Vertical Slowness Research Articles

Diving waves in acoustic factorized orthorhombic media

AbstractDiving waves propagating in the subsurface are massive sources of low‐frequency information that can be used to constrain the kinematic component of the velocity model. Compared to reflected waves, less is known about the behaviour of diving waves, especially in the presence of azimuthal anisotropy. Anisotropy is needed to place the events to the correct depths and match travel times in synthetics with recorded data. Obtaining more insights into the influence of anisotropy on diving wave propagation can help to find parameters with a low trade‐off for inversion. Here, we derive equations for diving qP‐waves in an acoustic factorized anisotropic model with orthorhombic anisotropy. The effects of the anisotropic parameters in the acoustic factorized orthorhombic model are tested by perturbing , , , and and observing differences in the ray paths, the effective vertical slowness and the relative geometrical spreading. The properties of diving waves in this model are also compared with those in an acoustic isotropic model and acoustic factorized anisotropic models with elliptical‐ and vertical transverse isotropic anisotropy. From our analysis, we found that perturbing and has the most significant influence on these characteristics. The , and parameters were shown to induce minor changes. Compared with the other models, the acoustic factorized orthorhombic model had the most in common with the acoustic factorized anisotropic model with elliptical anisotropy. Although, in general, none of the other models could fully represent the effects of orthorhombic anisotropy.

Reflection and transmission coefficients of spherical waves at an interface separating two dissimilar viscoelastic solids

SUMMARY Spherical wave reflection and transmission (R/T) coefficients at an interface are not only of theoretical significance but also play an important role in the amplitude variation with offset (AVO) analysis of wide-angle reflection seismic data and cross-borehole surveys. For sources close to the interface the resulting wavefields cannot be adequately described in terms of a single incident plane wave. Rather, the spherical waves must be viewed as the superposition of an infinite number of plane waves. Moreover, the R/T coefficients for each individual plane wave in viscoelastic media have proven to be more complicated than expected due to the difficulty in selecting the correct vertical slowness. In such attenuating media the R/T coefficients cannot be properly determined by simply replacing the real elastic parameters with their complex viscoelastic counterparts. In this study, the reflection and transmission coefficients of spherical waves at a plane interface separating two dissimilar viscoelastic solids are rigorously investigated. The difficulty in selecting the vertical slowness is shown to be circumvented if the spherical wavefields are calculated from the plane wavefields using the Sommerfeld integral appropriate for the dissipative materials. However, some resulting phase curves of the complex spherical wave R/T coefficients tend to be of opposite sign to the corresponding phase curves of plane waves due to non-uniqueness of the latter for post-critical wave incidence. In this contribution we propose a new definition of spherical wave R/T coefficients for viscoelastic media which differs from the conventional one. Its advantages are that it is not explicitly expressed as a function of the R/T angles, it is valid for both P and S waves, yet it is consistent with the existing definitions of spherical wave R/T coefficients but is more robust. By way of examples we compute both spherical wave reflection coefficients (SWRC) and spherical wave transmission coefficients (SWTC) for two different viscoelastic models. Unlike plane waves, both the SWRC and the SWTC of converted PS waves are found to be non-zero at vertical incidence and may be drastically affected by the existence of longitudinal PS waves which are confirmed by full waveform calculations for the converted PS waves.

Inversion of Fracture Weaknesses Based on Linearly Approximated Traveltime

Seismic traveltime is crucial for the inversion of anisotropy parameters. In the inversion for fractured rock, a typical transversely isotropic medium with a horizontal symmetry axis (HTI), the joint utilization of traveltime of P- and split shear waves can provide more anisotropy information than the utilization of only P-wave traveltime. The computational effort of nonlinear parameter inversion also increases with the involvement of split shear waves. Therefore, based on the series expansion of vertical slowness projection, we derive the linear approximations for the first-break traveltimes of P-, S1-, and S2-waves with respect to fracture weaknesses, which are used to accelerate and stabilize the inversion process. Linear coefficients are used to analyze the sensitivity of the traveltime to fracture weakness and thus the accuracy of the results. To make our proposed approximation more practical, we expand our linear equations to the traveltime difference between the HTI model and its isotropic background model and derive the joint inversion equation for fracture weaknesses in a vertical seismic profile (VSP) survey by jointly using P-, S1-, and S2-waves. Field data application shows that our method is feasible for estimating fracture weaknesses by using walkaround VSP data. The error caused by linear approximation can be reduced by the joint utilization of multiple wave modes.

Inhomogeneous wave reflection from the surface of a partially saturated thermoelastic porous media

PurposeThe purpose of this paper is to study the propagation of inhomogeneous waves in a partially saturated poro-thermoelastic media through the examples of the free surface of such media..Design/methodology/approachThe mathematical model evolved by Zhou et al. (2019) is solved through the Helmholtz decomposition theorem. The propagation velocities of bulk waves in partially saturated poro-thermoelastic media are derived by using the potential functions. The phase velocities and attenuation coefficients are expressed in terms of inhomogeneity angle. Reflection characteristics (phase shift, loci of vertical slowness, amplitude, energy) of elastic waves are investigated at the stress-free thermally insulated boundary of a considered medium. The boundary can be permeable or impermeable. The incident wave is portrayed with both attenuation and propagation directions (i.e. inhomogeneous wave). Numerical computations are executed by using MATLAB.FindingsIn this medium, the permanence of five inhomogeneous waves is found. Incidence of the inhomogeneous wave at the thermally insulated stress-free surface results in five reflected inhomogeneous waves in a partially saturated poro-thermoelastic media. The reflection coefficients and splitting of incident energy are obtained as a function of propagation direction, inhomogeneity angle, wave frequency and numerous thermophysical features of the partially saturated poro-thermoelastic media. The energy of distinct waves (incident wave, reflected waves) accompanying interference energies between distinct pairs of waves have been exhibited in the form of an energy matrix.Originality/valueThe sensitivity of propagation characteristics (velocity, attenuation, phase shift, loci of vertical slowness, energy) to numerous aspects of the physical model is analyzed graphically through a particular numerical example. The balance of energy is substantiated by virtue of the interaction energies at the thermally insulated stress-free surface (opened/sealed pores) of unsaturated poro-thermoelastic media through the bulk waves energy shares and interaction energy.

Continuous and elastically consistent viscoelastic reflection and transmission coefficient curves for plane inhomogeneousPandSwaves

SUMMARYFor inhomogeneous plane waves in dissipative media, correctly selecting the vertical slowness (q) is the key requirement to obtain physically acceptable reflection/transmission (R/T) coefficients (e.g. both continuous curves as a function of incidence angle, and consistency with the elastic coefficients at very low attenuation). Based on the fundamental branch-cut theory, the continuity criterion ensures the continuity of the R/T coefficient curves. The elastic consistence is obtained due to the definition of the mixed principal values and the consistent assumptions of time dependence of the harmonic plane wave, the Z-direction of the spatial coordinate system and the particle motion (polarization) vectors. The elastic consistence of R/T coefficients is checked by both elastic models with zero dissipation factor (1/Q) and the equal-Q model in which the Q values of the incident wave and the R/T waves are non-zero but equal for the P and S waves on both sides of the interface. In particular, the previously reported 180° phase difference between the viscoelastic coefficients with arbitrarily small attenuation but the same ratio of Q across the interface and the corresponding elastic coefficients is circumvented by introducing the mixed principal value. The continuity criterion is implemented directly in the complex vertical slowness squared (q2) plane in which the branch-cut is defined. Furthermore, the loci of q2 and several ‘critical angles’ defined for anelastic waves are clearly investigated and clarified. The loci of q2 are expressed as a function of the incidence angle and the incident wave inhomogeneity parameter D. The plots of wave inhomogeneity parameter (D and/or attenuation angle γ) versus incidence angle are calculated from the slowness vectors. The resultant D values, especially their equality for all vertically propagating R/T waves, are examined using the complex Snell's law to provide extra support to the correctness of the slowness vectors and thus of the R/T coefficients. It is worth noting that phase angle of the R/T waves from an inhomogeneous incident wave may exhibit rapid changes at vertical incidence because near-vertical reflection is still the dominant application of the exploration seismic method. To the best of our knowledge, this research is the first time it has been possible to obtain continuous and elastically consistent viscoelastic R/T coefficients.

Reflection and transmission of plane waves at an interface separating two poro-viscoelastic materials with continuity and elastic consistence

SUMMARYThe seismic reflection/transmission (R/T) problems have been investigated for various complicated porous materials described by various poro-viscoelastic theories. However, it was also reported that even for a simple plane wave at a plane interface between two dissimilar isotropic viscoelastic solids, they were proved to be more complicated than expected and still required further study. The main difficulty is to correctly select the signs of the vertical components of the slowness vectors (or vertical slowness q) of the viscoelastic R/T waves to calculate R/T coefficients (including the relevant displacement amplitudes and phase delays) without unphysical discontinuity but with elastic consistence. Logically, if this problem had not been solved in the relatively simple case of waves in isotropic viscoelastic materials, it would not be expected to be solved in the complicate porous media. The existing criterion to select the sign of vertical slowness for poro-viscoelastic waves is the radiation condition that has been reported to cause unphysical discontinuity for the R/T coefficients of viscoelastic waves. In this paper, the radiation condition is illustrated to cause the unphysical discontinuities. Meanwhile, the continuity criterion is for the first time applied in the R/T coefficients calculation for poro-viscoelastic waves. The continuity criterion is simply suggested to be conducted in the complex vertical slowness square (q2) plane by swapping the sign of the q for the relevant wave whose q2 locus crosses the branch cut. Furthermore, the elastic consistence is also for the first time considered for poro-viscoelastic waves. We stress the importance of consistence between the R/T coefficient equations of poro-viscoelastic waves and those of pure elastic waves, which includes three consistent assumptions: time dependence of harmonic waves, the z-direction of the coordinate system and particle motion (polarization) vectors. With the numerical examples of poro-viscoelastic interfaces, the R/T coefficients of three types of incident waves, that is, homogeneous S waves, inhomogeneous S waves and homogeneous P waves, are investigated for frequencies 1000 and 0.001 Hz, representing highly and weakly dissipative poro-elastic waves, respectively. The calculated R/T coefficients are shown to be continuous without unphysical discontinuity under the continuity criterion. For the cases of homogeneous S- or P-wave incidence, the R/T coefficients of poro-viscoelastic waves with 0.001 Hz well match the corresponding coefficients of elastic waves in terms of amplitudes and phases, and thus the elastic consistence is well confirmed. For the highly dissipative poro-elastic waves (1000 Hz), the R/T coefficients significantly depend on the degrees of inhomogeneity of the incident waves. In a similar manner to the viscoelastic wave, a higher degree of inhomogeneity of an incident wave better tends to smooth the R/T coefficients of poro-viscoelastic waves. The methods suggested in this paper to solve the problems of R/T coefficient continuity and elastic consistence for the poro-viscoelastic waves can also be applied for viscoelastic waves as the special case.

Traveltime and relative geometric spreading approximation in elastic orthorhombic medium

Wavefield properties such as traveltime and relative geometric spreading (traveltime derivatives) are highly essential in seismic data processing and can be used in stacking, time-domain migration, and amplitude variation with offset analysis. Due to the complexity of an elastic orthorhombic (ORT) medium, analysis of these properties becomes reasonably difficult, where accurate explicit-form approximations are highly recommended. We have defined the shifted hyperbola form, Taylor series (TS), and the rational form (RF) approximations for P-wave traveltime and relative geometric spreading in an elastic ORT model. Because the parametric form expression for the P-wave vertical slowness in the derivation is too complicated, TS (expansion in offset) is applied to facilitate the derivation of approximate coefficients. The same approximation forms computed in the acoustic ORT model also are derived for comparison. In the numerical tests, three ORT models with parameters obtained from real data are used to test the accuracy of each approximation. The numerical examples yield results in which, apart from the error along the y-axis in ORT model 2 for the relative geometric spreading, the RF approximations all are very accurate for all of the tested models in practical applications.

Dispersion of phase velocities in horizontally layered anisotropic slightly-contrasted periodic media

In this article, authors developed a method for estimating the Floquet waves velocity dispersion in a periodic horizontally layered medium with anisotropic layers. The method is based on the calculation of the effective system matrix — the logarithm of the period propagator. In the low-frequency range, the effective system matrix is approximated by the three first terms of the BCH (Baker-Campbell-Hausdorff) series. The eigenvalues of the effective system matrix are the vertical slowness of different wave modes of Floquet waves propagating up and down. To estimate the dispersion of the Floquet waves, the difference matrices are computed from the system matrices of the layers and the system matrix of the Backus averaged medium for the period — the increment matrices. By assuming that the increment matrices are small compared to the system matrix of the Backus medium, a second-order perturbation theory is applied. That allows to compute the eigenvalues of the effective system matrix. As a result, formulas for calculating the approximation of the dispersion of the vertical slowness and phase velocity of Floquet waves in a periodic horizontally layered medium with anisotropic layers are derived. These formulae are given by a weighted sum of the products of various pairs of increments of the system matrices of the layers and allow a very accurate approximation of the dispersion of phase velocities and vertical slowness in the low-frequency range. The accuracy of the calculations is demonstrated in a three-layer periodic medium with orthorhombic layers with different azimuths of symmetry planes. The obtained approximation of the dispersion of the squares of the vertical slowness and phase velocity of the Floquet waves is very accurate in the low-frequency range and gives satisfactory result in the first third of the corresponding pass band.

New acoustic approximation for transversely isotropic media with a vertical symmetry axis

Seismic data processing in the elastic anisotropic model is complicated due to multiparameter dependency. Approximations to the P-wave kinematics are necessary for practical purposes. The acoustic approximation for P-waves in a transversely isotropic medium with a vertical symmetry axis (VTI) simplifies the description of wave propagation in elastic media, and as a result, it is widely adopted in seismic data processing and analysis. However, finite-difference implementations of that approximation are plagued with S-wave artifacts. Specifically, the resulting wavefield also includes artificial diamond-shaped S-waves resulting in a redundant signal for many applications that require pure P-wave data. To derive a totally S-wave-free acoustic approximation, we have developed a new acoustic approximation for pure P-waves that is totally free of S-wave artifacts in the homogeneous VTI model. To keep the S-wave velocity equal to zero, we formulate the vertical S-wave velocity to be a function of the model parameters, rather than setting it to zero. Then, the corresponding P-wave phase and group velocities for the new acoustic approximation are derived. For this new acoustic approximation, the kinematics is described by a new eikonal equation for pure P-wave propagation, which defines the new vertical slowness for the P-waves. The corresponding perturbation-based approximation for our new eikonal equation is used to compare the new equation with the original acoustic eikonal. The accuracy of our new P-wave acoustic approximation is tested on numerical examples for homogeneous and multilayered VTI models. We find that the accuracy of our new acoustic approximation is as good as the original one for the phase velocity, group velocity, and the kinematic parameters such as vertical slowness, traveltime, and relative geometric spreading. Therefore, the S-wave-free acoustic approximation could be further applied in seismic processing that requires pure P-wave data.

Traveltime approximation for converted waves in elastic orthorhombic media

The moveout approximations are commonly used in seismic data processing such as velocity analysis, modeling, and time migration. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from the real data. To approximate the traveltime in an elastic orthorhombic (ORT) medium, we defined an explicit rational-form approximation for the traveltime of the converted [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves. To obtain the expression of the coefficients, the Taylor-series approximation is applied in the corresponding vertical slowness for three pure-wave modes. By using the effective model parameters for [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-waves, the coefficients in the converted-wave traveltime approximation can be represented by the anisotropy parameters defined in the elastic ORT model. The accuracy in the converted-wave traveltime for three ORT models is illustrated in numerical examples. One can see from the results that, for converted [Formula: see text]- and [Formula: see text]-waves, our rational-form approximation is very accurate regardless of the tested ORT model. For a converted [Formula: see text]-wave, due to the existence of cusps, triplications, and shear singularities, the error is relatively larger compared with PS-waves.

Estimation of in situ anisotropy parameters from two perpendicular walkaway VSP lines in South Pars field

Abstract Vertical phase slowness and polarization angle are the in situ parameters of P-wave propagation that can be derived from walkaway vertical seismic profiling (VSP) data. To use these data for estimating anisotropy parameters, we obtain an explicit equation of vertical slowness as a function of polarization angle for P-wave propagation in transversely isotropic with vertical symmetry axis (VTI) media. We use this equation to estimate anisotropy parameters of a target layer in the South Pars field, Iran. This field is one of the world's largest gas fields. We show that the orthorhombic symmetry is a reasonable assumption for this layer, providing some geological and petrophysical information. Two walkaway VSP lines along the symmetry axes of the presumed orthorhombic layer are used to estimate its parameters. Seven is the maximum number of parameters that can be estimated using P-wave data in this acquisition pattern. Of those estimated parameters are six of the Tsvankin style parameters for orthorhombic media, plus an approximate combination of two others that define vertical S-wave splitting. We show that a previous method, which is based on weak anisotropy approximation, leads to considerable errors, even in models where the magnitude of anisotropy parameters do not exceed 0.1. We design a numerical experiment to study the reliability of the estimated parameters by the exact approach and show the importance of acquisition pattern in this regard. To show applicability, these parameters are used to estimate the in situ fracture properties of the studied layer.

Imaging counterpart of postural instability and vertical ocular dysfunction in patients with PSP: A multimodal MRI study

IntroductionWe investigated the imaging counterpart of two functional domains (ocular motor dysfunction and postural instability) in progressive supranuclear palsy (PSP) patients classified according to the new clinical diagnostic criteria. MethodsForty-eight patients with probable PSP-Richardson's syndrome (PSP-RS), 30 with probable PSP-parkinsonism (PSP-P), 37 with Parkinson's disease (PD), and 38 controls were enrolled. For each functional domain, PSP patients were stratified by two certainty levels: vertical supranuclear gaze palsy (O1) and slowness of vertical saccades (O2) for ocular motor dysfunction; early unprovoked falls and tendency to fall on the pull-test for postural instability. Voxel-based morphometry (VBM), whole-brain fractional anisotropy (FA) and MR planimetric measurements were analysed and compared across patient groups. ResultsO1 was present in 64%, and O2 in 36% of all PSP patients. All PSP-RS patients showed early unprovoked falls. TBSS whole-brain analysis revealed that superior cerebellar peduncles (SCPs) were the only structures with significantly lower FA values in PSP-RS compared with PSP-P patients. PSP/O1 patients had lower FA values in midbrain than PSP/O2 patients. By contrast, VBM revealed no differences in grey matter volume between PSP patient groups. MR Planimetric measurements confirmed atrophy of midbrain and SCPs, in line with DTI findings. ConclusionsOur study demonstrates that SCPs were significantly more damaged in patients with PSP-RS in comparison with PSP-P patients, thus suggesting the role of SCPs in developing postural instability. Midbrain damage was less severe in O2 than in O1 patients, suggesting that the degree of vertical ocular dysfunction reflects the severity of midbrain atrophy.

Estimation of the conversion point position in elastic orthorhombic media

Determination of the conversion point position is very important to carry out seismic processing in the common conversion point gather of converted wave data. The anisotropic effect is very obvious for a converted wave when estimating the physical and processing parameters from real data. To estimate the conversion point in an elastic orthorhombic (ORT) medium, we have defined an explicit rational form approximation for the radial coordinate of the conversion point for converted [Formula: see text], [Formula: see text], and [Formula: see text] waves. To obtain the approximation coefficients, the Taylor series approximation in the corresponding vertical slowness for three pure wave modes is applied. The coefficients in our proposed approximation are computed within two vertical symmetry planes. The difference between the acquisition azimuth and the azimuth of the conversion point position is analyzed for different combinations of the wave modes. The accuracy of the conversion point position estimation for three ORT models is illustrated in the numerical examples. One can see from the results that for converted [Formula: see text] and [Formula: see text] waves, our approximation is very accurate in estimating the conversion point position regardless of the tested ORT model. For a converted [Formula: see text] wave, due to the existence of cusps, triplications, and shear singularities, the error in conversion point estimation is relatively larger compared with PS-waves in the vicinity of the singularity point.

MR parkinsonism index predicts vertical supranuclear gaze palsy in patients with PSP–parkinsonism

Objective:To identify a biomarker for predicting the appearance of vertical supranuclear gaze palsy (VSGP) in patients affected by progressive supranuclear palsy–parkinsonism (PSP-P).Methods:Twenty-four patients with PSP-P were enrolled in the current study. Patients were clinically followed up every 6 months until the appearance of VSGP or the end of the follow-up (4 years). Participants underwent MRI at baseline and at the end of follow-up. Magnetic resonance parkinsonism index (MRPI), an imaging measure useful for diagnosing PSP, was calculated.Results:Twenty-one patients with PSP-P completed follow-up, and 3 patients dropped out. Eleven of 21 patients with PSP-P developed VSGP after a mean follow-up period of 28.5 months (range 6–48 months), while the remaining 10 patients with PSP-P did not develop VSGP during the 4-year follow-up period. At baseline, patients with PSP-P who later developed VSGP had MRPI values significantly higher than those of patients not developing VSGP without overlapping values between the 2 groups. MRPI showed a higher accuracy (100%) in predicting VSGP than vertical ocular slowness (accuracy 33.3%) or postural instability with or without vertical ocular slowness (accuracy 71.4% and 42.9%, respectively).Conclusions:Our study demonstrates that MRPI accurately predicted, on an individual basis, the appearance of VSGP in patients with PSP-P, thus confirming clinical diagnosis in vivo.

P-wave slowness surface approximation for tilted orthorhombic media

We have developed an analytic and approximate formula for vertical slowness components of down- and upgoing plane P waves in 3D tilted orthorhombic media. A perturbation method and Shanks transform were used to derive the approximation for slowness surface of P waves in tilted orthorhombic media. We have also quantitatively described the validity range of the radial horizontal slowness components for the proposed formula. The validity range was affected by the strength of the anellipticity of an orthorhombic medium: the stronger the anellipticity, the smaller the validity range. Numerical examples determined that the proposed formula is accurate for tilted orthorhombic media with weak to strong anellipticity. We have also evaluated in detail the application of the proposed formula on calculating the P-wave intercept time in the [Formula: see text] domain for horizontally layered, tilted orthorhombic models. Our formula is useful for ray tracing, phase-shift migration, and [Formula: see text] domain intercept time approximation for tilted orthorhombic media.

Prestack elastic generalized-screen migration for multicomponent data

An efficient prestack depth migration method based on the elastic one-way wave equation was developed using an improved elastic generalized-screen propagator, which effectively describes the behavior of elastic waves with mode conversion at the interfaces and efficiently computes wave propagation in media with lateral velocity variations. The elastic propagator presented in this study was improved from the elastic generalized-screen propagator. Several terms of the vertical slowness right symbol with orders are corrected from the original formulation, and the vertical slowness operator in the propagator was expanded up to the 2nd order which yields a more accurate approximation. In each screen propagation step, the multicomponent wavefields are automatically separated into the P and S wavefields by the P–S decomposition operator included in the elastic generalized-screen propagator. This process facilitates the imaging of the P and S waves separately without any additional P and S separation process after the wavefield extrapolation. Impulse response tests of the improved elastic generalized-screen propagator in a uniform-property medium proved that propagation accuracy increases with order, even when large medium perturbations are assigned. Migration tests using the developed algorithm on a simple layered model and two complex models (the SEG/EAGE salt and elastic Marmousi-2 model) demonstrated the functional advantages and capabilities of the algorithm compared with elastic migration using the scalar wave equation.

Imaging tilted transversely isotropic media with a generalised screen propagator

One-way wave equation migration is computationally efficient compared with reverse time migration, and it provides a better subsurface image than ray-based migration algorithms when imaging complex structures. Among many one-way wave-based migration algorithms, we adopted the generalised screen propagator (GSP) to build the migration algorithm. When the wavefield propagates through the large velocity variation in lateral or steeply dipping structures, GSP increases the accuracy of the wavefield in wide angle by adopting higher-order terms induced from expansion of the vertical slowness in Taylor series with each perturbation term. To apply the migration algorithm to a more realistic geological structure, we considered tilted transversely isotropic (TTI) media. The new GSP, which contains the tilting angle as a symmetric axis of the anisotropic media, was derived by modifying the GSP designed for vertical transversely isotropic (VTI) media. To verify the developed TTI-GSP, we analysed the accuracy of wave propagation, especially for the new perturbation parameters and the tilting angle; the results clearly showed that the perturbation term of the tilting angle in TTI media has considerable effects on proper propagation. In addition, through numerical tests, we demonstrated that the developed TTI-GS migration algorithm could successfully image a steeply dipping salt flank with high velocity variation around anisotropic layers.

The offset-midpoint traveltime pyramid in 3D transversely isotropic media with a horizontal symmetry axis

Analytic representation of the offset-midpoint traveltime equation for anisotropy is very important for prestack Kirchhoff migration and velocity inversion in anisotropic media. For transversely isotropic media with a vertical symmetry axis, the offset-midpoint traveltime resembles the shape of a Cheops’ pyramid. This is also valid for homogeneous 3D transversely isotropic media with a horizontal symmetry axis (HTI). We extended the offset-midpoint traveltime pyramid to the case of homogeneous 3D HTI. Under the assumption of weak anellipticity of HTI media, we derived an analytic representation of the P-wave traveltime equation and used Shanks transformation to improve the accuracy of horizontal and vertical slownesses. The traveltime pyramid was derived in the depth and time domains. Numerical examples confirmed the accuracy of the proposed approximation for the traveltime function in 3D HTI media.

Inhomogeneous waves at the boundary of an anisotropic piezo-thermoelastic medium

A mathematical model for the propagation of harmonic plane waves at the boundary of an anisotropic piezo-thermoelastic medium is formulated and solved for slowness surfaces. Ten slowness surfaces are defined at the boundary of the medium. These surfaces are identified with the ten complex values of vertical slowness. Eight of them are associated with propagation of four waves towards/away from the boundary. Two of the slowness surfaces do not represent the propagating phases but the stationary modes. Transmission of outgoing inhomogeneous waves in an anisotropic piezo-thermoelastic medium is studied for the incidence of one of these waves at its plane boundary. These inhomogeneous waves are characterized by their phase velocities, propagation directions and amplitude decay rates with distance from the boundary. Numerical examples are solved to explain the implementation of the derived procedure and to analyse the effects of the medium properties on wave propagation.

DCTN1Mutation Analysis in Families With Progressive Supranuclear Palsy–Like Phenotypes

Progressive supranuclear palsy (PSP) is usually sporadic, but few pedigrees with familial clustering of PSP-like phenotypes have been described. Occasionally, MAPT, C9ORF72, and TARDBP mutations have been identified.To analyze the DCTN1 gene in 19 families with a clinical phenotype of PSP (PSP-like phenotype).Sequencing of the DCTN1 gene in familial forms of PSP at a referral center among 21 patients with familial PSP-like phenotypes. In addition, 8 patients and relatives from a family carrying a DCTN1 mutation were evaluated.Identification of the DCTN1 mutation and clinical description of DCTN1 mutation carriers.We identified a DCTN1 mutation in a large family characterized by high intrafamilial clinical phenotype variability. Two patients had PSP-like phenotypes with dystonia, vertical gaze slowness, dysexecutive syndrome, predominant axial rigidity, and midbrain atrophy on brain magnetic resonance imaging. The other patients manifested Perry syndrome, isolated parkinsonism, or a predominant behavioral variant of frontotemporal dementia.Mutations of the DCTN1 gene have been previously associated with amyotrophic lateral sclerosis and with Perry syndrome, a rare autosomal dominant disorder characterized by weight loss, parkinsonism, central hypoventilation, and psychiatric disturbances. Our study demonstrates that DCTN1 mutations should be searched for in patients with clinical PSP-like phenotypes and a behavioral variant of frontotemporal dementia, especially when a familial history of dementia, psychiatric disturbances, associated parkinsonism, or an autosomal dominant disorder is present.