The Linear Sensitivity of Helioseismic Ring Diagrams to Local Flows

Ring-diagram analysis is a technique of local helioseismology used to infer plasma flows in the solar convection zone which generates intermediate data products known as ring-fitting parameters. Knowing the sensitivity of ring- fittingparameterstoactualflowsintheSunisimportant for interpretingthesemeasurements.Workinginplane-parallel geometry, we compute the linear sensitivity of ring-fitting parameters to small changes inthe local power spectrum and thencomputethesensitivityofthepowerspectrumtotime-independentweaklocalflows.Wecombinethesetworesults to obtain the three-dimensional Frechet kernels that give the linear sensitivity of ring-fitting parameters to both vertical andhorizontallocalmassflows.Wefindthatringmeasurementsareessentiallyonlysensitivetoflowsthatarewithinthe spatialregionforwhichtheringdiagramiscomputed.Inaddition,wefindthatthedepthdependenceofthesensitivityis essentially given bythe modekineticenergydensity, ashas traditionally beenassumed.We showthatthe exact formof the sensitivity of ring measurements depends on the details of the fitting procedure.