Local Group Velocity Research Articles

Mathematical Modeling of Robotic Locomotion Systems

This article deals with the presentation of an alternative approach that uses methods of geometric mechanics, which allow one to see into the geometrical structure of the equations and can be useful not only for modeling but also during the design of symmetrical locomotion systems and their control and motion planning. These methods are based on extracting the symmetries of Lie groups from the locomotion system in order to simplify the resulting equations. In the second section, the special two-dimensional Euclidean group SE2 and its splitting into right and left actions are derived. The physical interpretation of the local group and spatial velocities is investigated, and by virtue of the fact that both of these velocities represent the same velocity from a physical point of view, the dependence between them can be found by means of the adjoint action. The third section is devoted to the modeling and analysis of the planar locomotion of the symmetrical serpentine robot; the positions and local group velocities of its links are derived, the vector fields for the local connections are given, and the trajectories of the individual variables in the lateral movement of the kinematic snake are shown. At the end of the article, the overall benefits of the scientific study are summarized, as is the comparison of the results from the simulation phase, while the most significant novelty compared to alternative publications in the field can be considered the realization of this study with a description of the relevant methodology at a detailed level; that is, the locomotion results confirm the suitability of the use of geometric mechanics for these symmetrical locomotion systems with nonholonomic constraints.

Evolution of temporal and frequency characteristics of spherical photon density waves in scattering media

The paper reports on the numerical study of temporal characteristics, frequency and phase responses of the photon density waves generated by a point-sized source in scattering media with different scattering anisotropy and absorption index. The study is performed with time-resolved Monte-Carlo simulations for a wide range of medium optical properties covering values typical for aerosols and sea water. We demonstrate that although the normalized pulse delay increases monotonically with distance in the course of propagation in the medium, for particular sets of optical properties its normalized width shows a non-monotonous trend with a maximum corresponding to distances where ballistic and multiply scattered photons give comparable contribution to the irradiance field. In the frequency responses of photon density waves for certain combinations of optical properties at particular distances a deep minimum is formed, also associated with the interference of partial waves. The dimensionless frequency corresponding to this minimum monotonically increases with the increase in anisotropy factor. Dependencies of local and averaged phase and group velocities on distance derived from phase responses revealed a formation of a minima in local group velocities dependencies with further increase to the average velocity values at higher distances, which is also associated with relative contribution of low- and multiply scattered photons. The revealed dependencies can be useful for verifying the analytical models of nonstationary radiation transfer and directly for assessing the achievable parameters of optical systems for various purposes operating in natural scattering media, such as the atmosphere and sea water.

Multipole expansion of the local expansion rate

We design a new observable, the expansion rate fluctuation $\ensuremath{\eta}$, to characterize deviations from the linear relation between redshift and distance in the local universe. We also show how to compress the resulting signal into spherical harmonic coefficients in order to better decipher the structure and symmetries of the anisotropies in the local expansion rate. We apply this analysis scheme to several public catalogs of redshift-independent distances, the Cosmicflows-3 and Pantheon datasets, covering the redshift range $0.01<z<0.05$. The leading anisotropic signal is stored in the dipole. Within the standard cosmological model, it is interpreted as a bulk motion ($307\ifmmode\pm\else\textpm\fi{}23\text{ }\text{ }\mathrm{km}/\mathrm{s}$) of the entire local volume in a direction aligned at better than 4 degrees with the bulk component of the Local Group (LG) velocity with respect to the cosmic microwave background (CMB). This term alone, however, provides an overly simplistic and inaccurate description of the angular anisotropies of the expansion rate. We find that the quadrupole contribution is non-negligible ($\ensuremath{\sim}50%$ of the anisotropic signal), in fact, statistically significant, and signaling a substantial shearing of gravity in the volume covered by the data. In addition, the 3D structure of the quadrupole is axisymmetric, with the expansion axis aligned along the axis of the dipole. Implications for the determination of the ${H}_{0}$ parameter are discussed. We find that Hubble constant estimates may show variation as high as $\mathrm{\ensuremath{\Delta}}{H}_{0}=(4.1\ifmmode\pm\else\textpm\fi{}1.1)\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ between antipodal directions along the dipole axis. In the case of the Pantheon sample, this systematic difference is reduced to $\mathrm{\ensuremath{\Delta}}{H}_{0}=(2.4\ifmmode\pm\else\textpm\fi{}1.1)\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ once model-dependent correction for peculiar velocity flows are implemented. Notwithstanding, the axial anisotropy in the general direction of the CMB dipole is still detected. We thus show how to optimally subtract redshift anisotropies from Pantheon data in a fully model-independent way by exploiting the $\ensuremath{\eta}$ observable. As a result, the value of the best fitting ${H}_{0}$ is systematically revised upwards by nearly $0.7\text{ }\text{ }\mathrm{km}/\mathrm{s}/\mathrm{Mpc}$ (about $2\ensuremath{\sigma}$) compared to the value deduced from the Hubble diagram using the uncorrected observed redshift. The goodness of fit is also improved.

Multifrequency Bessel beams with adjustable group velocity and longitudinal acceleration in free space

The group velocity of an optical beam in free space is usually considered to be equal to the speed of light in vacuum. However, it has been recently realized that, by structuring the beam’s angular and temporal spectra, one can achieve well pronounced and controlled subluminal and superluminal propagation. In this work, we consider multifrequency Bessel beams that are known to propagate without divergence and show a variety of possibilities to adjust the group velocity of the beam by means of designed angular dispersion. We present several examples of multifrequency Bessel beams with negative and arbitrary positive group velocities, as well as longitudinally accelerating beams and beams with periodically oscillating local group velocities. The results of these studies can be of interest to scientists working in the fields of optical beam engineering, light amplitude and intensity interferometry, ultrafast optics, and optical tweezers.

Theoretical Issues with Rayleigh Surface Waves and Geoelectrical Method Used for the Inversion of Near Surface Geophysical Structure

We numerically simulate the field measurements of Rayleigh surface waves and electrical resistivity in which the target depth is set to be less than 50-m. The Rayleigh surface waves are simulated in terms of fundamental mode group and phase velocities. The seismic field data is assumed to be collected through a conventional shot-gather. The group velocities are found from the application of the multiple filter technique in a single-station fashion while for the phase velocities the slant stacking, or linear radon transform are applied in fashion of multichannel analysis of surface waves (MASW). The average seismic structure from the source to the receiver (or geophone) is represented by the group velocity curve while the average seismic structure underneath the geophone array is represented by the phase velocity curve. The single-station group velocity curves are transformed into local group velocity curves by setting a linear system through grid points. The shear-wave velocity cross section underneath the examined area is constructed by inverting these local group velocity curves. The electrical resistivity structure of the underground is similarly studied. The field compilation of the resistivity data is assumed to be completed by the application of the multiple electrode Pole-Pole array. The actual resistivity assemble underneath the analyzed area is inverted by considering the apparent (measured) resistivity values. Unique forms such as ore body, cavity, sinkhole, melt, salt, and fluid within the Earth may be examined by joint interpretation of electrical resistivities and seismic velocities. These formations may be better outlined by following their distinct signs such as high/low resistivities and high/low seismic velocities. Doi: 10.28991/HEF-2021-02-03-01 Full Text: PDF

The growth rate of cosmic structures in the local Universe with the ALFALFA survey

ABSTRACT We investigate the growth rate of structures in the local Universe. For this, we use as a cosmological tracer the HI line extra-galactic sources from the Arecibo Legacy Fast ALFA (ALFALFA) survey to obtain a measurement of the normalized growth rate parameter, fσ8, considered a powerful tool to constrain alternative models of gravity. For these analyses, we calculate the Local Group velocity due to the matter structures distribution in the ALFALFA catalogue and compare it with the Local Group velocity relative to the Cosmic Microwave Background frame to obtain the velocity scale parameter, β. Using Monte Carlo realizations and lognormal simulations, our methodology quantifies the errors introduced by shot-noise and partial sky coverage of the analysed data. The measurement of the velocity scale parameter β and the calculation of the matter fluctuation of the cosmological tracer, $\sigma _{8}^{\text{tr}}$, lead us to fσ8 = 0.46 ± 0.06 at $\bar{z} = 0.013$, in good agreement (at 1σ level) with the value expected in the ΛCDM concordance model. In addition, our analyses of the ALFALFA sample also provide a measurement of the growth rate of structures $f = 0.56 \pm 0.07$, at $\bar{z} = 0.013$.

LOVE SURFACE WAVES AND ELECTRICAL RESISTIVITY USED TO DELINEATE THE NEAR SURFACE GEOPHYSICAL STRUCTURE: THEORETICAL CONSIDERATIONS

We invert Love surface waves and electrical resistivities to cooperatively examine the physical properties of the depth range shallower than 50-m. To analyze this depth range is essential for earthquake mitigation efforts. The shear-wave velocity (VS30) is particularly important to describe the dynamic characteristics of shallow Earth. The Love surface waves are treated in terms of both phase and group velocities. The phase velocities are obtained from the slant stacking while for the group velocities the multiple filter technique is utilized. A typical shot-gather is assumed to simulate the field collection of the surface wave data. The phase velocity curve represents the average structure beneath the geophone spread. The group velocity curve represents the average structure from the source to the geophone. In a single-station fashion, for each geophone location one group velocity curve is obtained. A linear system is set up to convert these single-station group velocity curves into local group velocity curves at grid points. The latter group velocities are inverted to attain the shear-wave velocity cross section. A similar approach is adopted to study the electrical resistivity structure of the underground. We simulate the field application using a theoretical model. Multiple electrode Pole-Pole array is assumed for the field collection of the resistivity data. The apparent (measured) resistivity values are inverted to attain the true resistivity structure in terms of a cross section. The inverted structures are one-dimensional reflecting depth dependent shear-wave velocities and electrical resistivities underneath the studied region.

The KBC void and Hubble tension contradict ΛCDM on a Gpc scale − Milgromian dynamics as a possible solution

ABSTRACT The KBC void is a local underdensity with the observed relative density contrast δ ≡ 1 − ρ/ρ0 = 0.46 ± 0.06 between 40 and 300 Mpc around the Local Group. If mass is conserved in the Universe, such a void could explain the 5.3σ Hubble tension. However, the MXXL simulation shows that the KBC void causes 6.04σ tension with standard cosmology (ΛCDM). Combined with the Hubble tension, ΛCDM is ruled out at 7.09σ confidence. Consequently, the density and velocity distribution on Gpc scales suggest a long-range modification to gravity. In this context, we consider a cosmological MOND model supplemented with $11 \, \rm {eV}/c^{2}$ sterile neutrinos. We explain why this νHDM model has a nearly standard expansion history, primordial abundances of light elements, and cosmic microwave background (CMB) anisotropies. In MOND, structure growth is self-regulated by external fields from surrounding structures. We constrain our model parameters with the KBC void density profile, the local Hubble and deceleration parameters derived jointly from supernovae at redshifts 0.023−0.15, time delays in strong lensing systems, and the Local Group velocity relative to the CMB. Our best-fitting model simultaneously explains these observables at the $1.14{{\ \rm per\ cent}}$ confidence level (2.53σ tension) if the void is embedded in a time-independent external field of ${0.055 \, a_{_0}}$. Thus, we show for the first time that the KBC void can naturally resolve the Hubble tension in Milgromian dynamics. Given the many successful a priori MOND predictions on galaxy scales that are difficult to reconcile with ΛCDM, Milgromian dynamics supplemented by $11 \, \rm {eV}/c^{2}$ sterile neutrinos may provide a more holistic explanation for astronomical observations across all scales.

Enhancement of superluminal weak values under Lorentz boost

The local group velocity defined as the weak value of the velocity operator in (1 + 1)-dimensional Klein-Gordon and Dirac theory is studied. As shown by Berry [J. Phys. A 45, 185308 (2012)], when the pre- and post-selected states for evaluating the weak value are chosen at random from an ensemble of available states, it gives rise to a universal probability distribution for the local group velocity which can have both subluminal and superluminal components. In this work, we explore the possibility of enhancement of the superluminal fraction of this total probability distribution by applying a Lorentz boost and show that it can indeed be enhanced both in the case of Klein–Gordon and Dirac theories.

Local Rossby Wave Packet Amplitude, Phase Speed, and Group Velocity: Seasonal Variability and Their Role in Temperature Extremes

AbstractTransient Rossby wave packets (RWPs) are a prominent feature of the synoptic to planetary upper-tropospheric flow at the midlatitudes. Their demonstrated role in various aspects of weather and climate prompts the investigation of characteristic properties like their amplitude, phase speed, and group velocity. Traditional frameworks for the diagnosis of the two latter have so far remained nonlocal in space or time, thus preventing a detailed view on the spatiotemporal evolution of RWPs. The present work proposes a method for the diagnosis of horizontal Rossby wave phase speed and group velocity locally in space and time. The approach is based on the analytic signal of upper-tropospheric meridional wind velocity and RWP amplitude, respectively. The new diagnostics are first applied to illustrative examples from a barotropic model simulation and the real atmosphere. The main seasonal and interregional variability features of RWP amplitude, phase speed, and group velocity are then explored using ERA5 reanalysis data for the time period 1979–2018. Apparent differences and similarities in these respects between the Northern and Southern Hemispheres are also discussed. Finally, the role of RWP amplitude and phase speed during central European short-lived and persistent temperature extremes is investigated based on changes of their distribution compared to the climatology of the region. The proposed diagnostics offer insight into the spatiotemporal variability of RWP properties and allow the evaluation of their implications at low computational demands.

The ultra-diffuse dwarf galaxies NGC 1052-DF2 and 1052-DF4 are in conflict with standard cosmology

ABSTRACT Recently van Dokkum et al. reported that the galaxy NGC 1052-DF2 (DF2) lacks dark matter if located at 20 Mpc from Earth. In contrast, DF2 is a dark-matter-dominated dwarf galaxy with a normal globular cluster population if it has a much shorter distance near 10 Mpc. However, DF2 then has a high peculiar velocity wrt. the cosmic microwave background of 886 $\rm {km\, s^{-1}}$, which differs from that of the Local Group (LG) velocity vector by 1298 $\rm {km\, s^{-1}}$ with an angle of $117 \, ^{\circ }$. Taking into account the dynamical M/L ratio, the stellar mass, half-light radius, peculiar velocity, motion relative to the LG, and the luminosities of the globular clusters, we show that the probability of finding DF2-like galaxies in the lambda cold dark matter (ΛCDM) TNG100-1 simulation is at most 1.0 × 10−4 at 11.5 Mpc and is 4.8 × 10−7 at 20.0 Mpc. At 11.5 Mpc, the peculiar velocity is in significant tension in the TNG100-1, TNG300-1, and Millennium simulations, but naturally in a Milgromian cosmology. At 20.0 Mpc, the unusual globular cluster population would challenge any cosmological model. Estimating that precise measurements of the internal velocity dispersion, stellar mass, and distance exist for 100 galaxies, DF2 is in 2.6σ (11.5 Mpc) and 4.1σ (20.0 Mpc) tension with standard cosmology. Adopting the former distance for DF2 and assuming that NGC 1052-DF4 is at 20.0 Mpc, the existence of both is in tension at ≥4.8σ with the ΛCDM model. If both galaxies are at 20.0 Mpc the ΛCDM cosmology has to be rejected by ≥5.8σ.

Quasioptical modeling of wave beams with and without mode conversion. I. Basic theory

This work opens a series of papers where we develop a general quasi-optical theory for mode-converting electromagnetic beams in plasma and implement it in a numerical algorithm. Here, the basic theory is introduced. We consider a general quasimonochromatic multicomponent wave in a weakly inhomogeneous linear medium with no sources. For any given dispersion operator that governs the wave field, we explicitly calculate the approximate operator that governs the wave envelope ψ to the second order in the geometrical-optics parameter. Then, we further simplify this envelope operator by assuming that the gradient of ψ transverse to the local group velocity is much larger than the corresponding parallel gradient. This leads to a parabolic differential equation for ψ (“quasioptical equation”) on the basis of the geometrical-optics polarization vectors. Scalar and mode-converting vector beams are described on the same footing. We also explain how to apply this model to electromagnetic waves in general. In the next papers of this series, we report successful quasioptical modeling of radio frequency wave beams in magnetized plasma based on this theory.

ANISOTROPIC PROPERTIES OF THE UPPER MANTLE IN CENTRAL ASIA ACCORDING TO THE GROUP VELOCITY DISPERSION CURVES FOR RAYLEIGH AND LOVE WAVES

The article presents the results of the study focused on the anisotropic properties of the upper mantle in Central Asia. The study is based on a representative set of the group velocity dispersion curves for Rayleigh and Love waves. The dispersion curves were calculated in the range of 10–250 s. The maps of group velocity distribution pat‐ terns and the horizontal resolution estimates were calculated by the surface‐wave tomography method developed for a spherical surface. Based on the maps, the local group velocity dispersion curves were reconstructed for the given points within the study region, which were then converted into the one‐dimensional velocity sections of SV‐ and SH‐waves, and a vertical anisotropy coefficient was estimated. A three‐dimensional anisotropic model shows the ve‐ locity distribution pattern of S‐waves in the crust and the mantle to the depth of 500 km. According to this model, ver‐ tical anisotropy in the upper mantle is observed to the depth of about 250 km and has maximum values in the depth interval from the crustal bottom to 150 km. The anisotropic properties are unevenly distributed and reflect the geo‐ logical structure of the study area. Therefore, tectonically active regions are characterized by the high values of the anisotropy coefficient and the reduced values of the S‐wave velocities. The presented results can contribute to the further development of more detailed and strictly proved geodynamic models of the study area.

Using velocity dispersion to estimate halo mass: Is the Local Group in tension with ΛCDM?

Satellite galaxies are commonly used as tracers to measure the line-of-sight velocity dispersion ($\sigma_{\rm LOS}$) of the dark matter halo associated with their central galaxy, and thereby to estimate the halo's mass. Recent observational dispersion estimates of the Local Group, including the Milky Way and M31, suggest $\sigma\sim$50 km/s, which is surprisingly low when compared to the theoretical expectation of $\sigma\sim$100s km/s for systems of their mass. Does this pose a problem for $\Lambda$CDM? We explore this tension using the {\small{SURFS}} suite of $N$-body simulations, containing over 10000 (sub)haloes with well tracked orbits. We test how well a central galaxy's host halo velocity dispersion can be recovered by sampling $\sigma_{\rm LOS}$ of subhaloes and surrounding haloes. Our results demonstrate that $\sigma_{\rm LOS}$ is biased mass proxy. We define an optimal window in $v_{\rm LOS}$ and projected distance ($D_p$) -- $0.5\lesssim D_p/R_{\rm vir}\lesssim1.0$ and $v_{\rm LOS} \lesssim0.5V_{\rm esc}$, where $R_{\rm vir}$ is the virial radius and $V_{\rm esc}$ is the escape velocity -- such that the scatter in LOS to halo dispersion is minimised - $\sigma_{\rm LOS}=(0.5\pm0.1)\sigma_{v,{\rm H}}$. We argue that this window should be used to measure line-of-sight dispersions as a proxy for mass, as it minimises scatter in the $\sigma_{\rm LOS}-M_{\rm vir}$ relation. This bias also naturally explains the results from \cite{mcconnachie2012a}, who used similar cuts when estimating $\sigma_{\rm LOS,LG}$, producing a bias of $\sigma_{\rm LG}=(0.44\pm0.14)\sigma_{v,{\rm H}}$. We conclude that the Local Group's velocity dispersion does not pose a problem for $\Lambda$CDM and has a mass of $\log M_{\rm LG, vir}/M_\odot=12.0^{+0.8}_{-2.0}$.

The Local Volume H i Survey (LVHIS)

The `Local Volume HI Survey' (LVHIS) comprises deep HI spectral line and 20-cm radio continuum observations of 82 nearby, gas-rich galaxies, supplemented by multi-wavelength images. Our sample consists of all galaxies with Local Group velocities v_LG < 550 km/s or distances D < 10 Mpc that are detected in the HI Parkes All Sky Survey (HIPASS). Using full synthesis observations in at least three configurations of the Australia Telescope Compact Array (ATCA), we obtain detailed HI maps for a complete sample of gas-rich galaxies with Dec < -30 deg. Here we present a comprehensive LVHIS Galaxy Atlas, including the overall gas distribution, mean velocity field, velocity dispersion, and position-velocity diagrams, together with a homogeneous set of measured and derived galaxy properties. Our primary goal is to investigate the HI morphologies, kinematics, and environment at high resolution and sensitivity. LVHIS galaxies represent a wide range of morphologies and sizes; our measured HI masses range from ~10^7 to 10^10 Msun, based on independent distance estimates. The LVHIS Galaxy Atlas (including FITS files) is available on-line.

Traveltimes and conversion-point positions for P-SV converted wave propagation in a transversely isotropic medium: numerical calculations and physical model studies

This study uses ultrasonic physical modelling to test the accuracies of numerical calculations of traveltimes and conversion-point (CP) positions for P-SV wave propagation in a horizontal transversely isotropic (TI) medium. Study results show that the traveltimes and CP positions for P-SV wave propagation on the isotropic plane of a TI medium computed using Fermat’s minimum-time principle are the same as those of using the isotropic non-hyperbolic moveout equation and the isotropic CP equation. However, for P-SV wave propagation on the symmetry-axis plane of a TI medium, the arrival times and CP positions of SV-waves are difficult to determine by any ray methods when the propagation directions of SV-waves are within the cuspoidal SV-wave group velocities zone. But the first arrival times and the propagation of the dominant energy of P-SV waves can still be analysed by ray methods. Based on the calculation of Fermat’s minimum-time principle, if the source-receiver offset is greater than a critical distance, the reflection angles of the converted SV-waves are fixed at a specific angle with a local maximum SV-wave group velocity of the neighbourhood area. This is because the converted SV-waves prefer to propagate along the cuspoidal directions with larger amplitude and higher velocity. Verified by the physical modelling, the Fermat’s minimum-time principle used to calculate traveltimes of P-SV waves is better than the anisotropic non-hyperbolic moveout equation. The physical modelling for the CP position experiment can give a clearer visualisation of the variations of CP positions in the profile, and the feasibility of using Fermat’s minimum-time principle to determine CP positions is also better than that of the anisotropic CP equations. Therefore, in the seismic data processing, Fermat’s minimum-time method is recommended to accurately determine the arrival times and CP positions of P-SV wave propagation in TI media.

Enhancement and suppression of turbulence by energetic-particle-driven geodesic acoustic modes

We propose a novel mechanism of enhancement of turbulence by energetic-particle-driven geodesic acoustic modes (EGAMs). The dynamics of drift-wave-type turbulence in the phase space is investigated by wave-kinetic equation. Spatially inhomogeneous turbulence in the presence of a transport barrier is considered. We discovered that trapping of turbulence clumps by the EGAMs is the key parameter that determines either suppress or enhance turbulence. In regions where turbulence is unstable, EGAM suppresses the turbulence. In contrast, in the stable region, EGAM traps clumps of turbulence and carries them across the transport barrier, so that the turbulence can be enhanced. The turbulence trapped by EGAMs can propagate independent of the gradients of density and temperature, which leads to non-Fickian transport. Hence, there appear a new global characteristic velocity, the phase velocity of GAMs, for turbulence dynamics, in addition to the local group velocity and that of the turbulence spreading. With these effect, EGAMs can deteriorate transport barriers and affect turbulence substantially. This manuscript provides a basis to consider whether a coherent wave breaks or strengthen transport barriers.

A traveling feature in Saturn’s rings

The co-orbital satellites of Saturn, Janus and Epimetheus, swap radial positions every 4.0 years. Since Cassini has been in orbit about Saturn, this has occurred on 21 January in 2006, 2010, and 2014. We describe the effects of this radial migration in the Lindblad resonance locations of Janus within the rings. When the swap occurs such that Janus moves towards Saturn and Epimetheus away, nonlinear interference between now-relocated density waves launches a solitary wave that travels through the rings with a velocity approximately twice that of the local spiral density wave group velocity in the A ring and commensurate with the spiral density wave group velocity in the B ring.

Slow-light effect via Rayleigh anomaly and the effect of finite gratings.

In this Letter, we investigate the slow-light effect of subwavelength diffraction gratings via the Rayleigh anomaly using a fully analytical approach without needing to consider specific grating structures. Our results show that the local group velocity of the transmitted light can be significantly reduced due to the optical vortex, which can inspire a new mechanism to enhance light-matter interactions for optical sensing and photodetection. However, the slow-light effect will diminish as the transmitted light propagates farther from the grating surface, and the slowdown factor decreases as the grating size shrinks.

A multiresolution approach to shear wave image reconstruction

Shear wave imaging techniques build maps of local elasticity estimating the local group velocity of induced mechanical waves. Velocity estimates are formed using the time delay in the motion profile of the medium at two or more points offset from the shear wave source. Because the absolute time-of-flight between any pair of locations scales with the distance between them, there is an inherent trade-off between robustness to time-of-flight errors and lateral spatial resolution based on the number and spacing of the receive points used for each estimate. This work proposes a method of using the time delays measured between all combinations of locations to estimate a noise-robust, high-resolution image. The time-of-flight problem is presented as an overdetermined system of linear equations that can be directly solved with and without spatial regularization terms. Finite element method simulations of acoustic radiation force-induced shear waves are used to illustrate the method, demonstrating superior contrast-to-noise ratio and lateral edge resolution characteristics compared with linear regression of arrival times. This technique may improve shear wave imaging in situations where time-of-flight noise is a limiting factor.