IMAGE EUV & RPI Derived Distributions of Plasmaspheric Plasma and Plasmaspheric Modeling

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

IMAGE EUV & RPI Derived Distributions of Plasmaspheric Plasma and Plasmaspheric Modeling

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