26,828 research outputs found
Full Waveform Inversion for Time-Distance Helioseismology
Inferring interior properties of the Sun from photospheric measurements of
the seismic wavefield constitutes the helioseismic inverse problem. Deviations
in seismic measurements (such as wave travel times) from their fiducial values
estimated for a given model of the solar interior imply that the model is
inaccurate. Contemporary inversions in local helioseismology assume that
properties of the solar interior are linearly related to measured travel-time
deviations. It is widely known, however, that this assumption is invalid for
sunspots and active regions, and likely for supergranular flows as well. Here,
we introduce nonlinear optimization, executed iteratively, as a means of
inverting for the sub-surface structure of large-amplitude perturbations.
Defining the penalty functional as the norm of wave travel-time
deviations, we compute the the total misfit gradient of this functional with
respect to the relevant model parameters %(only sound speed in this case) at
each iteration around the corresponding model. The model is successively
improved using either steepest descent, conjugate gradient, or quasi-Newton
limited-memory BFGS. Performing nonlinear iterations requires privileging
pixels (such as those in the near-field of the scatterer), a practice not
compliant with the standard assumption of translational invariance.
Measurements for these inversions, although similar in principle to those used
in time-distance helioseismology, require some retooling. For the sake of
simplicity in illustrating the method, we consider a 2-D inverse problem with
only a sound-speed perturbation.Comment: 24 pages, 10 figures, to appear in Ap
Directional Time-Distance Probing of Model Sunspot Atmospheres
A crucial feature not widely accounted for in local helioseismology is that
surface magnetic regions actually open a window from the interior into the
solar atmosphere, and that the seismic waves leak through this window, reflect
high in the atmosphere, and then re-enter the interior to rejoin the seismic
wave field normally confined there. In a series of recent numerical studies
using translation invariant atmospheres, we utilised a "directional
time-distance helioseismology" measurement scheme to study the implications of
the returning fast and Alfv\'en waves higher up in the solar atmosphere on the
seismology at the photosphere (Cally & Moradi 2013; Moradi & Cally 2014). In
this study, we extend our directional time-distance analysis to more realistic
sunspot-like atmospheres to better understand the direct effects of the
magnetic field on helioseismic travel-time measurements in sunspots. In line
with our previous findings, we uncover a distinct frequency-dependant
directional behaviour in the travel-time measurements, consistent with the
signatures of MHD mode conversion. We found this to be the case regardless of
the sunspot field strength or depth of its Wilson depression. We also isolated
and analysed the direct contribution from purely thermal perturbations to the
measured travel times, finding that waves propagating in the umbra are much
more sensitive to the underlying thermal effects of the sunspot.Comment: 9 pages, 8 figures, accepted for publication in Monthly Notices of
the Royal Astronomical Society Main Journa
Imaging the Solar Tachocline by Time-Distance Helioseismology
The solar tachocline at the bottom of the convection zone is an important
region for the dynamics of the Sun and the solar dynamo. In this region, the
sound speed inferred by global helioseismology exhibits a bump of approximately
0.4% relative to the standard solar model. Global helioseismology does not
provide any information on possible latitudinal variations or asymmetries
between the Northern and Southern hemisphere. Here, we develop a time-distance
helioseismology technique, including surface- and deep-focusing measurement
schemes and a combination of both, for two-dimensional tomographic imaging of
the solar tachocline that infers radial and latitudinal variations in the sound
speed. We test the technique using artificial solar oscillation data obtained
from numerical simulations. The technique successfully recovers major features
of the simplified tachocline models. The technique is then applied to SOHO/MDI
medium-l data and provides for the first time a full two-dimensional
sound-speed perturbation image of the solar tachocline. The one-dimensional
radial profile obtained by latitudinal averaging of the image is in good
agreement with the previous global helioseismology result. It is found that the
amplitude of the sound-speed perturbation at the tachocline varies with
latitude, but it is not clear whether this is in part or fully an effect of
instrumental distortion. Our initial results demonstrate that time-distance
helioseismology can be used to probe the deep interior structure of the Sun,
including the solar tachocline.Comment: accepted for publication by Ap
Probing sunspots with two-skip time-distance helioseismology
Previous helioseismology of sunspots has been sensitive to both the
structural and magnetic aspects of sunspot structure. We aim to develop a
technique that is insensitive to the magnetic component so the two aspects can
be more readily separated. We study waves reflected almost vertically from the
underside of a sunspot. Time-distance helioseismology was used to measure
travel times for the waves. Ray theory and a detailed sunspot model were used
to calculate travel times for comparison. It is shown that these large distance
waves are insensitive to the magnetic field in the sunspot. The largest travel
time differences for any solar phenomena are observed. With sufficient modeling
effort, these should lead to better understanding of sunspot structure
Generalization of the noise model for time-distance helioseismology
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 , , and , where is the duration of the
observations. For typical observation times of a few hours, the term
proportional to dominates and , where the are arbitrary travel times. This
result is confirmed for 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
Time-Distance Imaging of Solar Far-Side Active Regions
It is of great importance to monitor large solar active regions in the
far-side of the Sun for space weather forecast, in particular, to predict their
appearance before they rotate into our view from the solar east limb. Local
helioseismology techniques, including helioseismic holography and
time-distance, have successfully imaged solar far-side active regions. In this
Letter, we further explore the possibility of imaging and improving the image
quality of solar far-side active regions by use of time-distance
helioseismology. In addition to the previously used scheme with four acoustic
signal skips, a five-skip scheme is also included in this newly developed
technique. The combination of both four- and five-skip far-side images
significantly enhances the signal-to-noise ratio in the far-side images, and
reduces spurious signals. The accuracy of the far-side active region imaging is
also assessed using one whole year solar observation.Comment: 13 pages, 5 figures, accepted by ApJ Letter
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