980 research outputs found
Surface-wave group-delay and attenuation kernels
We derive both 3-D and 2-D FrĆ©chet sensitivity kernels for surface-wave group-delay and anelastic attenuation measurements. A finite-frequency group-delay exhibits 2-D off-ray sensitivity either to the local phase-velocity perturbation Ī“c/c or to its dispersion Ļ(ā/āĻ)(Ī“c/c) as well as to the local group-velocity perturbation Ī“C/C. This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of Ī“C/C a dubious procedure, unless the lateral variations in group velocity are extremely smooth
Ambiguity of the Moment Tensor
An earthquake on a fault separating two dissimilar materials does not have a well-defined moment density tensor. We present a complete characterization of this bimaterial ambiguity in the general case of slip on a fault in an anisotropic medium. The ambiguity can be eliminated by utilizing a potency density rather than a moment density representation of a bimaterial source
Spatiospectral concentration on a sphere
We pose and solve the analogue of Slepian's time-frequency concentration
problem on the surface of the unit sphere to determine an orthogonal family of
strictly bandlimited functions that are optimally concentrated within a closed
region of the sphere, or, alternatively, of strictly spacelimited functions
that are optimally concentrated within the spherical harmonic domain. Such a
basis of simultaneously spatially and spectrally concentrated functions should
be a useful data analysis and representation tool in a variety of geophysical
and planetary applications, as well as in medical imaging, computer science,
cosmology and numerical analysis. The spherical Slepian functions can be found
either by solving an algebraic eigenvalue problem in the spectral domain or by
solving a Fredholm integral equation in the spatial domain. The associated
eigenvalues are a measure of the spatiospectral concentration. When the
concentration region is an axisymmetric polar cap the spatiospectral projection
operator commutes with a Sturm-Liouville operator; this enables the
eigenfunctions to be computed extremely accurately and efficiently, even when
their area-bandwidth product, or Shannon number, is large. In the asymptotic
limit of a small concentration region and a large spherical harmonic bandwidth
the spherical concentration problem approaches its planar equivalent, which
exhibits self-similarity when the Shannon number is kept invariant.Comment: 48 pages, 17 figures. Submitted to SIAM Review, August 24th, 200
Tomographic inversion using -norm regularization of wavelet coefficients
We propose the use of regularization in a wavelet basis for the
solution of linearized seismic tomography problems , allowing for the
possibility of sharp discontinuities superimposed on a smoothly varying
background. An iterative method is used to find a sparse solution that
contains no more fine-scale structure than is necessary to fit the data to
within its assigned errors.Comment: 19 pages, 14 figures. Submitted to GJI July 2006. This preprint does
not use GJI style files (which gives wrong received/accepted dates).
Corrected typ
Corrections for gravitational lensing of supernovae: better than average?
We investigate the possibility of correcting for the magnification due to
gravitational lensing of standard candle sources, such as Type Ia supernovae.
Our method uses the observed properties of the foreground galaxies along the
lines-of-sight to each source and the accuracy of the lensing correction
depends on the quality and depth of these observations as well as the
uncertainties in translating the observed luminosities to the matter
distribution in the lensing galaxies. The current work is limited to cases
where the matter density is dominated by the individual galaxy halos. However,
it is straightforward to generalize the method to include also gravitational
lensing from cluster scale halos. We show that the dispersion due to lensing
for a standard candle source at z=1.5 can be reduced from about 7% to ~< 3%,
i.e. the magnification correction is useful in reducing the scatter in the Type
Ia Hubble diagram, especially at high redshifts where the required long
exposure times makes it hard to reach large statistics and the dispersion due
to lensing becomes comparable to the intrinsic Type Ia scatter.Comment: Matches accepted version, includes clarifications and additional
issues. 28 pages, 7 figures, accepted for publication in Ap
The Dwarf Starburst Host Galaxy of a Type Ia SN at z = 1.55 from CANDELS
We present VLT/X-shooter observations of a high redshift, type Ia supernova
host galaxy, discovered with HST/WFC3 as part of the CANDELS Supernova project.
The galaxy exhibits strong emission lines of Ly{\alpha}, [O II], H{\beta}, [O
III], and H{\alpha} at z = 1.54992(+0.00008-0.00004). From the emission-line
fluxes and SED fitting of broad-band photometry we rule out AGN activity and
characterize the host galaxy as a young, low mass, metal poor, starburst galaxy
with low intrinsic extinction and high Ly{\alpha} escape fraction. The host
galaxy stands out in terms of the star formation, stellar mass, and metallicity
compared to its lower redshift counterparts, mainly because of its high
specific star-formation rate. If valid for a larger sample of high-redshift SN
Ia host galaxies, such changes in the host galaxy properties with redshift are
of interest because of the potential impact on the use of SN Ia as standard
candles in cosmology.Comment: 25 pages, 8 figures. Accepted for publication in Ap
A new measure of using the lensing dispersion in high- type Ia SNe
The gravitational lensing magnification or demagnification due to large-scale
structures induces a scatter in peak magnitudes of high redshift type Ia
supernovae (SNe Ia). The amplitude of the lensing dispersion strongly depends
on that of density fluctuations characterized by the parameter.
Therefore the value of is constrained by measuring the dispersion in
the peak magnitudes. We examine how well SN Ia data will provide a constraint
on the value of using a likelihood analysis method. It is found that
the number and quality of SN Ia data needed for placing a useful constraint on
is attainable with Next Generation Space Telescope.Comment: 9 pages, 3 figures. Accepted for publication in The Astrophysical
Journa
Spherical Slepian functions and the polar gap in geodesy
The estimation of potential fields such as the gravitational or magnetic
potential at the surface of a spherical planet from noisy observations taken at
an altitude over an incomplete portion of the globe is a classic example of an
ill-posed inverse problem. Here we show that the geodetic estimation problem
has deep-seated connections to Slepian's spatiospectral localization problem on
the sphere, which amounts to finding bandlimited spherical functions whose
energy is optimally concentrated in some closed portion of the unit sphere.
This allows us to formulate an alternative solution to the traditional damped
least-squares spherical harmonic approach in geodesy, whereby the source field
is now expanded in a truncated Slepian function basis set. We discuss the
relative performance of both methods with regard to standard statistical
measures as bias, variance and mean-square error, and pay special attention to
the algorithmic efficiency of computing the Slepian functions on the region
complementary to the axisymmetric polar gap characteristic of satellite
surveys. The ease, speed, and accuracy of this new method makes the use of
spherical Slepian functions in earth and planetary geodesy practical.Comment: 14 figures, submitted to the Geophysical Journal Internationa
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