novel Acquisitions

◮ Marine: Coil surveys, multiple sources ◮ Marine vibrators ◮ Pseudo-random source/receiver geometry ◮ Survey refinement RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 45 / 55

slide-113
SLIDE 113

Current / Future Challenges: PDEs and Inverse Problems

Inverse Problems

◮ Source function is unknown ◮ Meshing complex topography

(seafloor, salts)

◮ Uncertainty quantification

PDEs

◮ Boundary conditions! ◮ Beyond finite difference RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 46 / 55

slide-114
SLIDE 114

Current / Future Challenges: PDEs and Inverse Problems

Inverse Problems

◮ Source function is unknown ◮ Meshing complex topography

(seafloor, salts)

◮ Uncertainty quantification

PDEs

◮ Boundary conditions! ◮ Beyond finite difference RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 46 / 55

slide-115
SLIDE 115

Current / Future Challenges: PDEs and Inverse Problems

Inverse Problems

◮ Source function is unknown ◮ Meshing complex topography

(seafloor, salts)

◮ Uncertainty quantification

PDEs

◮ Boundary conditions! ◮ Beyond finite difference RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 46 / 55

slide-116
SLIDE 116

Current / Future Challenges: PDEs and Inverse Problems

Inverse Problems

◮ Source function is unknown ◮ Meshing complex topography

(seafloor, salts)

◮ Uncertainty quantification

PDEs

◮ Boundary conditions! ◮ Beyond finite difference RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 46 / 55

slide-117
SLIDE 117

Current / Future Challenges: PDEs and Inverse Problems

Inverse Problems

◮ Source function is unknown ◮ Meshing complex topography

(seafloor, salts)

◮ Uncertainty quantification

PDEs

◮ Boundary conditions! ◮ Beyond finite difference

◮ Perfectly Matched Layers ◮ Anisotropy ◮ High-order ABCs

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 46 / 55

slide-118
SLIDE 118

Current / Future Challenges: PDEs and Inverse Problems

Inverse Problems

◮ Source function is unknown ◮ Meshing complex topography

(seafloor, salts)

◮ Uncertainty quantification

PDEs

◮ Boundary conditions! ◮ Beyond finite difference RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 46 / 55

slide-119
SLIDE 119

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

  • J. Chan, Z. Wang, RJH, T. Warburton (2016)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-120
SLIDE 120

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

  • J. Chan, Z. Wang, RJH, T. Warburton (2016)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-121
SLIDE 121

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

  • J. Chan, Z. Wang, RJH, T. Warburton (2016)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-122
SLIDE 122

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-123
SLIDE 123

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-124
SLIDE 124

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

  • J. Chan, RJH, T. Warburton (2016)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-125
SLIDE 125

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

  • J. Chan, RJH, T. Warburton (2016)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-126
SLIDE 126

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

  • J. Chan, RJH, T. Warburton (2016)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-127
SLIDE 127

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-128
SLIDE 128

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints)

Solution is polynomial inside each element.

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-129
SLIDE 129

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-130
SLIDE 130

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-131
SLIDE 131

Example: Discontinuous Galerkin Solvers

◮ Advantages

◮ Can resolve complex topography ◮ Natural mapping to accelerators ◮ Many tuning parameters

◮ Challenges

◮ Achieving peak performance

(beating finite difference)

◮ Application in inverse problems ◮ Absorbing boundaries ◮ Many tuning parameters

◮ Strategies

◮ Hybrid meshing (& adjoints) ◮ h- and p-refinement (& adjoints) ◮ Local time stepping (& adjoints) ◮ Optimal basis functions (& adjoints) RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 47 / 55

slide-132
SLIDE 132

Current / Future Challenges

Optimization for large-scale PDE constrained IPs

◮ Uncertainty quantification without

access to the Hessian

◮ What parameters can be inverted for? ◮ Seismic data is not sensitive to

density

◮ Shear velocity only visible through

S-P conversion

◮ What about Thomson parameters? ◮ Joint inversion with CSEM, gravity,

etc.

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 48 / 55

slide-133
SLIDE 133

Current / Future Challenges

HPC & Software engineering

◮ HPC portable codes ◮ Math operations obscured deep in

legacy codes – software architecture issues

◮ Domain experts are not expert

computational scientists

◮ Efficient automatic adjoints and

derivatives – numerical correctness vs HPC correctness

◮ Integration with rapidly developing

exascale software

◮ Incredible cost of future algorithms

◮ CPU only is not viable ◮ “All” new machines are

GPU machines

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 49 / 55

slide-134
SLIDE 134

Current / Future Challenges

HPC & Software engineering

◮ HPC portable codes ◮ Math operations obscured deep in

legacy codes – software architecture issues

◮ Domain experts are not expert

computational scientists

◮ Efficient automatic adjoints and

derivatives – numerical correctness vs HPC correctness

◮ Integration with rapidly developing

exascale software

◮ Incredible cost of future algorithms RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 49 / 55

slide-135
SLIDE 135

Current / Future Challenges

HPC & Software engineering

◮ HPC portable codes ◮ Math operations obscured deep in

legacy codes – software architecture issues

◮ Domain experts are not expert

computational scientists

◮ Efficient automatic adjoints and

derivatives – numerical correctness vs HPC correctness

◮ Integration with rapidly developing

exascale software

◮ Incredible cost of future algorithms RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 49 / 55

slide-136
SLIDE 136

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data?

1 2 3 ... ... ... ...

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 50 / 55

slide-137
SLIDE 137

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data?

1 2 3 ... ... ... ...

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 50 / 55

slide-138
SLIDE 138

Adjoint States: Least-Squares

J(x) =

1 2||b − Ax||2 2

∇J(x0) = − A∗(b − Ax0) = − AT (b − Ax0)

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 51 / 55

slide-139
SLIDE 139

Adjoint States: Deep Learning

J(w, b) =

1 2||d − F(w, b; I)||2 2

=

1 2||d − O6(w6, b6; C5(. . . ; P4(. . . ; C3(. . . ; P2(w2, b2; C1(w1, b1; I))))))||2 2

LeNet-5

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 52 / 55

slide-140
SLIDE 140

Adjoint States: Deep Learning

J(w, b) =

1 2||d − F(w, b; I)||2 2

=

1 2||d − O6(w6, b6; C5(. . . ; P4(. . . ; C3(. . . ; P2(w2, b2; C1(w1, b1; I))))))||2 2

∇J(w0, b0) = − F ∗(d − F(w, b; I)) = − C∗

1P ∗ 2 C∗ 3P ∗ 4 C∗ 5O∗ 6(d − F(w, b; I))

LeNet-5

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 52 / 55

slide-141
SLIDE 141

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data? RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 53 / 55

slide-142
SLIDE 142

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data? RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 53 / 55

slide-143
SLIDE 143

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data? RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 53 / 55

slide-144
SLIDE 144

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data? RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 53 / 55

slide-145
SLIDE 145

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data? RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 53 / 55

slide-146
SLIDE 146

Current and Future Challenges

Machine Learning / Deep Learning

◮ Flavor of the month year decade? ◮ “Universal function approximation” ◮ “High-dimensional interpolation

problem” (Mallat)

◮ Training is inverse problem,

backpropagation is adjoint state method!

◮ Autoencoders/generative models:

path to UQ?

◮ Integrating physical (PDE) constraints ◮ Availability of training data?

1 2 3 ... ... ... ...

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 53 / 55

slide-147
SLIDE 147

Summary

Computational Science R&D Flow

physics → math → algorithm → HPC computation In all of these aspects. . .

◮ Scale of exploration seismic inverse problems is astounding ◮ As academics we need to think bigger. . .

◮ . . . and train students to think bigger!

◮ There are lots of interesting and challenging computational,

mathematical, and numerical problems arising from seismic inverse problems

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 54 / 55

slide-148
SLIDE 148

Summary

◮ Give FWI a shot:

www.pysit.org

◮ Try the 1D FWI development exercise!

RJH (Virginia Tech) Computation & Geophysical Inversion Uppsala / April 9, 2019 55 / 55