44 research outputs found

    The influence of noise sources on cross-correlation amplitudes

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    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

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    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

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    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 88 years of space-based observations (2010−20172010 - 2017) 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 t=1t=1 and frequency ∼−80\sim -80 nHz. This mode is present in the entire convection zone. The presence of Rossby modes may be seen down to a depth of ∼0.83R⊙\sim 0.83R_\odot 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 0.92R⊙0.92 R_\odot 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

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    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

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    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 (∼0.15−0.2\sim 0.15-0.2 s with 10 yrs of data).Comment: Accepted, ApJ; 17 pages, 12 figure

    Seismic Halos Around Active Regions: An MHD Theory

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    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
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