Transcript IMAGE_EUV_&_RPI_Derived_Distributions_of_Plasmaspheric

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 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”
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One Kind of Hand Analysis
• Identify feature
• Trace boundaries
• Estimate density structure, simulate image, and compare
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Channel Matches as Observed,
but Outer Plasmaspheric Densities too High
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Exponential Decrease with L-Shell Outside
Channel Approximates Observation
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Same Approach Can be Used
Generally On an Event Basis
T5
T1
T4
T2
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T3
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TRACE 2
TRACE 1
Model
Model
Data
Data
TRACE 4
TRACE 3
TRACE 5
Model
Model
Data
Data
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In this Case,
Model
Results Work
Fairly Well
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Model
Data
RPI Inversion for June 10, 2001
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Guided & Direct Echoes @ 02:38:57
Guided echo
trace from local
hemisphere
Direct echo
trace from local
hemisphere
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Guided & Direct Echoes @ 02:52:57
Guided echo
trace from local
hemisphere
Direct echo
trace from local
hemisphere
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Guided & Direct Echoes @ 02:54:56
Guided echo
trace from local
hemisphere
Direct echo
trace from
local
hemisphere
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RPI Derived Field Aligned Density Distributions
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Inversion of EUV Images
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Genetic Algorithm:
Development and Application of
Impulse Response Matrix
•
Description of Problem
•
Development of Impulse Response Matrix
•
Matrix Inversion Method
•
Genetic Algorithm Approach
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Impulse Matrix
The Response (or Effect) of each
L Shell will be Different
This Diagram Suggests
that for a Given
Satellite Position and
Look Direction, there
is a Function that
Relates the Density
Along the x-axis to the
LOS Integration.
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Crossing a Particular L Shell.
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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.
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Impulse Matrix Inversion
A is not necessarily symmetric. If b is known then x can be obtained from
x = b[At(A At)-1]
5
xLmax = 9R
Grid spacing = 1R
# of Grid points = 9
4
3
4
3
2
2
1
1
0
0
-1
-1
-2
1
2
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3
4
5
6
7
8
xLmax = 9R
Non-uniform grid spacing
# of Grid points = 18
9
-2
1
2
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3
4
5
6
7
8
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.)
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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.
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Genetic Algorithm Results
5
6
iter=2
t=0.66s
5.5
iter=2
t=0.66s
4
3
2
5
4.5
4
3.5
1
3
2.5
0
2
-1
1.5
-2
1
2
3
4
5
6
7
8
9
1
4.2
4.4
x-axis density
4.6
4.8
5
5.2
5.4
5.6
LOS integration
5
6
iter=25
t=5.49s
4
3
iter=25
t=5.49s
5.5
5
4.5
4
2
3.5
1
3
2.5
0
2
-1
1.5
-2
1
2
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3
4
5
6
7
8
9
1
4.2
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4.4
4.6
4.8
5
5.2
5.4
5.6
Genetic Algorithm Results
5
6
iter=50
t=10.60s
4
3
2
iter=50
t=10.60s
5.5
5
4.5
4
3.5
1
3
2.5
0
2
-1
1.5
-2
1
2
3
4
5
6
7
9
8
1
4.2
4.4
x-axis density
4.6
4.8
5
5.2
5.4
5.6
LOS integration
5
6
iter=100
t=20.71s
4
3
2
iter=100
t=20.71s
5.5
5
4.5
4
3.5
1
3
2.5
0
2
-1
1.5
-2
1
2
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3
4
5
6
7
8
9
1
4.2
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4.4
4.6
4.8
5
5.2
5.4
5.6
Genetic Algorithm Results for
EUV Image from August 11, 2001
Original
With Noise Removal
n ps  (10 gh  1)  1000L4.5
46.387 
 
  L 


h  1  

  L pp 

 




- 1.0431
1422UT
Derived Densities
g  0.79 L  x
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Masked Image
Tomographic Algebraic
Reconstruction Technique (ART)
• Volume Reconstruction
– Back-projection
• Methodology:
1. Build 3D Grid
2. Trace Pixel Beams through Grid
a. Find Sampled Voxels
3. Construct Integration (Summation) Formulae
4. Solve Formulae -> Generate Density Volume
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Reconstruction: Outline
0
10
0
P1
P2
7
V(P1) = a1V2,0 + a2V2,1 + a3V3,2 + … + a10V3,10
Solve:
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Let’s Get Back to May 24, 2000
and Reduced Plasma in Outer PS
IMAGE ENA and EUV Observations
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What Does Physical Modeling Show?
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HENA
EUV
RC
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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
February 6, 2001
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