Current Status and Future Prospects of High-Degree Ridge Fitting

1
Current Status and Future Prospects of
High-Degree Ridge Fitting

• Johann Reiter, Edward Rhodes, and Jesper Schou
• HMI Science Team Meeting
• Monterey, CA
• February 16, 2006

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Recent Progress in Ridge-Fitting

• We have Made Progress in the Fitting of both
  un-averaged and m-averaged power spectra.
• Un-averaged spectra can now be fit for degrees
  between 45 and 1000.
• Averaged spectra now include n-leaks in fitted
  profile and have been fit up to degrees of 1467.
• Frequency errors have been greatly diminished in
  the fitting of un-averaged spectra.

3
Overview of Current Ridge-Fitting Methods

• The method which fits m-averaged spectra is our
  Windowed, Multiple-Peak, Averaged-Spectrum
  (WMLTP) Method
• This method requires that splitting coefficients
  be specified in the generation of the m-averaged
  spectra
• This method employs m-averaged leakage matrices
• The current version uses wide leakage matrices
  corrected for latitudinal differential rotation
• This method can use symmetric or asymmetric
  profiles
• This method produces frequencies, widths,
  amplitudes, asymmetries and their associated
  errors

4
Differential Rotation Correction Requires Input
of Rate Coefficients
5
Overview of Current Ridge-Fitting Methods (cont.)

• The method which fits un-averaged spectra is our
  Multiple-Peak, Tesseral-Spectrum (MPTS) Method
• This method employs zonal, sectoral, and tesseral
  power spectra rather than Fourier Transforms
• This method employs wide, unaveraged leakage
  matrices which are also corrected for latitudinal
  differential rotation
• This method can also employ symmetric or
  asymmetric profiles
• This method produces frequencies, widths,
  amplitudes, asymmetries and their associated
  errors
• This method also produces rotational
  frequency-splitting coefficients and their
  associated errors

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Problems which Affect Both WMLTP and MPTS Methods
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Recent Improvements in WMLTP Fitted Profiles
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Examples of WMLTP Method Fits for Modes and Ridges
9
Set of WMLTP Frequencies from 5.7-Day MDI Time
Series Using Nigam and Kosovichev Asymmetric
Profile for April 7-12, 2002
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Chronological History of Multiple-Peak
Tesseral-Spectrum Method Production Runs
Using JPL SGI Origin 2000 Supercomputers
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Recent Comparison of Frequencies Computed from
m-averaged and Un-averaged Power Spectra Using
WMLTP and MPTS Methods
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Recent Improvements in Rotational Splitting
Coefficients Computed Using MPTS Method
13
Rotational Inversion of High-Degree P-Mode
Splitting Coefficients for Degrees up to 500
Computed Using Multiple-Peak Tesseral-Spectrum
Fitting Method (Dec. 2004 run)
Inner Turning-Point Radius Dependence of Newer
Set Of P-Mode Splitting Coefficients Computed
Using Multiple-Peak Tesseral-Spectrum Method
for Degrees up to 1000 (July 2005 run)
14
Improvements in MPTS Frequencies Between 2001
and 2005
Reduction in MPTS Frequency Errors Between 2001
and 2005
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Improvements Currently Underway in
WMLTP Code

• Non-linear expansions of amplitude and widths of
  sidelobes versus degree must be completed
• Inclusion of n-leaks in theoretical profiles must
  be completed
• Code needs to be ported to Stanford pipeline

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Improvements Currently Underway
in MPTS Code

• Non-linear expansions of frequency, amplitude,
  and width of sidelobes versus degree must be
  implemented
• N-leaks must be included in theoretical profiles
• Theoretical Profiles Must be Convolved with
  Temporal Window Functions
• Adjustment of input values must be automated
• Code needs to be ported to Stanford pipeline

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Future Issues for Both WMLTP and MPTS
Methods

• Un-averaged power spectra must be re-computed
  with corrections for 1) improved model of MDI
  instrumental distortion, 2) a fixed error in MDI
  position angle, and 3) possible errors in the
  Carrington rotation elements
• Un-averaged leakage matrices need to have
  corrections included for instrumental
  point-spread function and finite pixel size
• Woodards 1989 theory for distortion from
  differential rotation needs to be refined
• An improved asymmetric profile formula is
  essential

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Conclusions

• High-degree modes are fundamental to improving
  our knowledge of the solar interior
• Current local helioseismic techniques are not
  valid substitutes for fits of spherical harmonic
  power spectra
• We have demonstrated two fitting methods which
  can fit both narrow modal peaks and broad power
  ridges
• We will soon be able to test MDI and GONG Fits
• Both of these methods hold great promise for use
  in the HMI Software Pipeline

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Manual Selection is Currently Required in Choice
of Input Parameters