Doug Nychka, CISL Sarah Gibson, HAO Kevin Dalmasse, HAO, CISL - - PowerPoint PPT Presentation

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Jul 09, 2023 930 likes •1.2k views

Doug Nychka, CISL Sarah Gibson, HAO Kevin Dalmasse, HAO, CISL Variations over time Flares CMEs Small-scale variation Corona Hydrogen ~ 91% Helium ~ 8.7% Oxygen ~ .078% Carbon ~ .043% Silicon ~ .0045%

SLIDE 1

Doug Nychka, CISL Sarah Gibson, HAO Kevin Dalmasse, HAO, CISL

SLIDE 2

Variations over time

Flares
CMEs
Small-scale variation

SLIDE 3

Corona

Hydrogen ~ 91%
Helium ~ 8.7%
Oxygen ~ .078%
Carbon ~ .043%
Silicon ~ .0045%
Iron ~ .0030%

SLIDE 4

What we have to work with:

White-light images
2-D images at different angles
Projection on the “plane of sky”

(POS defined by observer’s location)

SLIDE 5

Optically Thin Optically Thick

SLIDE 6

Sun Corona Us

Brightness Electron Density Scattering

View from north pole Plane of Sky

SLIDE 7

Tomography

The reconstruction of an object

f N dimensions through a series
f M-dimensional slices or
bservations where M < N.

Examples:

MRI
Ocean Acoustic Tomography
Quantum State Tomography

SLIDE 8

Radial Basis Functions

Basis vectors spanning a vector space Sines and cosines describing a function

Combination of functions X constants

SLIDE 9

3D Lattice

Spatial Dimensions “radius” defined by α

SLIDE 10

Basis Functions

Basis function node location Point in space Value of basis function Distance in normalized space α = “radius” of influence

SLIDE 11

x (points in space) b (node locations) b (node locations)

Looking down from north pole (polar plot)

SLIDE 12

Basis Functions

Integral and Sum Form

Kth line of sight

SLIDE 13

Matrix Form

SLIDE 14

Major algorithms in program

Determine LOS sample points
Find basis functions in range
Compute integral

Computing A

SLIDE 15

Determining LOS sample points

View from north pole

SLIDE 16

Find Basis Functions in Range

Radial Polar

SLIDE 17

1. Can invert pB to get c, and thus Ne
2. Allows us to check accuracy of the modeling method
Model with known density
Get c coefficients
Use c coefficients to get pB
Do inversion with pB to get new set of c coefficients (c*)
Compare c to c*
Minimize:

SLIDE 18

Ground truth

Reconstructed density with 24522 basis functions

Step 1: Model with known density Step 2: Obtain c coefficients

SLIDE 19

Step 3: Use c coefficients to get pB

SLIDE 20

Step 4: Do inversion with pB to get new set of c coefficients (c*)

426 Basis Functions 12 Viewing angles 100 LOS per angle 10873 Basis Functions 18 Viewing angles 360 LOS per angle 24522 Basis Functions 30 Viewing angles 400 LOS per angle

SLIDE 21

Mean square error: 3.1 Average error: -.27 Mean square error: .24 Average error: .0017 Mean square error: .012 Average error: -.00014

SLIDE 22

Predictive Science Model

Boundary-driven model
Solve through MHD equations
Provides density at all points
Datacube available for each

solar rotation (chosen to match data)

View from Earth

SLIDE 23

Mean square error: 1.01 e8 Average error: -2.6 e6

View from north pole

SLIDE 24

Final Milestone

Applying our method to actual data Completed Future Work

Some assessment of accuracy
Data Collection
Program to build A-matrix
Finish 2D testing
Extend testing to three dimensions
Finish R-C interface
Perform method with real data
Consider further improvements (?)

View from Earth (pB)