A COMMENT ON THE RELATIONSHIP BETWEEN THE MODAL AND TIME-DISTANCE FORMULATIONS OF LOCAL HELIOSEISMOLOGY

The relationship between the time-distance and modal-decomposition app roaches to solar active region seismology is clarified through the con sideration of the oscillations of a plane-parallel, isentropic polytro pe. It is demonstrated by direct construction that a wave packet forme d through the superposition of neighboring p-modes interferes construc tively along a ray bundle that follows the appropriate WKBJ ray path o btained by using the eikonal approximation. Because the actual power e nvelope of the solar 5 minute oscillations restricts the excited p-mod es to rather low radial orders, the ray bundles are diffuse and sample portions of the solar envelope that are some approximate to 10-30 Mm distant from the nominal WKBJ ray path. This behavior is consistent wi th the fact that the eikonal approximation becomes valid only in the l imiting case of large radial orders (n much greater than 1). The p-mod e wave packets that are isolated by employing the time-distance method s must therefore be described either as a superposition of individual p-modes (a wave packet), or as a sum of ray paths (a ray bundle), depe nding upon which representation proves to be optimal for the given cir cumstances.