d. gallagher, m. adrian, j. green, c. gurgiolo, g. khazanov, a. king, m. liemohn, t. newman, j....
TRANSCRIPT
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”
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
One Kind of Hand Analysis
• Identify feature
• Trace boundaries
• Estimate density structure, simulate image, and compare
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
T1
T2 T3
T4
T
Same Approach Can be UsedGenerally On an Event Basis
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
RPI Inversion for June 10, 2001
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Guided & Direct Echoes @ 02:38:57
Guided echo trace from local hemisphere
Direct echo trace from local hemisphere
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Guided & Direct Echoes @ 02:52:57
Guided echo trace from local hemisphere
Direct echo trace from local hemisphere
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Guided & Direct Echoes @ 02:54:56
Guided echo trace from local hemisphere
Direct echo trace from local hemisphere
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
RPI Derived Field Aligned Density Distributions
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Inversion of EUV Images
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Genetic Algorithm:Development and Application of
Impulse Response Matrix
• Description of Problem
• Development of Impulse Response Matrix
• Matrix Inversion Method
• Genetic Algorithm Approach
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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.
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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.)
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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.
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Reconstruction: Outline0 10
0
7
P1P2
V(P1) = a1V2,0 + a2V2,1 + a3V3,2 + … + a10V3,10
Solve:
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
Let’s Get Back to May 24, 2000and Reduced Plasma in Outer PS
IMAGE ENA and EUV Observations
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
What Does Physical Modeling Show?
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
HENA EUV
RC
February 6, 2001 Yosemite 2002: Magnetospheric Imaging
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