image euv & rpi derived distributions of plasmaspheric plasma and plasmaspheric modeling
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
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
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
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