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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” 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 Channel Matches as Observed, but Outer Plasmaspheric Densities too High February 6, 2001 Yosemite 2002: Magnetospheric Imaging Exponential Decrease with L-Shell Outside Channel Approximates Observation February 6, 2001 Yosemite 2002: Magnetospheric Imaging Same Approach Can be Used Generally On an Event Basis T5 T1 T4 T2 February 6, 2001 T3 Yosemite 2002: Magnetospheric Imaging TRACE 2 TRACE 1 Model Model Data Data TRACE 4 TRACE 3 TRACE 5 Model Model Data Data February 6, 2001 In this Case, Model Results Work Fairly Well Yosemite 2002: Magnetospheric Imaging Model Data 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 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. February 6, 2001 Crossing a Particular L Shell. 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] 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 February 6, 2001 3 4 5 6 7 8 xLmax = 9R Non-uniform grid spacing # of Grid points = 18 9 -2 1 2 Yosemite 2002: Magnetospheric Imaging 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.) 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 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 February 6, 2001 3 4 5 6 7 8 9 1 4.2 Yosemite 2002: Magnetospheric Imaging 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 February 6, 2001 3 4 5 6 7 8 9 1 4.2 Yosemite 2002: Magnetospheric Imaging 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 gh 1) 1000L4.5 46.387 L h 1 L pp - 1.0431 1422UT Derived Densities g 0.79 L x February 6, 2001 Yosemite 2002: Magnetospheric Imaging 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 February 6, 2001 Yosemite 2002: Magnetospheric Imaging Reconstruction: Outline 0 10 0 P1 P2 7 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, 2000 and 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 February 6, 2001 Yosemite 2002: Magnetospheric Imaging