D. Gallagher, M. Adrian, J. Green, C. Gurgiolo, G. Khazanov, A. King, M. Liemohn, T. Newman, J....

D. Gallagher, M. Adrian, J. Green, C. Gurgiolo, G. Khazanov, A. King, M.

Liemohn, T. Newman, J. Perez, J. Taylor, B. Sandel

IMAGE EUV & RPI Derived Distributions of Plasmaspheric

Plasma and Plasmaspheric Modeling

February 6, 2001 Yosemite 2002: Magnetospheric Imaging

Image Analysis Techniques

• Iterative Gurgiolo Approximation– Arbitrary plasma density distribution– One flux tube assumed to dominate each pixel

• Custom hand analysis• Genetic Algorithm

– Parameterized function– Arbitrary plasma density distribution

• Single Image Tomography– With or without a priori assumption for plasma distribution

along Earth’s magnetic field lines– Single equatorial location contributes to multiple pixels in

instrument image, i.e. “multiple perspective”


One Kind of Hand Analysis

• Identify feature

• Trace boundaries

• Estimate density structure, simulate image, and compare


Data

No OuterPlasmaspheric Erosion

0.70¥Noe0.50¥Noe0.20¥Noe0.20¥Noe0.10¥Noe0.10¥Noe

0.05¥Noe0.05¥Noe

0.07¥Noe0.07¥Noe

0.02¥Noe0.01¥Noe0.01¥Noe

Channel Matches as Observed,but Outer Plasmaspheric Densities too High


Data

Including OuterPlasmaspheric Erosion

0.70¥Noe0.50¥Noe0.20¥Noe0.20¥Noe0.10¥Noe0.10¥Noe

0.05¥Noe0.05¥Noe

0.07¥Noe0.07¥Noe

0.02¥Noe0.01¥Noe0.01¥Noe

Exponential Decrease with L-Shell OutsideChannel Approximates Observation


T1

T2 T3

T4

T

Same Approach Can be UsedGenerally On an Event Basis


Data

Model

TRACE 1

Data

Model

TRACE 2

Data

Model

TRACE 3

Data

Model

TRACE 4

Data

Model

TRACE 5

In this Case, Model

Results WorkFairly Well


RPI Inversion for June 10, 2001


Guided & Direct Echoes @ 02:38:57

Guided echo trace from local hemisphere

Direct echo trace from local hemisphere


RPI Derived Field Aligned Density Distributions


Inversion of EUV Images


Genetic Algorithm:Development and Application of

Impulse Response Matrix

• Description of Problem

• Development of Impulse Response Matrix

• Matrix Inversion Method

• Genetic Algorithm Approach


Crossing a Particular L Shell.

This Diagram Suggests that for a Given

Satellite Position andLook Direction, there

is a Function that Relates the Density

Along the x-axis to the LOS Integration.

The Response (or Effect) of eachL Shell will be Different

Impulse Matrix


Impulse Response Matrix

• Digital signal processing deconvolution techniques work using the impulse response of the system.

• In this situation the impulse response for each pixel is different, there is not a system impulse response, standard deconvolution techniques cannot be used.

• However, there is a specific impulse response for each pixel, this suggests an Impulse Response Matrix.

• x = density along x-axis;b = LOS integration at camera location;A = Impulse Response Matrix.

Ax = b.


Impulse Matrix Inversion

A is not necessarily symmetric. If b is known then x can be obtained from

x = b[At(A At)-1]

1 2 3 4 5 6 7 8 9-2

-1

0

1

2

3

4

xLmax = 9R Non-uniform grid spacing# of Grid points = 18

1 2 3 4 5 6 7 8 9-2

-1

0

1

5

2

3

4

xLmax = 9R Grid spacing = 1R# of Grid points = 9


Genetic Algorithm Approach

• The genetic algorithm approach works by randomly “guessing” solutions, comparing them to the satellite image, selecting the best solutions, using those to generate more solutions, then testing them etc..

• The genetic algorithm approach is now be feasible since density distributions x can be “guessed”, then tested using Ax=b. (The method was not feasible before because for each x “guessed” an entire LOS integration was necessary, now only a matrix multiplication is necessary.)


Genetic Algorithm Approach Applied to 2D Problem

• 300 solutions (density at 18 grid locations along x-axis) were randomly generated.

• The solutions were transferred and compared to the LOS integration.

• The top 50 solutions were used as “parents” to generate a new set of 300 solutions. The parents for each solution were randomly chosen with “best” solutions having a higher likelihood of being chosen.

• The location where the two parents joined to form the new solution was randomly chosen.

• Each new solution had a 50-50 chance of having values mutated.


4.2 4.4 4.6 4.8 5 5.2 5.4 5.61

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

1 2 3 4 5 6 7 8 9-2

-1

0

1

2

3

4

5

1 2 3 4 5 6 7 8 9-2

-1

0

1

2

3

4

5

Genetic Algorithm Results

iter=25

t=5.49s

4.2 4.4 4.6 4.8 5 5.2 5.4 5.61

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

iter=25

t=5.49s

iter=2

t=0.66s

LOS integration

t=0.66s

x-axis density

iter=2


Genetic Algorithm Results

1 2 3 4 5 6 7 8 9-2

-1

0

1

2

3

4

5

4.2 4.4 4.6 4.8 5 5.2 5.4 5.61

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

4.2 4.4 4.6 4.8 5 5.2 5.4 5.61

1.5

2

2.5

3

3.5

4

4.5

5

5.5

6

1 2 3 4 5 6 7 8 9-2

-1

0

1

2

3

4

5

iter=50

iter=100

t=10.60s

t=20.71s

iter=50

t=10.60s

iter=100

t=20.71s

LOS integrationx-axis density


Original With Noise Removal

Masked ImageDerived Densities

Genetic Algorithm Results forEUV Image from August 11, 2001

1422UT

5.41000)110( Ln hgps

1.0431-46.387

1

ppL

Lh

xLg 79.0


Tomographic Algebraic Reconstruction Technique (ART)

• Volume Reconstruction– Back-projection

• Methodology:1. Build 3D Grid

2. Trace Pixel Beams through Grida. Find Sampled Voxels

3. Construct Integration (Summation) Formulae

4. Solve Formulae -> Generate Density Volume


Reconstruction: Outline0 10

0

7

P1P2

V(P1) = a1V2,0 + a2V2,1 + a3V3,2 + … + a10V3,10

Solve:


Let’s Get Back to May 24, 2000and Reduced Plasma in Outer PS

IMAGE ENA and EUV Observations


What Does Physical Modeling Show?


HENA EUV

RC


Where is PS IMAGE Inversion Leading?

• Comparison of physical models of PS, RC, & RB relative to mutual interactions between populations and model advancement GEM

• Study of PS refilling across all LT & L• Derivation of subauroral electric fields

through feature tracking• A new breed of PS statistical modeling

D. Gallagher, M. Adrian, J. Green, C. Gurgiolo, G. Khazanov, A. King, M. Liemohn, T. Newman, J....

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