inversion techniques for recovering DEMs Iain Hannah Eduard Kontar amp Lauren Braidwood University of Glasgow UK Introduction amp Motivation Current methods of recovering Differential Emission Measures DEMsT from multifilter data are not satisfactory ID: 499519
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Slide1
Regularized inversion techniques for recovering DEMs
Iain Hannah
,
Eduard Kontar & Lauren Braidwood
University of Glasgow, UKSlide2
Introduction & Motivation
Current methods of recovering Differential Emission Measures DEMs(T) from multi-filter data are not satisfactory
Ratio methods, Spine forward fitting
Model assumptions, Slow, Poor error analysisInstead propose to use Regularised InversionUsed in RHESSI software to invert counts to electronsComputationally fastNo model assumptionReturns x and y errors: so and Applied this to XRT simulated and real data, SDO/AIA simulated dataStill some issues/optimisations neededAlso beginning to work on applying this to EIS with P. Young (NRL)
2Slide3
DEM: What is the problem?
To find the line of sight
for
[cm-5K-1] is to solve the system of linear equations
This problem is ill-posed The system is underdetermined and the system of linear equations has no unique solution (Craig & Brown 1986
).
Solve via
Ratio Method: assume isothermal, divide Forward Fitting: assume model (i.e. spline) and iterateInversion: Try to invert/solve the above equation
3
Data observed through
filter
Temperature response of filter, in total
Noise
DEM for each temperature
Slide4
Regularised Inversion
Based on
Tikhonov
RegularisationRHESSI implementation by Kontar et al. 2004Applies a constraint to the recast problem to avoid noise amplification, resulting in following least squares problem to solve is the constraint matrix, a “guess” solutionSolved via Generalized SVD is the regularized inverse
Error: Difference between true and our solution
4
Temperature resolution
(x error) from
Noise propagation (y error)Slide5
XRT Filter Response
Added complications:
With simulated DEM do not know duration so error estimate tricky
Time dependent surface contamination on XRT CCDWith real data do not get all filters & saturated pixels
515 possible filter combinationsSlide6
XRT: Simulated DEM
Using all filter combinations and 12-Nov-2006 (pre-contamination)
6
Ratio Method
Forward Fit
Forward Fit MC Errors
Regularized InversionSlide7
XRT: Simulated DataMore simulated examples, still all filters combinationsTwo Gaussians
Fainter source
7Slide8
XRT: Simulated DataNow using more realistic filter combinations and durations
8
Same combinations as
Schmelz
et al. 2009(XRT data tricky….
)
Same combinations as
Reeves & Weber 2009(XRT data on next slide)Slide9
XRT: 10-Jul-07 13:10
7 filter combinations of post flare loops (C8 12:35UT)
Summed over indicated region of maps
Produces single per map 9Slide10
SDO/AIA Temperature ResponseVery preliminary but huge potentialNot sure if temperature responses are correct
Regularized Inversion working but some issues…..
10Slide11
Conclusions & Future Work Regularized Inversion provides a fast, model independent way of recovering a DEM with error estimates in both T and DEM
Though some bugs to
sort out
With XRT tricky because of temperature response, contaminations and available dataSDO/AIA looks very promisingThough some bugs to sort out in regularized inversion implementationEIS should also provide some useful dataAwaiting temperature responses from Peter YoungNo doubt there will be bugs to sort out…..11