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Register a new userComparison of Travel-Time and Amplitude Measurements for Deep-Focusing Time--Distance Helioseismology
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The purpose of deep-focusing time--distance helioseismology is to construct seismic measurements that have a high sensitivity to the physical conditions at a desired target point in the solar interior. With this technique, pairs of points on the solar surface are chosen such that acoustic ray paths intersect at this target (focus) point. Considering acoustic waves in a homogeneous medium, we compare travel-time and amplitude measurements extracted from the deep-focusing cross-covariance functions. Using a single-scattering approximation, we find that the spatial sensitivity of deep-focusing travel times to sound-speed perturbations is zero at the target location and maximum in a surrounding shell. This is unlike the deep-focusing amplitude measurements, which have maximum sensitivity at the target point. We compare the signal-to-noise ratio for travel-time and amplitude measurements for different types of sound-speed perturbations, under the assumption that noise is solely due to the random excitation of the waves. We find that, for highly localized perturbations in sound speed, the signal-to-noise ratio is higher for amplitude measurements than for travel-time measurements. We conclude that amplitude measurements are a useful complement to travel-time measurements in time--distance helioseismology.
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A key component of solar interior dynamics is the meridional circulation (MC), whose poleward component in the surface layers has been well observed. Time-distance helioseismic studies of the deep structure of MC, however, have yielded conflicting inferences. Here, following a summary of existing results we show how a large center-to-limb systematics (CLS) in the measured travel times of acoustic waves affect the inferences through an analysis of frequency dependence of CLS, using data from the Helioseismic and Doppler Imager (HMI) onboard Solar Dynamics Observatory (SDO). Our results point to the residual systematics in travel times as a major cause of differing inferences on the deep structure of MC.
Time-distance helioseismology has shown that f-mode travel times contain information about horizontal flows in the Sun. The purpose of this study is to provide a simple interpretation of these travel times. We study the interaction of surface-gravity waves with horizontal flows in an incompressible, plane-parallel solar atmosphere. We show that for uniform flows less than roughly 250 m s$^{-1}$, the travel-time shifts are linear in the flow amplitude. For stronger flows, perturbation theory up to third order is needed to model waveforms. The case of small-amplitude spatially-varying flows is treated using the first-order Born approximation. We derive two-dimensional Fr{e}chet kernels that give the sensitivity of travel-time shifts to local flows. We show that the effect of flows on travel times depends on wave damping and on the direction from which the observations are made. The main physical effect is the advection of the waves by the flow rather than the advection of wave sources or the effect of flows on wave damping. We compare the two-dimensional sensitivity kernels with simplified three-dimensional kernels that only account for wave advection and assume a vertical line of sight. We find that the three-dimensional f-mode kernels approximately separate in the horizontal and vertical coordinates, with the horizontal variations given by the simplified two-dimensional kernels. This consistency between quite different models gives us confidence in the usefulness of these kernels for interpreting quiet-Sun observations.
In time-distance helioseismology, information about the solar interior is encoded in measurements of travel times between pairs of points on the solar surface. Travel times are deduced from the cross-covariance of the random wave field. Here we consider travel times and also products of travel times as observables. They contain information about e.g. the statistical properties of convection in the Sun. The basic assumption of the model is that noise is the result of the stochastic excitation of solar waves, a random process which is stationary and Gaussian. We generalize the existing noise model (Gizon and Birch 2004) by dropping the assumption of horizontal spatial homogeneity. Using a recurrence relation, we calculate the noise covariance matrices for the moments of order 4, 6, and 8 of the observed wave field, for the moments of order 2, 3 and 4 of the cross-covariance, and for the moments of order 2, 3 and 4 of the travel times. All noise covariance matrices depend only on the expectation value of the cross-covariance of the observed wave field. For products of travel times, the noise covariance matrix consists of three terms proportional to $1/T$, $1/T^2$, and $1/T^3$, where $T$ is the duration of the observations. For typical observation times of a few hours, the term proportional to $1/T^2$ dominates and $Cov[tau_1 tau_2, tau_3 tau_4] approx Cov[tau_1, tau_3] Cov[tau_2, tau_4] + Cov[tau_1, tau_4] Cov[tau_2, tau_3]$, where the $tau_i$ are arbitrary travel times. This result is confirmed for $p_1$ travel times by Monte Carlo simulations and comparisons with SDO/HMI observations. General and accurate formulae have been derived to model the noise covariance matrix of helioseismic travel times and products of travel times. These results could easily be generalized to other methods of local helioseismology, such as helioseismic holography and ring diagram analysis.
A time-distance helioseismic technique, similar to the one used by Ilonidis et al (2011), is applied to two independent numerical models of subsurface sound-speed perturbations to determine the spatial resolution and accuracy of phase travel time shift measurements. The technique is also used to examine pre-emergence signatures of several active regions observed by the Michelson Doppler Imager (MDI) and the Helioseismic Magnetic Imager (HMI). In the context of similar measurements of quiet sun regions, three of the five studied active regions show strong phase travel time shifts several hours prior to emergence. These results form the basis of a discussion of noise in the derived phase travel time maps and possible criteria to distinguish between true and false positive detection of emerging flux.
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