A New Technique for Bridging the Gap Between Global and Local Helioseismology

Edward Rhodes, Sarbani Basu, Rick Bogart, Sasha Kosovichev, Johann

Reiter, Thad Szabo, and Jesper Schou

HMI Science Team Meeting Monterey, CA 2/14/06

Red Kernels and Sound-Speed Inversion Show Importance ofInclusion of High-Degree P-Mode Frequencies for Degrees upto 1467

Green Kernels and Sound-Speed Inversion Were Computed UsingOnly Intermediate-Degree P-Mode Frequencies

Basu, Antia, and Bogart (2004) Compared Active and Quiet Sets of Ring-Diagram Frequencies Using 5.7-Day MDI Time Series

Quiet Region NOAA AR9901

Set of Global-fitFrequencies from 5.7-DayMDI Time Series UsingNigam and KosovichevAsymmetric Profile forApril 7-12, 2002

Corresponding Set ofRing-fit FrequenciesComputed from Same 5.7-DayTime Series Centered onAR9901

Differences BetweenGlobal-fit and Ring-fitFrequencies for April 7-12, 2002

Error Magnification ofRing-fit FrequenciesRelative to Global-fitFrequencies for April7-12, 2002

Comparison of Global-fitFrequencies with TheoreticalFrequencies

Comparison of Ring-fitFrequencies with TheoreticalFrequencies

Differences Between ActiveAnd Quiet Global-fit Frequencies

Differences Between ActiveAnd Quiet Ring-fit Frequencies

Two Examples of Regions of Tighter-Apodization Applied to Same Pair of Active and Quiet Regions

Quiet Region NOAA AR9901

Differences in Two Sets ofFrequencies Computed Using0.5 Solar Radius Inner ApodizationRegion and 4-day Time Series Instead of 5.7-day Time Series

Differences in TwoSets of Original 5.7-day Ring-fit Frequencies(regression line slope is14 times larger than at left)

Comparison of Error MagnificationsOf Ring-fit (Upper Curve) and Tighter-Apodization (Lower Curves)Methods of Frequency Computation

Comparison of Ratios ofActive-Quiet FrequencyDifferences Divided byTheir Errors for Ring-fits(Upper Curve) and Tighter-Apodization (LowerCurves)

Comparison ofRadial Profiles ofSound-Speedand AdiabaticExponent StructuralInversions UsingActive-QuietFrequency Differences From Ring-fits For AR9901 andTighter-ApodizationMethod

Rotational Inversion of High-Degree P-Mode Splitting Coefficients forDegrees up to 500 ComputedUsing Multiple-Peak Tesseral-Spectrum Fitting Method

Inner Turning-Point RadiusDependence of Newer SetOf P-Mode Splitting CoefficientsComputed Using Multiple-PeakTesseral-Spectrum Method forDegrees up to 1000

Planned Extension of Tighter-Apodization for Increased Sensitivity

Elliptical Region Surrounding NOAAAR9901 for 4-Day Time Interval

Conclusions Use of Spherical Harmonic Decompositions with Tighter-

Apodization Can Result in Substantial Increases in Sensitivity of P-Mode Frequencies to Local Conditions Without the Increases in Formal Frequency Errors and Mode-to-Mode Scatter that is Associated with the Ring-Diagram Method

Further Tightening of Apodization Regions Beyond Those Tried Thus Far Are Still Required to Approach Current Sensitivity of Ring-fit Frequencies to Local Conditions

Both Structural and Rotational Inversions Are Possible with the Tighter-Apodization Technique