GEOS 657 MICROWAVE REMOTE SENSING - University of Alaska

Spring 2017 – UAF Class GEOS 657

GEOS 657 – MICROWAVE REMOTE SENSINGSPRING 2017

Lecturer: F.J. Meyer, Geophysical Institute, University of Alaska Fairbanks; [email protected]

Lecture 14: On the Use of InSAR in Geophysics

mailto:[email protected]

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 2

REVIEW OF INSAR WORKFLOW FOR A GEOPHYSICAL APPLICATION

Franz J Meyer, UAF


How InSAR Works

• InSAR phase is a function of distance from satellite to ground (range)

Path difference results in phase shift

780 k

m

By precisely measuring the phase difference 𝝓, the change in distance from satellite to ground can be calculated to an accuracy of sub-wavelength.

Franz J Meyer, UAF


How InSAR Works


Pass 1 Pass 2No phase shift

No deformation

Franz J Meyer, UAF


How InSAR Works


Pass 1 Pass 2

phase shift:

120 degrees

Ground subsidence: 9 mm

Franz J Meyer, UAF


InSAR Processing – Steps 1 – 7:Find and Download Images, Co-Register & Form Interferogram

=∙

• To form interferogram, we calculate: 𝐼 = 𝑢1 ∙ 𝑢2∗ (where ∎∗ is complex

conjugate)

SAR Image 𝑢1: SAR Image 𝑢2:∗

Interferogram 𝐼:

Example: Mt. Peulik volcano, Alaska

Franz J Meyer, UAF


InSAR Processing – Step 8:Subtraction of Flat Earth Phase

• Example:

– ERS-2 Interferogram of Mt. Peulik volcano, Alaska

Before Flat Earth Phase Compensation After Flat Earth Phase Compensation

Flat Earth Phase

Franz J Meyer, UAF


InSAR Processing – Step 9 & 10:Phase Filtering & Topographic Phase Correction using DEM

Sim

ula

ted

To

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grap

hy-

on

ly i

nte

rfe

rogr

am

0 360

DEM

in R

adar

Co

ord

inat

es

InSAR Imaging Geometry & Parameters

Topographic Phase Correction using DEMin

terf

ero

gram

Top

ogr

aph

y-o

nly

in

terf

ero

gram

Def

orm

atio

n in

terf

ero

gram

0 2.83 cm

𝜟𝝓 ≈ 𝝓𝒅𝒆𝒇𝒐 =𝟒𝝅

𝝀∆𝑹𝒅𝒆𝒇𝒐

9

Filtering 𝜟𝝓 for Noise Suppression

Filt

ere

d d

efo

rmat

ion

inte

rfe

rogr

am

0 2.83 cm

10

InSAR Processing Step 9 - Deformation interferogram in map projection

(including phase unwrapping and geocoding)Interpretation of Geocoded Differential Phase 𝜟𝝓

11


(including phase unwrapping and geocoding)Representation of Interferometric Phase

28 mm0

28.3

84.9

Uplift mm

Courtesy of G. Bawden, USGS12


(including phase unwrapping and geocoding)Deformation Modeling – Concept [Mt. Peulik Example]

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RESIDUAL

575

0

574

0

574

5

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OBSERVED

4 Oct. 95 - 9 Oct. 97

5 km

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SYNTHETIC

Best-fit source parameters:• Spherical point source (Mogi source)• The model source is located at a depth of 6.5 ± 0.2 km. • The calculated volume change of magma reservoir is 0.043 0.002 km3.

0 2.83 cm

13

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 14

InSAR Coherence: A Phase Quality Descriptor

m5

m25

ERS resolution element

interferogram

InSAR

processor

receiver noise

temporal

changes of

surface

scattering

conditions

propagation

effects

processor errors

Coherence:• Quality measure describing

noise level of InSAR phase

Useful for:• How accurate is a

topography or deformation

estimate from InSAR

• Contributions to Phase Noise:

L-band (𝝀 = 𝟐𝟓𝒄𝒎): Higher coherenceC-band (𝝀 = 𝟓. 𝟔𝒄𝒎): Lower coherence

Wavelength Vs. Coherence

15

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 16

AN EXAMPLE OF THE USE OF INSAR IN GEOPHYSICS

Deformation Modeling Problem

17

Magma intrusion

deformation: what we see (InSAR)

magma dynamics: what we want to know

?

Deformation Modeling Problem

18

Estimate source characteristics from InSAR deformation data

up

s

forward model

InSAR image

displacement

(vector)source

parameters

G s = d

design matrix

inverse

model

s = G dinv

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 19

Solving for Model Parameters using Model Inversion

𝐺 ∙ 𝑥 = 𝑏

• If the covariance matrix for errors in the observation (𝑏) is Σ𝑏, then the weighted least-squares (maximum likelihood) solution for 𝑥 is

ො𝑥 = 𝐺𝑇 ∙ Σ𝑏−1 ∙ 𝐺

−1∙ 𝐺𝑇 ∙ Σ𝑏

−1 ∙ 𝑏

and the covariance matrix for the estimated vector components is

Σ𝑥 = 𝐺𝑇 ∙ Σ𝑏−1 ∙ 𝐺

−1

• In the case where we assume that observation errors are independent and have equal standard deviations, 𝜎, we get

Σ𝑥 = 𝜎2 𝐺𝑇 ∙ 𝐺 −1

– The square roots of the diagonal terms of Σ𝑥 are the standard errors of the estimated parameters

What is the Forward Model in Volcano Deformation?

20

Predicts deformation (u) caused by magma intrusion(relates magma intrusion to deformation)

z

magma

intrusion

displacement

x

2 ui + = – Fi

2uk

(1-2) xi yk

elasto-static behavior

u = ƒ(model parameters)

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 21

What Is the Forward Model?Simple Model: Inflating Point Source Model

• A component of deformation vector (𝑢𝑖) and the displacement at the free surface (𝑥3 = 0) takes the form

𝑢𝑖 𝑥1 − 𝒙𝟏′ , 𝑥2 − 𝒙𝟐

′ , −𝒙𝟑′ = 𝑪

𝑥𝑖 − 𝒙𝒊′

𝑅3

– 𝒙𝒊′ is a source location, 𝑪 is a combination of material properties and source strength, and 𝑅 is

the distance from the source to the surface location

• 𝑪 is defined as follows:

𝑪 = ∆𝑃 1 − 𝜈𝑟𝑠3

𝐺= 𝜟𝑽

1 − 𝜈

𝜋

– ∆𝑃 - change in pressure of magma chamber

– 𝛥𝑉 - change in volume of magma chamber

– 𝜈 - Poisson’s ratio

– 𝑟𝑠 - radius of the sphere

– 𝐺 - shear modulus of country rock

Unknown (target) parameters marked in red

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 22

Forward Model: Inflating Point Source

Courtesy of M. Lisowski

α << d

D. Dzurisin, 2007

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 23

Forward Model: Inflating Point Source

Courtesy of M. Lisowski

α << d

D. Dzurisin, 2007

Horizontal

Vertical

α/d = 0.4

α/d = 0.6

α/d = 0 (point source)

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 24

Forward Model: Sill Model

Horizontal

Vertical

Point source

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 25

Forward Model: Dike Model

Ultimate Goal of Deformation Modeling:

26

Minimize

2)],(),(),([ yxobsyxlosyxu iii

ui is a theoretical calculation of ground surface deformation vector (i=1, 2, 3)losi is the InSAR line-of-sight vectorobsi is the observed deformation (InSAR image)(x, y) is the image coordinate

Non-linear inversion!!!!

Find the best-fitting Model ParametersA Simple Approach

27

1. Loop through model parameters

2. calculate the residual (observed – modeled) for each set of model parameters

3. Find the set of model parameters that renders the smallest residual

best-fitting model parameters

A Matlab Lab for Estimating Source Parameters

28

xy_gridsearch.m

• defines search space for source model location – Source Depth and volume change

is fixed for this experiment

• For each set of x and y coordinate parameters:

– Run forward model to produce predicted surface deformation result [mogi2InSAR.m]

– Calculate difference (residuals) between predicted and measured deformation

• Best fitting model parameters are those that minimize residuals

Z (depth)

v (volume change)

Mt. Peulik Example

29

Best-fit source parameters:

• The model source is located at a depth of 6.5 ± 0.2 km.

• The calculated volume change of magma reservoir is 0.043 0.002 km3.

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RESIDUAL

575

0

574

0

574

5

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OBSERVED

5 km

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SYNTHETIC

0 2.83 cm

VR

xxvxxxxu ii

i

32211

)1()0,,(

where x1, x2 , and x3 are horizontal locations and depth of the center of the sphere, R is the distance

between the sphere and the location of observation (x1, x2 , and 0), and v is the Poisson’s ratio of host rock.

Spherical point source (Mogi source)

Model Inversion for Multiple Sources

30

• Superimposition of individual deformation sources

• Smoothing (spatial + temporal)

– The total displacement on a

given patch…

– …is related to that of patches

adjacent to it, by a finite-

difference Laplacian

approximation

(schematic)

a1

a2

a3

a4

a5

a6

a7

a8

a9

aM

(a2–a5)–(a5–a8)+(a4–a5)–(a5–a6) = 0

a2 + a4 – 4a5 + a6 + a8 = 0

31

Example: Earthquake Modeling

32

Afar –triple junction

33

Smith and Cann, JGR, 2000

34

Quaternary strain localized to ~60 km long zones of fissures, aligned eruptive centers and faults -“magmatic segments“

Courtesy of T. Wright

35Courtesy of T. Wright

14/9/2005 to11/05/2005

163 earthquakes (mb<6) detected by NEIC.

Relocated by Anna Stork

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 3636

3D displacements measured from radar data

37

Deflating

Magma

ChambersDeflating

Magma

Chambers

Collapsed

Zone

along Rift

Collapsed Zone

along Rift

Map view

Cross section

Deformation Modelling

38

• 2.2 km3 magma intruded along dyke (Mt St Helens 1980 1.2 km3)

• 0.5 km3 sourced from Dabbahu and Gabho volcanoes at North.

• Earthquakes can be responsible for < 10 % of moment release.

Wright et al., Nature, 2005

Franz J Meyer, UAF

GEOS 657, Spring 2016 - 39

What’s Next?

• This is what awaits next:

– Thursday : Lab on InSAR Processing Using the SNAP Toolbox

– Next week Tuesday: Project Concept Presentations

Documents

GEOS 657 MICROWAVE REMOTE SENSING - University of Alaska