A New Technique for Bridging the Gap Between

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 of Inclusion of High-Degree P-Mode Frequencies for Degrees up to 1467 Green Kernels and Sound-Speed Inversion Were Computed Using Only 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 AR 9901

Set of Global-fit Frequencies from 5. 7 -Day MDI Time Series Using Nigam and Kosovichev Asymmetric Profile for April 7 -12, 2002 Corresponding Set of Ring-fit Frequencies Computed from Same 5. 7 -Day Time Series Centered on AR 9901

Differences Between Global-fit and Ring-fit Frequencies for April 7 -12, 2002 Error Magnification of Ring-fit Frequencies Relative to Global-fit Frequencies for April 7 -12, 2002

Comparison of Global-fit Frequencies with Theoretical Frequencies Comparison of Ring-fit Frequencies with Theoretical Frequencies

Differences Between Active And Quiet Global-fit Frequencies Differences Between Active And Quiet Ring-fit Frequencies

Two Examples of Regions of Tighter-Apodization Applied to Same Pair of Active and Quiet Regions Quiet Region NOAA AR 9901

Differences in Two Sets of Frequencies Computed Using 0. 5 Solar Radius Inner Apodization Region and 4 -day Time Series Instead of 5. 7 -day Time Series Differences in Two Sets of Original 5. 7 -day Ring-fit Frequencies (regression line slope is 14 times larger than at left)

Comparison of Error Magnifications Of Ring-fit (Upper Curve) and Tighter-Apodization (Lower Curves) Methods of Frequency Computation Comparison of Ratios of Active-Quiet Frequency Differences Divided by Their Errors for Ring-fits (Upper Curve) and Tighter-Apodization (Lower Curves)

Comparison of Radial Profiles of Sound-Speed and Adiabatic Exponent Structural Inversions Using Active-Quiet Frequency Differences From Ring-fits For AR 9901 and Tighter. Apodization Method

Rotational Inversion of High-Degree P-Mode Splitting Coefficients for Degrees up to 500 Computed Using Multiple-Peak Tesseral-Spectrum Fitting Method 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

Planned Extension of Tighter-Apodization for Increased Sensitivity Elliptical Region Surrounding NOAA AR 9901 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