Correct Mode Identification Research Articles

Full wavefield modeling and dispersion characteristics of underwater MASW

The underwater multichannel analysis of surface wave (UMASW) is becoming an essential tool for surveying subbottom shear wave velocity. Current practice is limited to interpretation based on the fundamental mode. This paper investigates the full dynamic response of the underwater-multilayered structure under two different types of sources (impact and explosion). Fundamental solutions in the transformed domain, after applying both Fourier transform and Fourier–Bessel transform, are derived utilizing the global stiffness matrix method, analogous to a 1-D finite element approach. Solutions in the physical domain are then obtained using the fast and accurate Fourier series and Fourier–Bessel series approach proposed in this paper. The most attractive feature of this novel approach is that the expansion coefficients (or Love numbers) can be pre-calculated, saved, and repeatedly used for other field points. Through numerical analyses, we quantitatively investigate the effect of the water depth and source/receiver types/locations on different wave features (i.e., Scholte, fast-guided, and acoustic modes) from different perspectives (i.e., dispersion curve, Green’s function, frequency-velocity spectrum (FVS), and waveform). We find that (1) unlike the impact source, stronger acoustic waves can be produced by the explosive source, which sometimes causes difficulty in identifying the Scholte waves. (2) The acoustic and interface-guided waves exhibit distinct behaviors depending on the source and receiver locations. Scholte waves and fast-guided waves are weakened when the source and receivers are elevated far from the water/soil interface. Moreover, (3) the response of the Scholte wave can be enhanced by muting the direct acoustic waves. However, (4) the fast-guided wave may also arise in underwater surveys when the Vs of the underlying half-space is much higher than those of the upper layers, exerting a significant influence on the shallow water scenarios and posing challenges for correct mode identification. With the ability to model the entire wavefield (or FVS) that takes into account all propagation modes and the actual survey configuration, inversion can be performed by fitting the entire FVS. This approach eliminates the need to pick dispersion curves and provides a more accurate and stronger model constraint.

Fast and Automated Peak Bagging with DIAMONDS (FAMED)

Stars of low and intermediate mass that exhibit oscillations may show tens of detectable oscillation modes each. Oscillation modes are a powerful tool to constrain the internal structure and rotational dynamics of the star, hence allowing one to obtain an accurate stellar age. The tens of thousands of solar-like oscillators that have been discovered thus far are representative of the large diversity of fundamental stellar properties and evolutionary stages available. Because of the wide range of oscillation features that can be recognized in such stars, it is particularly challenging to properly characterize the oscillation modes in detail, especially in light of large stellar samples. Overcoming this issue requires an automated approach, which has to be fast, reliable, and flexible at the same time. In addition, this approach should not only be capable of extracting the oscillation mode properties of frequency, linewidth, and amplitude from stars in different evolutionary stages, but also able to assign a correct mode identification for each of the modes extracted. Here we present the new freely available pipeline FAMED (Fast and AutoMated pEak bagging with DIAMONDS), which is capable of performing an automated and detailed asteroseismic analysis in stars ranging from the main sequence up to the core-helium-burning phase of stellar evolution. This, therefore, includes subgiant stars, stars evolving along the red giant branch (RGB), and stars likely evolving toward the early asymptotic giant branch. In this paper, we additionally show how FAMED can detect rotation from dipolar oscillation modes in main sequence, subgiant, low-luminosity RGB, and core-helium-burning stars.

Anisotropic Elasticity of APS and HVOF CoNiCrAlY Coatings Studied by Resonant Ultrasound Spectroscopy with Laser Doppler Interferometry

The splat-based layered structure of thermal spray coatings leads to elastic anisotropy; however, elucidating the anisotropic elastic properties of such coatings is a challenging subject because of the limited sample size and microstructural factors such as high defect level. The objective of this study is to investigate the anisotropic elasticity of the as-sprayed and heat-treated CoNiCrAlY coatings prepared by atmospheric plasma spraying (APS) and high-velocity oxygen fuel (HVOF) spraying. For this purpose, we measure all five elastic constants accurately using resonant ultrasound spectroscopy with laser Doppler interferometry. This approach realizes the correct mode identification of the measured resonance frequencies, even for coatings with high internal friction by comparing the measured and calculated displacement distributions, providing a precise determination of the elastic constants with inverse calculation. We determined that an oriented array of defects causes a significantly low Young’s modulus along the spraying direction in both the as-sprayed coatings. Our measurements on the heat-treated coatings revealed that thermal treatment makes the APS coating stiffer than the HVOF coating, whereas the stiffness anisotropy of the APS coating remains stronger compared to the HVOF coating, even after heating. This phenomenon is consistently explained by focusing on the oxides in the coatings.

Eclipse mapping of Algol-type systems with oscillating δ Scuti type components

The oscillating Algol-type (oEA) stars are the former secondaries of evolved, semi-detached eclipsing binaries which are (still) undergoing mass transfer and form a newly detected class of pulsators close to the main sequence. Their unique feature consists of mass accretion onto the atmosphere of the pulsating star. Mass accretion affects the mass, radius, density as well as the star’s evolution. Such stars are therefore very attractive targets for asteroseismic studies. A new tool for mode identification of pulsating components in eclipsing binaries consists in using the event of primary eclipse as a spatial filter to resolve the pulsations across the stellar surface of the pulsator. During an eclipse, depending on the spatial structure of modes represented by the wave numbers (l,m), different shapes of the pulsation amplitude and phase variations can be observed. A comparison between the modelled and the observed amplitudes and phases then provides the correct mode identification. The method needs a geometrical model, the pulsation frequencies and the light curves as input. The geometrical model can be obtained from a simultaneous modelling of the light and radial velocity curves. The pulsation frequencies are obtained from subtracting a binary model from the original light curves followed by a frequency analysis of the residuals. We will identify and illustrate systems where observations with a fast CCD camera equipping the 3.6-m DOT telescope could deliver the data needed for the application of the eclipse mapping method.

Fast magnetohydrodynamic waves in a solar coronal arcade

Aims. Our aim is to investigate detailed properties of fast magnetohydrodynamic (MHD) modes of a three-dimensional waveguide for a cylindrical magnetic arcade.Methods. We derive governing equations and dispersion relations for different density profiles and numerically solve them to obtain discrete eigenvalues for fast modes and the corresponding eigenfunctions.Results. We find that small changes in the density structure in the vicinity of the field lines can lead to drastic effects on propagating solutions and, under certain conditions, two evanescent waves arise.Conclusions. We investigate coronal loop oscillations in an arcade as fast MHD modes of oscillations. We find that coronal loops with slightly different density structures can exhibit different oscillatory behaviour and some eigenmodes can be present or absent depending on this density structure. Though the model has a simple potential field, the role of a cylindrical waveguide in conjunction with differing density structures is demonstrated clearly. Multiple-wavelength observations at several points in the coronal loop arcades is suggested for correct mode identification; this is crucial for unraveling the plasma properties of the oscillating loops.

Sequential filtering for dispersion tracking and sediment sound speed inversion.

Dispersion curves in ocean environments are accurately estimated from received signals through the extraction of instantaneous modal frequencies and corresponding arrival times for long-range propagation. The ultimate goal is to estimate sediment sound speed using the extracted dispersion pattern. The approach extends work previously conducted in dispersion tracking with sequential filtering, improving on the latter technique. The sequential state-space method that is developed for the extraction of time-frequency information from specific time instances relies on a representation of those as a sum of elemental pulses, resulting from analysis of the received field. The method is tested on synthetic noisy data with different noise levels. After dispersion probability density functions are estimated via a particle filter, they are subsequently employed for sound speed inversion. Correct mode identification is a challenge impacting inversion; this is demonstrated through two examples and a way to remedy the problem is discussed.

CALCULATING ASTEROSEISMIC DIAGRAMS FOR SOLAR-LIKE OSCILLATIONS

With the success of the Kepler and CoRoT missions, the number of stars with detected solar-like oscillations has increased by several orders of magnitude, for the first time we are able to perform large-scale ensemble asteroseismology of these stars. In preparation for this golden age of asteroseismology we have computed expected values of various asteroseismic observables from models of varying mass and metallicity. The relationships between these asteroseismic observables, such as the separations between mode frequencies, are able to significantly constrain estimates of the ages and masses of these stars. We investigate the scaling relation between the large frequency separation, Delta nu, and mean stellar density. Furthermore we present model evolutionary tracks for several asteroseismic diagrams. We have extended the so-called C-D diagram beyond the main sequence to the subgiants and the red-giant branch. We also consider another asteroseismic diagram, the epsilon diagram, which is more sensitive to variations in stellar properties at the subgiant stages and can aid in determining the correct mode identification. The recent discovery of gravity-mode period spacings in red giants forms the basis for a third asteroseismic diagram. We compare the evolutionary model tracks in these asteroseismic diagrams with results from pre-Kepler studies of solar-like oscillations, and early results from Kepler.

Mode identified resonant ultrasound spectroscopy.

Resonant ultrasound spectroscopy (RUS) is a powerful tool for determining all independent elastic constants (Cij) of solids. Successful inverse calculation for Cij requires mode identification for measured resonance frequencies. In this lecture, two mode‐identified RUS methods developed by the author are presented. One is the electromagnetic acoustic resonance (EMAR) [Ogi et al., J. Acoust. Soc. Am. 106, 660 (1999)]. Using a solenoid coil and static magnetic field, vibrations of a specimen are measured through the electromagnetic‐force mechanisms. Detectable vibrational modes are controlled by changing the magnetic‐field direction. Because of the noncontacting measurement, it is applied to measurements at high temperatures easily. The second method incorporates the laser‐Doppler interferometry into RUS (RUS‐LDI method) [Ogi et al., J. Acoust. Soc. Am. 112, 2553 (2002)]. The specimen is set on the needle piezoelectric tripod in vacuum, and its displacement distributions at resonances are measured by laser interferometry for mode identification. It was applied to determine the piezoelectric coefficients and internal‐friction tensors as well as Cij of various piezoelectric materials, and also to thin‐film Cij. Because the contributions of the piezoelectric coefficients and thin‐film Cij to resonance frequencies are very small, correct mode identification becomes significantly important in their determination.

Mode identification in rapidly rotating stars

Context: Recent calculations of pulsation modes in rapidly rotating polytropic models and models based on the Self-Consistent Field method (MacGregor et al. 2007) have shown that the frequency spectrum of low degree pulsation modes can be described by an empirical formula similar to Tassoul's asymptotic formula (Tassoul 1980), provided that the underlying rotation profile is not too differential (Lignieres & Georgeot 2008, Reese et al. 2009). Aims: Given the simplicity of this asymptotic formula, we investigate whether it can provide a means by which to identify pulsation modes in rapidly rotating stars. Methods: We develop a new mode identification scheme which consists in scanning a multidimensional parameter space for the formula coefficients which yield the best-fitting asymptotic spectra. This mode identification scheme is then tested on artificial spectra based on the asymptotic formula, on random frequencies and on spectra based on full numerical eigenmode calculations for which the mode identification is known beforehand. We also investigate the effects of adding random frequencies to mimic the effects of chaotic modes which are also expected to show up in such stars (Lignieres & Georgeot 2008).

Abundance analysis of prime B-type targets for asteroseismology

Seismic modelling of the β Cephei stars promises major advances in our understanding of the physics of early B-type stars on (or close to) the main sequence. However, a precise knowledge of their physical parameters and metallicity is a prerequisite for correct mode identification and inferences regarding their internal structure. Here we present the results of a detailed NLTE abundance study of nine prime targets for theoretical modelling: γ Peg, δ Cet, ν Eri, β CMa, ξ1 CMa, V836 Cen, V2052 Oph, β Cep and DD (12) Lac (hereafter 12 Lac). The following chemical elements are considered: He, C, N, O, Mg, Al, Si, S and Fe. Our curve-of-growth abundance analysis is based on a large number of time-resolved, high-resolution optical spectra covering in most cases the entire oscillation cycle of the stars. Nitrogen is found to be enhanced by up to 0.6 dex in four stars, three of which have severe constraints on their equatorial rotational velocity, , from seismic or line-profile variation studies: β Cep ( ~ 26 km s-1), V2052 Oph ( ~ 56 km s-1), δ Cet ( < 28 km s-1) and ξ1 CMa ( 10 km s-1). The existence of core-processed material at the surface of such largely unevolved, slowly-rotating objects is not predicted by current evolutionary models including rotation. We draw attention to the fact that three stars in this subsample have a detected magnetic field and briefly discuss recent theoretical work pointing to the occurrence of diffusion effects in β Cephei stars possibly capable of altering the nitrogen surface abundance. On the other hand, the abundances of all the other chemical elements considered are, within the errors, indistinguishable from the values found for OB dwarfs in the solar neighbourhood. Despite the mild nitrogen excess observed in some objects, we thus find no evidence for a significantly higher photospheric metal content in the studied β Cephei stars compared to non-pulsating B-type stars of similar characteristics.

Resonance ultrasound spectroscopy with laser-Doppler interferometry for studying elastic properties of thin films

We propose an advanced method to determine the elastic-stiffness coefficients C ij of thin films using resonance ultrasound spectroscopy (RUS). It uses free-vibration resonance frequencies of a film/substrate layered solid and derives inversely the film’s C ij from the resonance frequencies. We develop a piezoelectric tripod consisting of two pinducers and one support to place the specimen on it and measure the resonance frequencies with high enough accuracy. Furthermore, we achieve mode identification by measuring deformation distributions on the vibrating specimen surface using laser-Doppler interferometry. Accurate measurements of frequencies and correct mode identification are the keys for deducing reliable C ij of the film. We applied this technique to copper thin films deposited of Si substrates. The resulting film’s C ij are considerably smaller than the bulk’s C ij and show anisotropy between the out-of-plane direction and in-plane direction.