Horizontal Symmetry Plane Research Articles

On obtaining the coupled-mode theory using a model of coupled plane waves for symmetric resonant diffraction gratings

We consider two analytical models describing resonant scattering of light by resonant diffraction gratings possessing a horizontal symmetry plane. For the case of oblique incidence, a multiple interference model is formulated, on the basis of which, a new approach for deriving the coupled-mode theory for the considered structures is proposed. Both considered models describe resonances in the reflectance and transmittance spectra of the studied diffraction gratings arising due to the excitation of quasiguided modes and Fabry–Pérot modes. Interaction of these modes leads to the appearance of bound states in the continuum, which are also described by the proposed models.

Analysis of the Thermally Induced Packaging Effects on the Frequency Drift of Micro-Electromechanical System Resonant Accelerometer.

Due to the working principle of MEMS resonant accelerometers, their thermally induced frequency drift is an inevitable practical issue for their extensive application. This paper is focused on reducing the thermally induced packaging effects on the frequency drift. A leadless ceramic chip carrier package with a stress-buffering layer was proposed for a MEMS resonant accelerometer, and the influences of packaging structure parameters on the frequency drift were investigated through finite element simulations and verified experimentally. Because of the thermal mismatch between dissimilar materials, the thermo-mechanical stress within the resonant beam leads to a change in the effective stiffness and causes the frequency drift to decrease linearly with increasing temperature. Furthermore, our investigations reveal that increasing the stress-buffering layer thickness and reducing the solder layer thickness can significantly minimize the thermo-mechanical stress within the resonant beam. As the neutral plane approaches the horizontal symmetry plane of the resonant beam when optimizing the packaging structure, the effects of the compressive and tensile stresses on the effective stiffness of the resonant beam will cancel each other out, which can dramatically reduce the frequency drift. These findings provide guidelines for packaging design through which to improve the temperature stability of MEMS resonant accelerometers.

Effects of Oxygen-Enhanced Combustion Methods on Combustion Characteristics of Non-Premixed Swirling Flames

The objective of the present study was to experimentally investigate and compare the characteristics of three oxygen-enhanced combustion (OEC) methods; premix enrichment (PE), air-oxy/fuel combustion (AO), and additionally also oxygen lancing (OL) method. The overall oxygen concentration varied from 21% to 38%. Combustion tests were carried out using the gas burner with the thermal input of 750 kW fired by natural gas. The characteristics of OEC methods, such as the concentration of nitrogen oxides and carbon monoxide in flue gas, in-flame temperatures distribution in the horizontal symmetry plane of the combustion chamber, heat flux to the combustion chamber wall, flue gas temperature, and the stability of flame were investigated. NOx emissions increased by more than 40 times and by 20 times for the PE method. The tests using the AO and OL methods with NOx emissions below 150 mg/Nm3 at all oxygen concentrations showed significantly better results. For all OEC methods, radiative heat transfer increased with increasing oxygen concentration. The available heat was 20% higher at 38% O2 than at 21% O2. The flue gas temperature decreased with increasing oxygen concentration, which was affected by a decrease in N2 concentration in the oxidizer and a simultaneous increase in radiant heat flux.

Three-dimensional characteristics of turbulent flow and heat transfer in Czochralski silicon melt with different cusp magnetic field configurations

Three-dimensional unsteady simulations are performed for the turbulent flow and heat transfer in a Czochralski silicon melt for 300 mm crystal growth. The influence of the horizontal symmetry plane in the cusp magnetic field on the melt flow, temperature field, and crystal/melt interface is systematically analyzed. The numerical results show that the melt velocity and its fluctuation near the interface decrease, while the temperature and its fluctuation increase gradually with the downward horizontal symmetry plane position. For each horizontal symmetry plane position, the oscillation frequencies of melt temperature and velocity consist of a basic frequency and its integer multiple frequencies. Thermal waves with a regular shape rotate on the melt-free surface, and the rotational direction is consistent with the crucible rotation. The interface shape is strongly associated with the heat transfer near the interface, which depends on the melt flow direction and velocity magnitude as well as the temperature gradient below the crystal. In addition, the oscillation of interface temperature is affected by the melt flow below the crystal, changing from high-frequency small fluctuation to low-frequency large fluctuation with the horizontal symmetry plane moving down.

Frequency-dependent anisotropy due to non-orthogonal sets of mesoscale fractures in porous media

SUMMARY The monoclinic medium with a horizontal symmetry plane is gradually being studied for seismic anisotropy characterization. The principle goal of this paper is to investigate the effect of fracture parameters (azimuth angle, density, aspect ratio, scale) on the exact and approximate monoclinic anisotropy parameters. We derive the monoclinic porous media based on the Chapman model which accounts for the wave-induced fluid flow and give the expressions of the Thomsen-style anisotropy parameters (nine orthorhombic anisotropy parameters: VP0, VS0, ϵ1, ϵ2, γ1, γ2, δ1, δ2, δ3, three exact monoclinic parameters: ζ1, ζ2, ζ3 and three approximate monoclinic parameters: $\widetilde{\zeta _{1}}, \widetilde{\zeta _{2}}, \widetilde{\zeta _{3}}$). The dependence of Thomsen-style anisotropy parameters associated with azimuth angle between two fracture sets is analysed. The orthorhombic anisotropy parameters and monoclinic anisotropy parameters have the same period (π) on the azimuth angle between two fracture sets. The exact and approximate monoclinic anisotropy parameters responsible for the rotation of the P-wave NMO ellipse have a similar trend versus the azimuth angle, while those responsible for the rotation of the S1- and S2-wave NMO ellipses have significant discriminations. The influence of fracture density, aspect ratio, and scale on the monoclinic parameters are also analysed. The monoclinic anisotropy parameters responsible for the rotation of the P-wave NMO ellipse decrease with fracture density and aspect ratio increasing from 0 to 0.1, while those responsible for the rotation of S1- and S2-wave NMO ellipses increase with the fracture parameters. The fracture density has a bigger influence on the monoclinic anisotropy parameters than the fracture aspect ratio. When saturated with different fluids (water and CO2), the monoclinic parameters have a similar behaviour versus the azimuth angle between two fracture sets.

Determination of the "Privileged Structure" of 8-Hydroxyquinoline.

An accurate semi-experimental equilibrium structure of 8-hydroxyquinoline (8-HQ) has been determined combining experiment and theory. The cm-wave rotational spectrum of 8-HQ was recorded in a pulsed supersonic jet using broadband dual-path reflection and narrowband Fabry-Perot-type resonator Fourier-transform microwave spectrometers. Accurate rotational and quartic centrifugal distortion constants and 14 N quadrupole coupling constants are determined. Rotational constants of all 13 C, 18 O and 15 N singly substituted isotopologues in natural abundance and those of a chemically synthesized OD isotopologue were used to obtain geometric parameters for all the heavy atoms and the hydroxyl hydrogen from a number of structure determination models. Theoretical approaches allowed for the determination of a semi-experimental equilibrium structure, in which computed rovibrational and electronic corrections were utilized to convert vibrational ground state constants into equilibrium constants. Despite the molecule having only a horizontal plane of symmetry and possessing 11 individual heavy atoms, microwave spectroscopy has allowed for a reliable and accurate structure determination. A mass dependent, structure was determined and proved to be equally reliable by comparison with the B3LYP-D3(BJ)/aVTZ equilibrium structure.

Perturbation in monoclinic medium with a horizontal symmetry plane

Summary The perturbation method applied for the phase velocities in the monoclinic model with a horizontal symmetry plane gives insight into the seismic signatures of P, S1 and S2 wave modes associated with the monoclinic stiffness coefficients. The perturbation-based approximations are very accurate and can be used for modelling and inversion purposes.

On parameterization in monoclinic media with a horizontal symmetry plane

I have derived accurate anisotropy parameters for a monoclinic anisotropy model with a horizontal symmetry plane based on normal moveout (NMO) ellipses for P-, S1-, S2-, and converted waves. The NMO velocity ellipse is also defined for all types of converted waves. The parameters are defined in the phase domain and compared with existing approximate monoclinic anisotropy parameters. These parameters are evaluated for two benchmark models consisting of two nonorthogonal fracture sets embedded into a transversely isotropic medium with a vertical symmetry axis. The dependence of monoclinic parameters on the azimuth angle between the fracture sets is analyzed. Being linearized with respect to fracture weaknesses, the monoclinic anisotropy parameters can be decomposed into sine functions of double and quartic azimuth angle between the fracture sets with the weights given by the stiffness coefficients of the background model. The discrimination between the fracture parameters computed from a given set of monoclinic parameters is dependent on the background model and controlled by the azimuth angle between the fracture sets.

Practical concept of traveltime inversion of simulated P-wave vertical seismic profile data in weak to moderate arbitrary anisotropy

We have developed a practical concept of compressional wave (P-wave) traveltime inversion in weakly to moderately anisotropic media of arbitrary symmetry and orientation. The concept provides sufficient freedom to explain and reproduce observed anisotropic seismic signatures to a high degree of accuracy. The key to this concept is the proposed P-wave anisotropy parameterization (A-parameters) that, together with the use of the weak-anisotropy approximation, leads to a significantly simplified theory. Here, as an example, we use a simple and transparent formula relating P-wave traveltimes to 15 P-wave A-parameters describing anisotropy of arbitrary symmetry. The formula is used in the inversion scheme, which does not require any a priori information about anisotropy symmetry and its orientation, and it is applicable to weak and moderate anisotropy. As the first step, we test applicability of the proposed scheme on a blind inversion of synthetic P-wave traveltimes generated in vertical seismic profile experiments in homogeneous models. Three models of varying anisotropy are used: tilted orthorhombic and triclinic models of moderate anisotropy (approximately 10%) and an orthorhombic model of strong anisotropy (>25%) with a horizontal plane of symmetry. In all cases, the inversion yields the complete set of 15 P-wave A-parameters, which make reconstruction of corresponding phase-velocity surfaces possible with high accuracy. The inversion scheme is robust with respect to noise and the source distribution pattern. Its quality depends on the angular illumination of the medium; we determine how the absence of nearly horizontal propagation directions affects inversion accuracy. The results of the inversion are applicable, for example, in migration or as a starting model for inversion methods, such as full-waveform inversion, if a model refinement is desired. A similar procedure could be designed for the inversion of S-wave traveltimes in anisotropic media of arbitrary symmetry.

Exact and approximate reflection/transmission responses from a layer containing vertical fractures

SUMMARYAnalyses of vertical fractures are of great interest in characterizing the fluid flow and minimum in situ stress direction in reservoirs. Long-wavelength equivalent orthorhombic (ORT) media typically characterize the anisotropy induced by a set of vertical parallel fractures or two sets of vertical and mutually orthogonal fractures embedded into a transversely isotropic medium with a vertical symmetry axis (VTI). Reflection and transmission (R/T) responses quantify wave amplitude variations in 1-D media and help to reveal the model property enclosing the heterogeneity. Conventionally, the R/T responses are analysed for an interface bounded by two half-spaces. However, for a plane wave travelling through a subsurface layer, the wave scattering effects at the top and bottom of the layer interact with each other. For a continuous infinite ORT space cut in two halves along the horizontal symmetry plane, we focus on the plane wave R/T responses from an ORT layer that is placed between the two halves, where the azimuths of the vertical symmetry plane in the layer and in the upper and lower half-spaces are identical. The R/T coefficient modelling method can be found in many publications for the ORT layer with an arbitrary finite thickness. We decompose the exact R/T coefficients into series expansions that correspond to different orders of intrabed multiples in the ORT layer. Under the weak-contrast assumption for the ORT half-spaces and the ORT layer, we use the anisotropic background medium to obtain the first-order R/T coefficient approximations and second-order reflectivity approximations. There is no constraint for the middle layer thickness in the obtained first-order reflectivity approximations. In the proposed first-order transmissivity approximations and second-order reflectivity approximations, the layer thickness is assumed to be thin to obtain appropriate approximations for a few wave modes. The isotropic background medium is also considered for weakly anisotropic models to obtain simpler approximations that facilitate parametric analyses. For the ORT layer with its thickness much smaller than the propagating wave's wavelength, the influences of the layer thickness on R/T coefficients can be inspected conveniently from the derived approximations. Particularly, the R/T coefficients are analysed for the model which would be a homogeneous VTI medium, if the vertical parallel fractures were absent from the middle layer. Numerical tests demonstrate that the proposed R/T coefficient approximations perform well for the thin ORT layer. The approximation accuracy decreases when the thin layer thickness increases.

Reflection and transmission approximations for monoclinic media with a horizontal symmetry plane

We have considered a horizontal plane interface bounded by two monoclinic half-spaces to approximate the reflection and transmission (R/T) responses normalized by the vertical energy flux. We assume the monoclinic media have a horizontal symmetry plane, and the exact R/T coefficients can be analytically obtained for P-, S1-, and S2-waves. The exact R/T coefficients depend on the absolute model parameters of both half-spaces, whereas the R/T responses indicate the heterogeneity at the interface and, thus, can be characterized with model parameter contrasts across the interface. Compared with the exact R/T solutions, appropriate approximations with desirable accuracy can be determined by fewer model parameter contrasts and facilitate the parametric analyses and inversions. We first consider the weak-contrast assumption and use the perturbation method to obtain first-order approximations based on the homogeneous monoclinic background medium. To accommodate the strong-contrast interface, the published second-order approximations are then revised for the monoclinic media. For weakly anisotropic media, the first- and second-order approximations are proposed based on the isotropic background medium. Two pseudowaves are introduced as intermediate waves to legitimize our approximations for S1, S2, and converted waves in the applications. The derived approximations are verified on monoclinic models numerically. The second-order approximation method based on the monoclinic background medium is proven to have the overall best accuracy.

Tomo-PIV measurements in the wake of a tethered sphere undergoing VIV

The 3D flow field in the wake of a tethered sphere ( D=6 mm, m∗=7.77, L∗=4.1) undergoing vortex induced vibrations (VIV) in a water tunnel, was measured using tomographic particle image velocimetry (tomo-PIV). The flow field was investigated for four different reduced velocities ranging between 3.6<U∗<13.2, corresponding to Reynolds numbers ranging between 382< ReD<1,392. At U∗=3.6, the sphere did not oscillate and shed vortices resembled a train of “hairpin” heads having a vertical plane of symmetry. At U∗=5.8, sphere oscillations were highly periodic and “omega”-shaped vortices having a horizontal plane of symmetry were alternately shed, and transformed into vortex rings further downstream while still connected to upstream structures by a thin vortex filament. At U∗=7.9 and 13.2, the sphere’s transverse amplitude response was intermittent and vortices in the sphere’s wake were characterized by longitudinal and vertical “struts” as well as “arches”, with seemingly little organization.

Tunable Spin-Superconductor Coupling of Spin 1/2 Vanadyl Phthalocyanine Molecules.

Atomic-scale magnetic moments in contact with superconductors host rich physics based on the emergence of Yu-Shiba-Rusinov (YSR) magnetic bound states within the superconducting condensate. Here, we focus on a magnetic bound state induced into Pb nanoislands by individual vanadyl phthalocyanine (VOPc) molecules deposited on the Pb surface. The VOPc molecule is characterized by a spin magnitude of 1/2 arising from a well-isolated singly occupied d xy-orbital and is a promising candidate for a molecular spin qubit with long coherence times. X-ray magnetic circular dichroism (XMCD) measurements show that the molecular spin remains unperturbed even for molecules directly deposited on the Pb surface. Scanning tunneling spectroscopy and density functional theory (DFT) calculations identify two adsorption geometries for this "asymmetric" molecule (i.e., absence of a horizontal symmetry plane): (a) oxygen pointing toward the vacuum with the Pc laying on the Pb, showing negligible spin-superconductor interaction, and (b) oxygen pointing toward the Pb, presenting an efficient interaction with the Pb and promoting a Yu-Shiba-Rusinov bound state. Additionally, we find that in the first case a YSR state can be induced smoothly by exerting mechanical force on the molecules with the scanning tunneling microscope (STM) tip. This allows the interaction strength to be tuned continuously from an isolated molecular spin case, through the quantum critical point (where the bound state energy is zero) and beyond. DFT indicates that a gradual bending of the VO bond relative to the Pc ligand plane promoted by the STM tip can modify the interaction in a continuously tunable manner. The ability to induce a tunable YSR state in the superconductor suggests the possibility of introducing coupled spins on superconductors with switchable interaction.

Fourth-order normal moveout velocity in elastic layered orthorhombic media — Part 2: Offset-azimuth domain

Based on the theory derived in part 1, in which we obtained the azimuthally dependent fourth-order normal-moveout (NMO) velocity functions for layered orthorhombic media in the slowness-azimuth/slowness and the slowness-azimuth/offset domains, in part 2, we extend the theory to the offset-azimuth/slowness and offset-azimuth/offset domains. We reemphasize that this paper does not suggest a new nonhyperbolic traveltime approximation; rather, it provides exact expressions of the NMO series coefficients, computed for normal-incidence rays, which can then be further used within known azimuthally dependent traveltime approximations for short to moderate offsets. The same type of models as in part 1 are considered, in which the layers share a common horizontal plane of symmetry, but the azimuths of their vertical symmetry planes are different. The same eight local (single-layer) and global (overburden multilayer) effective parameters are used. In addition, we have developed an alternative set of global effective parameters in which the “anisotropic” effective parameters are normalized, classified into two groups: two “azimuthally isotropic” parameters and six “azimuthally anisotropic” parameters. These parameters have a clearer physical interpretation and they are suitable for inversion purposes because they can be controlled and constrained. Next, we propose a special case, referred to as “weak azimuthal anisotropy,” in which only the azimuthally anisotropic effective parameters are assumed to be weak. The resulting NMO velocity functions are considerably simplified, reduced to the form of the slowness-azimuth/slowness formula. We verify the correctness of our method by applying it to a multilayer orthorhombic medium with strong anisotropy. We introduce our derived, fourth-order slowness-azimuth/offset domain NMO velocity function into the well-known nonhyperbolic asymptotic traveltime approximation, and we compare the approximate traveltimes with exact traveltimes obtained by two-point ray tracing. The comparison shows an accurate match up to moderate offsets. Although the accuracy with the weak azimuthal anisotropic formula is inferior, it can still be considered reasonable for practical use.

A new parameterization for waveform inversion in acoustic orthorhombic media

Orthorhombic anisotropic model inversion is extra challenging because of the multiple parameter nature of the inversion problem. The high number of parameters required to describe the medium exerts considerable trade-off and additional nonlinearity to a full-waveform inversion (FWI) application. Choosing a suitable set of parameters to describe the model and designing an effective inversion strategy can help in mitigating this problem. Using the Born approximation, which is the central ingredient of the FWI update process, we have derived radiation patterns for the different acoustic orthorhombic parameterizations. Analyzing the angular dependence of scattering (radiation patterns) of the parameters of different parameterizations starting with the often used Thomsen-Tsvankin parameterization, we have assessed the potential trade-off between the parameters and the resolution in describing the data and inverting for the parameters. The analysis led us to introduce new parameters [Formula: see text], [Formula: see text], and [Formula: see text], which have azimuthally dependent radiation patterns, but keep the scattering potential of the transversely isotropic parameters stationary with azimuth (azimuth independent). The novel parameters [Formula: see text], [Formula: see text], and [Formula: see text] are dimensionless and represent a measure of deviation between the vertical planes in orthorhombic anisotropy. Therefore, these deviation parameters offer a new parameterization style for an acoustic orthorhombic medium described by six parameters: three vertical transversely isotropic (VTI) parameters, two deviation parameters, and one parameter describing the anisotropy in the horizontal symmetry plane. The main feature of any parameterization based on the deviation parameters, is the azimuthal independency of the modeled data with respect to the VTI parameters, which allowed us to propose practical inversion strategies based on our experience with the VTI parameters. This feature of the new parameterization style holds for even the long-wavelength components of the model constrained by traveltimes.

Vortex dynamics and associated fluid forcing in the near wake of a light and heavy tethered sphere in uniform flow

Time-resolved particle image velocimetry measurements of vortex-induced vibrations of a negatively (“heavy”) and positively (“light”) buoyant tethered sphere in uniform flow, and its wake characteristics were performed in a closed-loop water channel. Experiments for both spheres were performed at similar bulk velocities, ranging between 0.048 < U < 0.32 m/s, corresponding to reduced velocities, 2.2 < U * < 13.5. Initially stationary, with increasing U, the amplitude response displayed periodic oscillations beyond the Hopf bifurcation as a result of “lock-in” between vortex shedding and the natural structural frequency. However, while the heavy sphere’s amplitude decreased beyond U * = 7.0, the light sphere’s amplitude continuously increased. In the periodic oscillation region, flow field characteristics in the wakes of both spheres (at comparable U * ) were similar, characterized by alternately shed hairpin vortices having a horizontal symmetry plane. Primary vortex trajectories in the frame of reference of the sphere collapsed for different U * (but not for different m * ) when scaled by f 2,s/U, where f 2,s is the sphere’s transverse oscillation frequency. This allows determination of vortex positions based on sphere dynamics and bulk flow conditions only. Associated vortex convection velocities as a function of downstream position from the sphere also nearly collapsed when normalized by U. In addition, fluid forcing and energy transfer from fluid to sphere were estimated based on an analogy between aircraft trailing vortices and hairpin vortices. Maximum forcing occurred at vortex pinch-off. For the highest comparable U * , despite different amplitudes, total transferred energy during one oscillation period was similar for both spheres. Changes in sphere dynamics must therefore be related to differences in inertia.

Permeability tensor versus permittivity one in theory of nonreciprocal optical components

We discuss symmetry properties of the combined systems: electromagnetic field (TE and TM modes)+medium (nondiagonal permeability tensor [μ] and nondiagonal permittivity one [ϵ]) in 2D photonic crystals with transverse magnetization. We show that the origin of orthogonality of the pairs (TE mode+[ϵ]) and (TM mode+[μ]) is different parities of the corresponding fields with respect to the horizontal plane of symmetry of the crystal. As a result of this symmetry, a common use only of the permittivity tensor [ϵ] in the electromagnetic theory of nonreciprocal optical components, ignoring the permeability tensor [μ], leads to loss of a significant part of possible solutions related to TE modes.

Estimation of azimuthal anisotropy from VSP data using multicomponent S-wave velocity analysis

Observation of azimuthal shear wave anisotropy can be useful for characterization of fractures or stress fields. Shear wave anisotropy is often estimated by measuring splitting of individual shear wave events in vertical seismic profile (VSP) data. However, this method may become unreliable for zero-offset (marine) VSP where the seismogram often contains no strong individual shear events, such as direct downgoing shear wave, but often contains many low-amplitude PS mode converted waves. We have developed a new approach for estimation of the fast and slow shear wave velocities and orientation of polarization planes based on the multicomponent linear traveltime moveout velocity analysis. This technique is applicable to zero-offset VSP data, and should take advantage of the presence of a large number of shear wave events with the same apparent velocity (which, for a horizontally layered medium, should be close to the interval velocity). The approach assumes that the VSP data are acquired in a vertical well drilled in an orthorhombic medium with a horizontal symmetry plane (including horizontal transverse isotropy). The main idea is to estimate the dominant apparent velocity for a given polarization direction by measuring the coherency of the seismic signal of a large number of events as a function of the apparent velocity. The algorithm was tested on marine three-component (3C) VSP acquired in the North West Shelf of Australia, and on land 3C VSP acquired with different sources in the same borehole located in Otway Basin, Victoria. These tests show good agreement between anisotropy parameters (magnitude and orientation) derived from the VSP and cross-dipole sonic log data.

Estimation of interval anisotropic attenuation from reflection data

Knowledge of interval attenuation can be highly beneficial in reservoir characterization and lithology discrimination. We combine the spectral-ratio method with velocity-independent layer stripping to develop a technique for the estimation of the interval attenuation coefficient from reflection seismic data. The layer-stripping procedure is based on identifying the reflections from the top and bottom of the target layer that share the same ray segments in the overburden. The algorithm is designed for heterogeneous, arbitrarily anisotropic target layers, but the overburden is assumed to be laterally homogeneous with a horizontal symmetry plane. Although no velocity information about the overburden is needed, interpretation of the computed anisotropic attenuation coefficient involves the phase angle in the target layer. Tests on synthetic P-wave data from layered transversely isotropic and orthorhombic media confirm the high accuracy of 2D and 3D versions of the algorithm. We also demonstrate that the interval attenuation estimates are independent of the inhomogeneity angle of the incident and reflected waves.

Estimation of interval anisotropy parameters using velocity-independent layer stripping

Moveout analysis of long-spread P-wave data is widely used to estimate the key time-processing parameter [Formula: see text] in layered transversely isotropic media with a vertical symmetry axis (VTI). Inversion for interval [Formula: see text] values, however, suffers from instability caused by the trade-off between the effective moveout parameters and by subsequent error amplification during Dix-type layer stripping. We propose an alternative approach to nonhyperbolic moveout inversion based on the velocity-independent layer-stripping (VILS) method of Dewangan and Tsvankin. Also, we develop the 3D version of VILS and apply it to interval parameter estimation in orthorhombic media using wide-azimuth, long-spread data. If the overburden is laterally homogeneous and has a horizontal symmetry plane, VILS produces the exact interval traveltime-offset function in the target layer without knowledgeof the velocity field. Hence, Dix-type differentiation of moveout parameters used in existing techniques is replaced by the much more stable layer stripping of reflection traveltimes. The interval traveltimes are then inverted for the moveout parameters using the single-layer nonhyperbolic moveout equation. The superior accuracy and stability of the algorithm are illustrated on ray-traced synthetic data for typical VTI and orthorhombic models. Even small correlated noise in reflection traveltimes causes substantial distortions in the interval [Formula: see text] values computed by conventional Dix-type differentiation. In contrast, the output of VILS is insensitive to mild correlated traveltime errors. The algorithm is also tested on wide-azimuth P-wave reflection data recorded above a fractured reservoir at Rulison field in Colorado. The interval moveout parameters estimated by VILS in the shale layer above the reservoir are more plausible and less influenced by noise than those obtained by the Dix-type method.