Surface-wave group-delay and attenuation kernels

We derive both 3-D and 2-D Fréchet 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 δc/c or to its dispersion ω(∂/∂ω)(δc/c) as well as to the local group-velocity perturbation δC/C. This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of δC/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 ℓ1\ell_1-norm regularization of wavelet coefficients

We propose the use of $\ell_1$ regularization in a wavelet basis for the solution of linearized seismic tomography problems $Am=d$, allowing for the possibility of sharp discontinuities superimposed on a smoothly varying background. An iterative method is used to find a sparse solution $m$ that contains no more fine-scale structure than is necessary to fit the data $d$ 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

A new measure of σ8\sigma_8 using the lensing dispersion in high-zz 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 $\sigma_8$ parameter. Therefore the value of $\sigma_8$ 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 $\sigma_8$ using a likelihood analysis method. It is found that the number and quality of SN Ia data needed for placing a useful constraint on $\sigma_8$ is attainable with Next Generation Space Telescope.Comment: 9 pages, 3 figures. Accepted for publication in The Astrophysical Journa

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

GRB 070714B - Discovery of the Highest Spectroscopically Confirmed Short Burst Redshift

Gemini Nod & Shuffle spectroscopy on the host of the short GRB 070714B shows a single emission line at 7167 angstroms which, based on a grizJHK photometric redshift, we conclude is the 3727 angstrom [O II] line. This places the host at a redshift of z=.923 exceeding the previous record for the highest spectroscopically confirmed short burst redshift of z=.546 held by GRB 051221. This dramatically moves back the time at which we know short bursts were being formed, and suggests that the present evidence for an old progenitor population may be observationally biased.Comment: Conference procedings for Gamma Ray Bursts 2007 November 5-9, 2007 Santa Fe, New Mexico (4 pages, 2 figures

Synoptic Sky Surveys and the Diffuse Supernova Neutrino Background: Removing Astrophysical Uncertainties and Revealing Invisible Supernovae

The cumulative (anti)neutrino production from all core-collapse supernovae within our cosmic horizon gives rise to the diffuse supernova neutrino background (DSNB), which is on the verge of detectability. The observed flux depends on supernova physics, but also on the cosmic history of supernova explosions; currently, the cosmic supernova rate introduces a substantial (+/-40%) uncertainty, largely through its absolute normalization. However, a new class of wide-field, repeated-scan (synoptic) optical sky surveys is coming online, and will map the sky in the time domain with unprecedented depth, completeness, and dynamic range. We show that these surveys will obtain the cosmic supernova rate by direct counting, in an unbiased way and with high statistics, and thus will allow for precise predictions of the DSNB. Upcoming sky surveys will substantially reduce the uncertainties in the DSNB source history to an anticipated +/-5% that is dominated by systematics, so that the observed high-energy flux thus will test supernova neutrino physics. The portion of the universe (z < 1) accessible to upcoming sky surveys includes the progenitors of a large fraction (~ 87%) of the expected 10-26 MeV DSNB event rate. We show that precision determination of the (optically detected) cosmic supernova history will also make the DSNB into a strong probe of an extra flux of neutrinos from optically invisible supernovae, which may be unseen either due to unexpected large dust obscuration in host galaxies, or because some core-collapse events proceed directly to black hole formation and fail to give an optical outburst.Comment: 11 pages, 6 figure