Phase time and envelope time in time-distance analysis and acoustic imaging

Time-distance analysis and acoustic imaging are two related techniques for probing the local properties of the solar interior. In this study, we discu ss the relation of phase time and envelope time between the two techniques. The location of the envelope peak of the cross-correlation function in tim e-distance analysis is identified as the travel time of the wave packet for med by modes with the same horizontal phase velocity. The phase time of the cross-correlation function provides information on the phase change accumu lated along the wave path, including the phase change at the boundaries of the mode cavity. The acoustic signals constructed with the technique of aco ustic imaging contain both phase and intensity information. The phase of co nstructed signals can be studied by computing the crosscorrelation function between time series constructed with ingoing and outgoing waves. We use a simple theory of wave packets to obtain two predictions about the cross-cor relation function of constructed ingoing and outgoing time series. First, i f the envelope time measured in time-distance analysis is used to construct signals in acoustic imaging, the envelope time of the cross-correlation is zero. Second, the phase time of the cross-correlation is twice the differe nce between the phase time and envelope time measured in time-distance anal ysis. In this study, we use data taken with the Taiwan Oscillation Network (TON) instrument and the Michelson Doppler Imager (MDI) instrument. The ana lysis is carried out for the quiet Sun. We use the relation of envelope tim e versus distance measured in time-distance analysis to construct the acous tic signals in acoustic imaging analysis. The phase time of the cross-corre lation function of constructed ingoing and outgoing time series is twice th e difference between phase time and envelope time in time-distance analysis , as predicted. The envelope peak of the crosscorrelation function between constructed ingoing and outgoing time series is located at zero time, as pr edicted for one-bounce results at 3 mHz for all four data sets and two-boun ce results at 3 mHz for two TON data sets, but it is different from zero fo r other cases. The deviation of the envelope peak from zero has the same si gn for all these cases. The cause is not known.