Toward an automatic full-wave inversion: Synthetic study cases

Full-waveform inversion (FWI) in seismic scenarios continues to be a complex procedure for subsurface imaging that might require extensive human interaction in terms of model setup, constraints, and data preconditioning. The underlying reason is the strong nonlinearity of the problem that forces the addition of a priori knowledge (or bias) in order to obtain geologically sound results. In particular, when the use of a long-offset receiver is not possible or may not favor the reconstruction of the fine structure of the model, one needs to rely on reflection data. As a consequence, the inversion process is more prone to becoming stuck in local minima. Nevertheless, misfit functionals can be devised that can either cope with missing long-wavenumber features of initial models (e.g., cross-correlation-based misfit) or invert reflection-dominated data whenever the models are sufficiently good (e.g., normalized offset-limited least-squares misfit). By combining both, high-frequency data content with poor initial models can be successfully inverted. If one can figure out simple parameterizations for such functionals, the amount of uncertainty and manual work related to tuning FWI would be substantially reduced. Thus, FWI might become a semiautomatized imaging tool.We want to thank Repsol for funding this research by means of the Aurora project. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 644202. Additionally, the research leading to these results has received funding from the European Union’s Horizon 2020 Programme (2014-2020) and from Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP) under the HPC4E Project (www.hpc4e.eu), grant agreement No 689772. We acknowledge Chevron for the dataset that was used in our second example.Peer ReviewedPostprint (author's final draft

The Top Ten List of Gravitational Lens Candidates from the HST Medium Deep Survey

A total of 10 good candidates for gravitational lensing have been discovered in the WFPC2 images from the HST Medium Deep Survey (MDS) and archival primary observations. These candidate lenses are unique HST discoveries, i.e. they are faint systems with sub-arcsecond separations between the lensing objects and the lensed source images. Most of them are difficult objects for ground-based spectroscopic confirmation or for measurement of the lens and source redshifts. Seven are ``strong lens'' candidates which appear to have multiple images of the source. Three are cases where the single image of the source galaxy has been significantly distorted into an arc. The first two quadruply lensed candidates were reported in Ratnatunga et al 1995 (ApJL, 453, L5) We report on the subsequent eight candidates and describe them with simple models based on the assumption of singular isothermal potentials. Residuals from the simple models for some of the candidates indicate that a more complex model for the potential will probably be required to explain the full structural detail of the observations once they are confirmed to be lenses. We also discuss the effective survey area which was searched for these candidate lens objects.Comment: 26 pages including 12 figures and 10 tables. AJ Vol. 117, No.

A More Fundamental Plane

We combine strong-lensing masses with SDSS stellar velocity dispersions and HST-ACS effective (half-light) radii for 36 lens galaxies from the Sloan Lens ACS (SLACS) Survey to study the mass dependence of mass-dynamical structure in early-type galaxies. We find that over a 180--390 km/s range in velocity dispersion, structure is independent of lensing mass to within 5%. This result suggests a systematic variation in the total (i.e., luminous plus dark matter) mass-to-light ratio as the origin of the tilt of the fundamental plane (FP) scaling relationship between galaxy size, velocity dispersion, and surface brightness. We construct the FP of the lens sample, which we find to be consistent with the FP of the parent SDSS early-type galaxy population, and present the first observational correlation between mass-to-light ratio and residuals about the FP. Finally, we re-formulate the FP in terms of surface mass density rather than surface brightness. By removing the complexities of stellar-population effects, this mass-plane formulation will facilitate comparison to numerical simulations and possible use as a cosmological distance indicator.Comment: 4+epsilon pages, 1 figure, emulateapj. Revised version accepted for publication in the ApJ Letter

Quantifying dwarf satellites through gravitational imaging: the case of SDSS J120602.09+514229.5

SDSS J120602.09+514229.5 is a gravitational lens system formed by a group of galaxies at redshift z=0.422 lensing a bright background galaxy at redshift z=2.001. The main peculiarity of this system is the presence of a luminous satellite near the Einstein radius, that slightly deforms the giant arc. This makes SDSS J120602.09+514229.5 the ideal system to test our grid-based Bayesian lens modelling method, designed to detect galactic satellites independently from their mass-to-light ratio, and to measure the mass of this dwarf galaxy despite its high redshift. Thanks to the pixelized source and potential reconstruction technique of Vegetti and Koopmans 2009a we are able to detect the luminous satellite as a local positive surface density correction to the overall smooth potential. Assuming a truncated Pseudo-Jaffe density profile, the satellite has a mass M=(2.75+-0.04)10^10 M_sun inside its tidal radius of r_t=0.68". We determine for the satellite a luminosity of L_B=(1.6+-0.8)10^9 L_sun, leading to a total mass-to-light ratio within the tidal radius of (M/L)_B=(17.2+-8.5) M_sun/L_sun. The central galaxy has a sub-isothermal density profile as in general is expected for group members. From the SDSS spectrum we derive for the central galaxy a velocity dispersion of sigma_kinem=380+-60 km/s within the SDSS aperture of diameter 3". The logarithmic density slope of gamma=1.7+0.25-0.30 (68% CL), derived from this measurement, is consistent within 1-sigma with the density slope of the dominant lens galaxy gamma~1.6, determined from the lens model. This paper shows how powerful pixelized lensing techniques are in detecting and constraining the properties of dwarf satellites at high redshift.Comment: Submitted to MNRAS; Abstract abridge

A determination of H_0 with the CLASS gravitational lens B1608+656: II. Mass models and the Hubble constant from lensing

EDITED FROM PAPER: We present mass models of the four-image gravitational lens system B1608+656. A mass model for the lens galaxies has been determined that reproduces the image positions, two out of three flux-density ratios and the model time delays. Using the time delays determined by Fassnacht et al. (1999a), we find that the best isothermal mass model gives H_0=59^{+7}_{-6} km/s/Mpc for Omega_m=1 and Omega_l=0.0, or H_0=(65-63)^{+7}_{-6} km/s/Mpc for Omega_m=0.3 and Omega_l = 0.0-0.7 (95.4% statistical confidence). A systematic error of +/-15 km/s/Mpc is estimated. This cosmological determination of H_0 agrees well with determinations from three other gravitational lens systems (i.e. B0218+357, Q0957+561 and PKS1830-211), SNe Ia, the S-Z effect and local determinations. The current agreement on H_0 from four out of five gravitational lens systems (i) emphasizes the reliability of its determination from isolated gravitational lens systems and (ii) suggests that a close-to-isothermal mass profile can describe disk galaxies, ellipticals and central cluster ellipticals. The average of H_0 from B0218+357, Q0957+561, B1608+656 and PKS1830-211, gives H_0(GL)=69 +/-7 km/s/Mpc for a flat universe with Omega_m=1 or H_0(GL)=74 +/-8 km/s/Mpc for Omega_m=0.3 and Omega_l=0.0-0.7. When including PG1115+080, these values decrease to 64 +/-11 km/s/Mpc and 68 +/-13 km/s/Mpc (2-sigma errors), respectively.Comment: Accepted for publication in ApJ. 34 pages, 4 figure

New "Einstein Cross" Gravitational Lens Candidates in HST WFPC2 Survey Images

We report the serendipitous discovery of ``Einstein cross'' gravitational lens candidates using the Hubble Space Telescope. We have so far discovered two good examples of such lenses, each in the form of four faint blue images located in a symmetric configuration around a red elliptical galaxy. The high resolution of HST has facilitated the discovery of this optically selected sample of faint lenses with small (~1 arcsec) separations between the (I ~ 25-27) lensed components and the much brighter (I ~ 19-22) lensing galaxies. The sample has been discovered in the routine processing of HST fields through the Medium Deep Survey pipeline, which fits simple galaxy models to broad band filter images of all objects detected in random survey fields using WFPC2. We show that the lens configuration can be modeled using the gravitational field potential of a singular isothermal ellipsoidal mass distribution. With this model the lensing potential is very similar, both in ellipticity and orientation, to the observed light distribution of the elliptical galaxy, as would occur when stars are a tracer population. The model parameters and associated errors have been derived by 2-dimensional analysis of the observed images. The maximum likelihood procedure iteratively converges simultaneously on the model for the lensing elliptical galaxy and the source of the lensed components. A systematic search is in progress for other gravitational lens candidates in the HST Medium Deep Survey. This should eventually lead to a good statistical estimate for lensing probabilities, and enable us to probe the cosmological component of the observed faint blue galaxy population.Comment: Accepted for Astrophysical Journal Letters, 1995 November 1 LaTex, 10 pages, includes 2 figures 1 table, tarred gzip uuencoded using uufiles scrip

Shear and Ellipticity in Gravitational Lenses

Galaxies modeled as singular isothermal ellipsoids with an axis ratio distribution similar to the observed axis ratio distribution of E and S0 galaxies are statistically consistent with both the observed numbers of two-image and four-image lenses and the inferred ellipticities of individual lenses. However, no four-image lens is well fit by the model (typical $\chi^2/N_{dof} \sim 20$), the axis ratio of the model can be significantly different from that of the observed lens galaxy, and the major axes of the model and the galaxy may be slightly misaligned. We found that models with a second, independent, external shear axis could fit the data well (typical $\chi^2/N_{dof} \sim 1$), while adding the same number of extra parameters to the radial mass distribution does not produce such a dramatic improvement in the fit. An independent shear axis can be produced by misalignments between the luminous galaxy and its dark matter halo, or by external shear perturbations due to galaxies and clusters correlated with the primary lens or along the line of sight. We estimate that the external shear perturbations have no significant effect on the expected numbers of two-image and four-image lenses, but that they can be important perturbations in individual lens models. However, the amplitudes of the external shears required to produce the good fits are larger than our estimates for typical external shear perturbations (10-15% shear instead of 1-3% shear) suggesting that the origin of the extra angular structure must be intrinsic to the primary lens galaxy in most cases.Comment: 38 pages, 9 figures, submitted to Ap

A new method for the estimate of H_0 from quadruply imaged gravitational lens systems

We present a new method to estimate the Hubble constant H_0 from the measured time delays in quadruply imaged gravitational lens systems. We show how it is possible to get an estimate of H_0 without the need to completely reconstruct the lensing potential thus avoiding any a priori hypotheses on the expression of the galaxy lens model. Our method only needs to assume that the lens potential may be expressed as r^{\alpha} F(\theta), whatever the shape function F(\theta) is, and it is thus able to fully explore the degeneracy in the mass models taking also into account the presence of an external shear. We test the method on simulated cases and show that it does work well in recovering the correct value of the slope \alpha of the radial profile and of the Hubble constant H_0. Then, we apply the same method to the real quadruple lenses PG1115+080 and B1422+231 obtaining H_0 = 58_{-15}^{+17} km/s/Mpc (68% CL).Comment: 12 pages, 5 figures, accepted for publication on Astronomy & Astrophysic

Smoothing Algorithms and High-order Singularities in Gravitational Lensing

We propose a new smoothing method for obtaining surface densities from discrete particle positions from numerical simulations. This is an essential step for many applications in gravitational lensing. This method is based on the ``scatter'' interpretation of the discrete density field in the Smoothed Particle Hydrodynamics. We use Monte Carlo simulations of uniform density fields and one isothermal ellipsoid to empirically derive the noise properties, and best smoothing parameters (such as the number of nearest neighbors used). A cluster from high-resolution simulations is then used to assess the reality of high-order singularities such as swallowtails and butterflies in caustics, which are important for the interpretation of substructures in gravitational lenses. We also compare our method with the Delaunay tesselation field estimator using the galaxy studied by Bradac et al. (2004), and find good agreements. We show that higher order singularities are not only connected with bound subhaloes but also with the satellite streams. However, the presence of high-order singularities are sensitive to not only the fluctuation amplitude of the surface density, but also the detailed form of the underlying smooth lensing potential (such as ellipticity and external shear).Comment: ApJ, Accepted,(Released November 1st). The high resolution figures are availabel at http://202.127.29.4/mppg/english/data