Inversion for Anisotropic Velocity Parameter

The problem under study concerns the robust computation of a certain parameter of anisotropy from observed travel-times of a seismic shear wave propagating through a geological medium. We have obtained an exact mathematical description of a geoseismic signal propagating through an anisotropic medium using a constant coefficient wave equation as the basic model. This model captures exactly the elliptical velocity profile required in the formulation of the geophysical model from which we obtained exact formulas describing the travel-time through a two layer geological structure, and an exact inversion formula for computing the anisotropic velocity parameter (gamma). A robust numerical method based on a minimization technique was presented as an accurate method of computing both travel-time and the inverted gamma. The exact formulas and robust numerical methods are significant improvements over the approximations and root finding methods discussed in the background material, and we note our formulation is no more difficult than these background methods. We derived asymptotic formulas valid for the near vertical case, which describe accurately the high sensitivity of gamma to the input parameters in this case. Our numerical work also confirms this sensitivity, even using exact formulas and robust numerical methods. We conclude that the computation of the anisotropic velocity parameter (gamma) for the given physical measurements from a series of surface signals and single borehole receiver is intrinsically unstable. By changing to the alpha,beta velocity parameter space, we obtain an inversion method that is much less sensitive to input errors. For certain geophysical problems, the alpha,beta parameters may suffice for an accurate description of the material. When the anisotropic velocity parameter (gamma) is needed directly, a different measurement technique is required. This route will require further investigation, and we have proposed a number of promising possibilities involving a differential time measure

S wave velocity structure below central Mexico using high-resolution surface wave tomography

Shear wave velocity of the crust below central Mexico is estimated using surface wave dispersion measurements from regional earthquakes recorded on a dense, 500 km long linear seismic network. Vertical components of regional records from 90 well-located earthquakes were used to compute Rayleigh-wave group-velocity dispersion curves. A tomographic inversion, with high resolution in a zone close to the array, obtained for periods between 5 and 50 s reveals significant differences relative to a reference model, especially at larger periods (>30 s). A 2-D S wave velocity model is obtained from the inversion of local dispersion curves that were reconstructed from the tomographic solutions. The results show large differences, especially in the lower crust, among back-arc, volcanic arc, and fore-arc regions; they also show a well-resolved low-velocity zone just below the active part of the Trans Mexican Volcanic Belt (TMVB) suggesting the presence of a mantle wedge. Low densities in the back arc, inferred from the low shear wave velocities, can provide isostatic support for the TMVB

Kinematic model inversions of hot star recurrent DAC data - tests against dynamical CIR models

The Discrete Absorption Components (DACs) commonly observed in the ultraviolet lines of hot stars have previously been modelled by dynamical simulations of Corotating Interaction Regions (CIRs) in their fine-driven stellar winds. Here we apply the kinematic DAC inversion method of Brown et al. to the hydrodynamical CIR models and test the reliability of the results obtained. We conclude that the inversion method is able to recover valuable information on the velocity structure of the mean wind and to trace movement of velocity plateaux in the hydrodynamical data, though the recovered density profile of the stream is correct only very near to the stellar surface

Subsonic near-surface P-velocity and low S-velocity observations using propagator inversion

Detailed knowledge of near-surface P- and S-wave velocities is important for processing and interpreting multicomponent land seismic data because (1) the entire wavefield passes through and is influenced by the near-surface soil conditions, (2) both source repeatability and receiver coupling also depend on these conditions, and (3) near-surface P- and S-wave velocities are required for wavefield decomposition and demultiple methods. However, it is often difficult to measure these velocities with conventional techniques because sensitivity to shallow-wave velocities is low and because of the presence of sharp velocity contrasts or gradients close to the earth's free surface. We demonstrate that these near-surface P- and S-wave velocities can be obtained using a propagator inversion. This approach requires data recorded by at least one multicomponent geophone at the surface and an additional multicomponent geophone at depth. The propagator between them then contains all information on the medium parameters governing wave propagation between the geophones at the surface and at depth. Hence, inverting the propagator gives local estimates for these parameters. This technique has been applied to data acquired in Zeist, the Netherlands. The near-surface sediments at this site are unconsolidated sands with a thin vegetation soil on top, and the sediments considered are located above the groundwater table. A buried geophone was positioned 1.05 m beneath receivers on the surface. Propagator inversion yielded low near-surface velocities, namely, 270 ± 15 m/s for the compressional-wave velocity, which is well below the sound velocity in air, and 150 ± 9 m/s for the shear velocity. Existing methods designed for imaging deeper structures cannot resolve these shallow material properties. Furthermore, velocities usually increase rapidly with depth close to the earth's surface because of increasing confining pressure. We suspect that for this reason, subsonic near-surface P-wave velocities are not commonly observed

Velocity estimation via registration-guided least-squares inversion

This paper introduces an iterative scheme for acoustic model inversion where the notion of proximity of two traces is not the usual least-squares distance, but instead involves registration as in image processing. Observed data are matched to predicted waveforms via piecewise-polynomial warpings, obtained by solving a nonconvex optimization problem in a multiscale fashion from low to high frequencies. This multiscale process requires defining low-frequency augmented signals in order to seed the frequency sweep at zero frequency. Custom adjoint sources are then defined from the warped waveforms. The proposed velocity updates are obtained as the migration of these adjoint sources, and cannot be interpreted as the negative gradient of any given objective function. The new method, referred to as RGLS, is successfully applied to a few scenarios of model velocity estimation in the transmission setting. We show that the new method can converge to the correct model in situations where conventional least-squares inversion suffers from cycle-skipping and converges to a spurious model.Comment: 20 pages, 13 figures, 1 tabl

Spectropolarimetric NLTE inversion code SNAPI

Inversion codes are computer programs that fit a model atmosphere to the observed Stokes spectra, thus retrieving the relevant atmospheric parameters. The rising interest in the solar chromosphere, where spectral lines are formed by scattering, requires developing, testing, and comparing new non-local thermal equilibrium (NLTE) inversion codes. We present a new NLTE inversion code that is based on the analytical computation of the response functions. We named the code SNAPI, which is short for spectropolarimetic NLTE analytically powered inversion. SNAPI inverts full Stokes spectrum in order to obtain a depth-dependent stratification of the temperature, velocity, and the magnetic field vector. It is based on the so-called node approach, where atmospheric parameters are free to vary in several fixed points in the atmosphere, and are assumed to behave as splines in between. We describe the inversion approach in general and the specific choices we have made in the implementation. We test the performance on one academic problem and on two interesting NLTE examples, the Ca\,II\,8542 and Na\,I\,D spectral lines. The code is found to have excellent convergence properties and outperforms a finite-difference based code in this specific implementation by at least a factor of three. We invert synthetic observations of Na lines from a small part of a simulated solar atmosphere and conclude that the Na lines reliably retrieve the magnetic field and velocity in the range $-3<\log \tau < -0.5$.Comment: To appear in A&