44 research outputs found
The influence of noise sources on cross-correlation amplitudes
We use analytical examples and asymptotic forms to examine the mathematical
structure and physical meaning of the seismic cross correlation measurement. We
show that in general, cross correlations are not Green's functions of medium,
and may be very different depending on the source distribution. The modeling of
noise sources using spatial distributions as opposed to discrete collections of
sources is emphasized. When stations are illuminated by spatially complex
source distributions, cross correlations show arrivals at a variety of time
lags, from zero to the maximum surface-wave arrival time. Here, we demonstrate
the possibility of inverting for the source distribution using the energy of
the full cross-correlation waveform. The interplay between the source
distribution and wave attenuation in determining the functional dependence of
cross correlation energies on station-pair distance is quantified. Without
question, energies contain information about wave attenuation. However, the
accurate interpretation of such measurements is tightly connected to the
knowledge of the source distribution.Comment: 19 pages, 17 figures; Geophysical Journal Internationa
Measurements and Kernels for Source-Structure Inversions in Noise Tomography
Seismic noise cross correlations are used to image crustal structure and
heterogeneity. Typically, seismic networks are only anisotropically illuminated
by seismic noise, a consequence of the non-uniform distribution of sources.
Here, we study the sensitivity of such a seismic network to structural
heterogeneity in a 2-D setting. We compute finite-frequency cross-correlation
sensitivity kernels for travel-time, waveform-energy and waveform-difference
measurements. In line with expectation, wavespeed anomalies are best imaged
using travel times and the source distribution using cross-correlation
energies. Perturbations in attenuation and impedance are very difficult to
image and reliable inferences require a high degree of certainty in the
knowledge of the source distribution and wavespeed model (at least in the case
of transmission tomography studied here). We perform single-step Gauss-Newton
inversions for the source distribution and the wavespeed, in that order, and
quantify the associated Cram\'{e}r-Rao lower bound. The inversion and
uncertainty estimate are robust to errors in the source model but are sensitive
to the theory used to interpret of measurements. We find that when classical
source-receiver kernels are used instead of cross-correlation kernels, errors
appear in the both the inversion and uncertainty estimate, systematically
biasing the results. We outline a computationally tractable algorithm to
account for distant sources when performing inversions.Comment: 19 pages, 12 figures, Geophysical Journal Internationa
Probing Depth Variations of Solar Inertial Modes through Normal Mode Coupling
Recently discovered inertial waves, observed on the solar surface, likely
extend to the deeper layers of the Sun. Utilizing helioseismic techniques, we
explore these motions, allowing us to discern inertial-mode eigenfunctions in
both radial and latitudinal orientations. We analyze years of space-based
observations () taken by the Helioseismic and Magnetic Imager
(HMI) onboard the Solar dynamic observatory (SDO) using normal-mode coupling.
Coupling between same and different-degree acoustic modes and different
frequency bins are measured in order to capture the various length scales of
inertial modes. We detect inertial modes at high latitude with azimuthal order
and frequency nHz. This mode is present in the entire
convection zone. The presence of Rossby modes may be seen down to a depth of
and the Rossby signal is indistinguishable from noise below
that depth for high azimuthal order. We find that the amplitudes of these modes
increase with depth down to around and decrease below that
depth. We find that the latitudinal eigenfunctions of Rossby modes deviate from
sectoral spherical harmonics if we use a similar approach as adopted in earlier
studies. We found that spatial leakage and even pure noise in the measurements
of non-sectoral components can also explain the above-mentioned characteristics
of the latitudinal eigenfunctions. This realization underscores the necessity
for careful interpretation when considering the latitudinal eigenfunctions of
Rossby modes. Exploring the depth-dependent characteristics of these modes will
enable us to capture interior dynamics distinctly, separate from p-mode
seismology.Comment: 17 pages, 9 figures, submitted to Ap
A spectral solver for solar inertial waves
Inertial waves, which are dominantly driven by the Coriolis force, likely
play an important role in solar dynamics, and additionally, provide a window
into the solar subsurface. The latter allows us to infer properties that are
inaccessible to the traditional technique of acoustic-wave helioseismology.
Thus, a full characterization of these normal modes holds promise in enabling
the investigation of solar subsurface dynamics. In this work, we develop a
spectral eigenvalue solver to model the spectrum of inertial waves in the Sun.
We model the solar convection zone as an anelastic medium, and solve for the
normal modes of the momentum and energy equations. We demonstrate that the
solver can reproduce the observed mode frequencies and line-widths well, not
only of sectoral Rossby modes, but also the recently observed high-frequency
inertial modes. In addition, we believe that the spectral solver is a useful
contribution to the numerical methods on modeling inertial modes on the Sun.Comment: 6 Figures, accepted for publication in ApJ
Sub-Wavelength Resolution Imaging of the Solar Deep Interior
We derive expectations for signatures in the measured travel times of waves
that interact with thermal anomalies and jets. A series of numerical
experiments that involve the dynamic linear evolution of an acoustic wave field
in a solar-like stratified spherical shell in the presence of fully 3D
time-stationary perturbations are performed. The imprints of these interactions
are observed as shifts in wave travel times, which are extracted from these
data through methods of time-distance helioseismology \citep{duvall}. In
situations where at least one of the spatial dimensions of the scatterer was
smaller than a wavelength, oscillatory time shift signals were recovered from
the analyses, pointing directly to a means of resolving sub-wavelength
features. As evidence for this claim, we present analyses of simulations with
spatially localized jets and sound-speed perturbations. We analyze 1 years'
worth solar observations to estimate the noise level associated with the time
differences. Based on theoretical estimates, Fresnel zone time shifts
associated with the (possible) sharp rotation gradient at the base of the
convection zone are of the order 0.01 - 0.1 s, well below the noise level that
could be reached with the currently available amount of data ( s
with 10 yrs of data).Comment: Accepted, ApJ; 17 pages, 12 figure
Seismic Halos Around Active Regions: An MHD Theory
Comprehending the manner in which magnetic fields affect propagating waves is
a first step toward constructing accurate helioseismic models of active region
sub-surface structure and dynamics. Here, we present a numerical method to
compute the linear interaction of waves with magnetic fields embedded in a
solar-like stratified background. The ideal Magneto-Hydrodynamic (MHD)
equations are solved in a 3-dimensional box that straddles the solar
photosphere, extending from 35 Mm within to 1.2 Mm into the atmosphere. One of
the challenges in performing these simulations involves generating a
Magneto-Hydro-Static (MHS) state wherein the stratification assumes horizontal
inhomogeneity in addition to the strong vertical stratification associated with
the near-surface layers. Keeping in mind that the aim of this effort is to
understand and characterize linear MHD interactions, we discuss a means of
computing statically consistent background states. Power maps computed from
simulations of waves interacting with thick flux tubes of peak photospheric
field strengths 600 G and 3000 G are presented. Strong modal power reduction in
the `umbral' regions of the flux tube enveloped by a halo of increased wave
power are seen in the simulations with the thick flux tubes. These enhancements
are also seen in Doppler velocity power maps of active regions observed in the
Sun, leading us to propose that the halo has MHD underpinnings.Comment: submitted to Ap