Vertical Velocity Ratio Research Articles

Perturbation-based moveout approximation in the elastic transversely isotropic media with a vertical symmetry axis

Explicit approximations in traveltime are usually used in seismic data processing such as simulation through ray tracing, velocity analysis for model building, and imaging from time migration. Accurate approximation is key to achieving high-resolution imaging of the structure. We have proposed a perturbation-based approximation for P- and S-waves traveltime in a transversely isotropic medium with a vertical symmetry axis. The perturbation coefficients in this approximation are derived directly from the implicit parametric offset-traveltime equation. The comparison with the generalized moveout approximation (GMA) for P and S waves is applied in numerical examples. We find that our proposed approximation indicates higher accuracy than the GMA counterpart for P and S waves. The error sensitivity of P and S waves in the depth, vertical velocity ratio, and the anellipticity parameter also is analyzed to examine the influence of these factors. In addition, we investigate the anisotropy estimation through two approximations for P and S waves and find that our proposed perturbation method results in high accuracy, which can significantly improve the data processing quality. For the S wave, our approximation also is more accurate than the GMA counterpart and could be implemented for joint tomographic inversions.

The approximation for relative geometric spreading in the elastic vertical transversely isotropic medium

In seismic data processing, compensation for geometric spreading along the raypath is necessary. The accurate approximation of the relative geometric spreading is critical because the traveltime parameters in the approximation can be estimated from velocity analysis. Two approximation types (direct and indirect) are generalized based on the procedure to derive the explicit expression. We develop perturbation-based approximations of the relative geometric spreading for P and S waves with these two types in the elastic transversely isotropic media with a vertical symmetry axis (VTI). The rational approximation and the general moveout approximation counterparts are compared to verify the superiority of our approach. Our study compares the performance of direct and indirect approximations for optimal selection under different cases. In the numerical examples, we apply the error sensitivity in the layer depth, anellipticity value, and vertical velocity ratio. It is found that the P-wave case is much more accurate than the S-wave case, and the direct type obtains relatively higher accuracy than the indirect one. In addition, the perturbation coefficients for the acoustic VTI model are derived not only with a much simpler expression but also achieve a highly accurate result that is recommended for the P-wave seismic processing.

Effect of Foundation Geometry and Structural Properties of Buildings on Railway-Induced Vibration: An Experimental Modeling

This paper considers the impact of foundation geometry on the vibrations transferred to a building in the vicinity of a railway line from the aspect of choosing an appropriate foundation type. For this purpose, a 1-g scale physical model is developed that includes the main parts containing dry sandy soil, a rigid soil container, and a five-story structure with three types of foundations, i.e., single, strip and mat. Next, the effects of the floor slab frequency associated with the local bending mode, the dominant soil frequency in vertical translation, and foundation geometry on the vibration level in the building are investigated. The experimental results obtained from the impulse loading exciting the frequency range of 0–156 Hz and scaled train axle load show that the vibration level transmitted to the floors in a structure with mat foundation is the smallest. Additionally, the strip and mat foundations reduced the root mean square ratio of vertical velocity on the first floor by, respectively, almost 8% and 53% in comparison with the single foundation, confirming the superior performance of the mat foundation. When the natural frequency of the slab bending mode approaches the dominant frequency of the ground’s vertical motion, resonance amplification becomes an inevitable phenomenon.

Prestack migration velocity analysis based on simplified two-parameter moveout equation

Stacking velocity VC2, vertical velocity ratio γ0, effective velocity ratio γeff, and anisotropic parameter χeff are correlated in the PS-converted-wave (PS-wave) anisotropic prestack Kirchhoff time migration (PKTM) velocity model and are thus difficult to independently determine. We extended the simplified two-parameter (stacking velocity VC2 and anisotropic parameter keff) moveout equation from stacking velocity analysis to PKTM velocity model updating and formed a new four-parameter (stacking velocity VC2, vertical velocity ratio γ0, effective velocity ratio γeff, and anisotropic parameter keff) PS-wave anisotropic PKTM velocity model updating and process flow based on the simplified two-parameter moveout equation. In the proposed method, first, the PS-wave two-parameter stacking velocity is analyzed to obtain the anisotropic PKTM initial velocity and anisotropic parameters; then, the velocity and anisotropic parameters are corrected by analyzing the residual moveout on common imaging point gathers after prestack time migration. The vertical velocity ratio γ0 of the prestack time migration velocity model is obtained with an appropriate method utilizing the P- and PS-wave stacked sections after level calibration. The initial effective velocity ratio γeff is calculated using the Thomsen (1999) equation in combination with the P-wave velocity analysis; ultimately, the final velocity model of the effective velocity ratio γeff is obtained by percentage scanning migration. This method simplifies the PS-wave parameter estimation in high-quality imaging, reduces the uncertainty of multiparameter estimations, and obtains good imaging results in practice.

Impacts of Updraft Size and Dimensionality on the Perturbation Pressure and Vertical Velocity in Cumulus Convection. Part I: Simple, Generalized Analytic Solutions

Abstract This study investigates relationships between vertical velocity, perturbation pressure, updraft size, and dimensionality for cumulus convection. Generalized theoretical expressions are derived from approximate analytic solutions of the governing momentum and mass continuity equations for both two-dimensional (2D) and axisymmetric quasi-three-dimensional (3D) steady-state updrafts. These expressions relate perturbation pressure and vertical velocity to updraft radius R, height H, and thermal buoyancy. They suggest that the vertical velocity at the level of neutral buoyancy is reduced from perturbation pressure effects by factors of and in 2D and 3D, respectively, where is a nondimensional length, with somewhat different scalings lower in the updraft (α is a parameter equal to the ratio of vertical velocity horizontally averaged across the updraft to that at the updraft center). They also indicate that updrafts are weaker in 2D than 3D, all else being equal, with a difference of up to a factor of 2 in vertical velocity for as a direct result of differences in mass continuity between 2D and axisymmetric 3D flow. Differences between these expressions and other analytic solutions, including those derived from single normal mode Fourier/Fourier–Bessel expansion of the buoyant perturbation pressure Poisson equation, are discussed. Part II of this study compares the theoretical expressions with numerical solutions of the buoyant perturbation pressure Poisson equation for a wide range of thermal buoyancy profiles representing shallow-to-deep moist convection and also with fully dynamical 2D and 3D updraft simulations.

3D numerical simulations of the 110 GHz, 220 GHz coaxial cavity double-beam gyrotron

Since to break the limitation of traditional single anode magnetron injection electron gun can only produce a lower power, this paper, based on an independent research and development of particle simulation software CHIPIC, will take the 110 GHz, 220 GHz coaxial cavity double-beam gyrotron for full three-dimensional numerical simulation study. By theoretical analysis for the initial parameters of the coaxial double-beam electron gun and to optimize the design by CHIPIC, we obtain the high-performance electron beam with the horizontal and vertical velocity ratio of 1.0 and the maximum velocity spread of 5.4%, and use the optimized electron gun to replace the traditional gyrotron emission for numerical simulation of the 110 GHz, 220 GHz gyrotron system, as well as the four-process parallel MPI in computing. Finally we obtain that the double bands are 110 and 220 GHz respectively, a TE02 mode, and the average output power about 70 kW. The efficiency can reach 8.75% for the high performance double-beam gyrotron oscillating tube.

Compensation for transmission losses based on one-way propagators in the mixed domain

Most true-amplitude migration algorithms based on one-way wave equations involve corrections of geometric spreading and seismic [Formula: see text] attenuation. However, few papers discuss the compensation of transmission losses (CTL) based on one-way wave equations. Here, we present a method to compensate for transmission losses using one-way wave propagators for a 2D case. The scheme is derived from the Lippmann-Schwinger integral equation. The CTL scheme is composed of a transmission term and a phase-shift term. The transmission term compensates amplitudes while the wave propagates through subsurfaces. The transmission term is a function of the vertical wavenumbers of two adjacent heterogeneous screens. The phase-shift term is a Fourier finite-difference (FFD) propagator implemented in a mixed domain via Fourier transform. The transmission term can be flexibly incorporated into the conventional phase-shift migration algorithm, i.e., FFD, at every depth step. We analyze the effects of frequency, lateral velocity contrast, and vertical velocity ratio on the accuracy of the presented formulae. Numerical examples from a flat model and a fault model with lateral velocity variations are presented to demonstrate the ability of the proposed scheme for compensation of transmission losses.

Seismic anisotropy estimated from P-wave arrival times in crosshole measurements

Seismic anisotropy is evidenced in the inner core, upper mantle and the lower crust in large scale, and the evidence is generally provided by shear wave splitting analysis. Here this paper searches for the evidence of anisotropy in the uppermost crust, by using P-wave arrival times from crosshole seismic measurement to directly estimate velocity anisotropy associated with the fine-layering effect of multiple sedimentary beds. Conceptually fine layering causes the so-called VTI (vertical transverse isotropy) anisotropy with a vertical symmetry and the effect is parametrized by the horizontal and vertical velocity ratio. It is found however that the VTI anisotropic parameter does not have a simple vertical symmetry but is also azimuth dependent. This azimuthal anisotropy may reflect the fracture orientation due to large-scale tectonic movements, and is very important in the production of oil reservoirs, as the seismically fast directions can indicate preferred directions of fluid flow. This paper presents innovative methods for anisotropy analysis in both vertical and horizontal plane. Integrated seismic anisotropy interpretation clearly indicates distinguished strain orientations forming fractures in Oligocenic, Miocenic and Pliocenic sediment, in the edge of the extensional basin immediately next to Tan-Lu Fault, an active continental strike-slip fault zone.

Dynamic Connection of Hydrostatic and Non-Hydrostatic Zone for Coastal Hydrodynamic Model

Application limit of hydrostatic approximation for coastal hydrodynamic model was investigated, and a dynamic connection method of hydrostatic zone with non-hydrostatic zone was developed. By theoretical consideration employing parameter δ and e which represent the ratio of mesh size Δz to Δx and the ratio of vertical velocity to horizontal velocity, it was found that hydrostatic approximation can be applied if δe and e2 are minute. To examine the developed method, simulations for vertical jet under oscillating current was conducted. The result by the present model was similar to that of non-hydrostatic model in the case that hydrostatic approximation was applied on the area of δe <0.005 and e2<0.005.

Effect of errors in the migration velocity model of PS-converted waves on traveltime accuracy in prestack Kirchhoff time migration in weak anisotropic media

We investigated the effect of errors in the migration-velocity model of PS-converted waves on the traveltime calculated in prestack Kirchhoff time migration in weak anisotropic media. The prestack-Kirchhoff-time-migration operator contains four parameters: the PS-converted-wave velocity, the vertical velocity ratio, the effective velocity ratio, and the anisotropic parameter. We derived four error factors that correspond to those parameters. Theoretical and numerical analyses of the error factors show them all to be inversely proportional to the velocity and to traveltime. Traveltime errors for shallow events usually are larger than for deep events. Error in PS-converted-wave velocity causes the largest traveltime error, and error in the vertical velocity ratio causes the smallest traveltime error. For a small horizontal-distance/depth ratio, the error in the effective velocity ratio affects traveltime more than does the anisotropic-parameter error. However, the anisotropic-parameter error affects traveltime more when the horizontal-distance/depth ratio is larger. Traveltime errors caused by errors in effective velocity ratio and the anisotropic parameter mainly stem from the converted-S-wave raypath of the PS-converted waves. To save processing time and cost, PS-wave velocity can be estimated accurately without an accurate vertical velocity ratio, effective velocity ratio, and anisotropic parameter. These findings are useful for understanding PS-wave behavior and for PS-wave imaging in anisotropic media.

Four-parameter velocity analysis and its applications to the Ken-71 area converted-wave data

3-D converted-wave data were acquired using digital MEMS (micro-electromechanical system) three component (3C) sensors in the alternating sand and shale sequence in the overburden of the Shengli Ken-71 area. This gives rise to serious non-hyperbolic moveout effects in the converted-wave data due to both the asymmetrical ray path and anisotropic effects. Conventional velocity analysis and moveout correction based on isotropic methods do not flatten reflections events. Here, we use a four-parameter theory to evaluate these effects and process the data. These four parameters include the PS converted wave stacking velocity (VC2), the vertical velocity ratio (y0), the effective velocity ratio (yeff), and the anisotropy parameter (xeff). The method utilizes the moveout information at different offsets to estimate the different parameters and ensures that the events are properly aligned for stacking. As a result, this four-parameter theory leads to an improvement in imaging quality and correlation between the P-waves and converted-waves.

Converted-wave moveout and conversion-point equations in layered VTI media: theory and applications

We have developed improved equations for calculating the conversion point of the P-SV converted wave (C-wave) in transversely isotropic media with a vertical symmetry axis (vertical transverse isotropy (VTI)). We have also derived modified C-wave moveout equations for layered VTI media. The derived equations for the conversion-point are valid for offsets about three-times the reflector depth (x/z=3.0) and those for the C-wave moveout about twice the reflector depth (x/z=2.0). The new equations reveal some additional analytical insights into the converted-wave properties. The anisotropy has a more significant effect on the conversion point than on the move-out, and using the effective binning velocity ratio γeff only is often insufficient to account for the anisotropic effect, even when higher-order terms are considered. Also for C-wave propagation, the anisotropy appears to affect the P-wave leg more than the S-wave leg. The ratio of the anisotropic contributions from P- and S-waves is close to the vertical velocity ratio γ0. Consequently S-wave anisotropic parameters may be recovered from converted-waves when P-wave anisotropic parameters are known. The new equations suggest that the C-wave moveout in layered VTI media over intermediate-to-far offsets is determined by the anisotropic parameter χeff in addition to C-wave stacking velocity VC2, and the velocity ratios γ0 and γeff. We refer to these four parameters as the C-wave “stacking velocity model”. Two practical work flows are presented for determining this model: the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that although the single-scanning flow is less accurate than the double-scanning flow, it is more efficient and, in most cases, can yield sufficiently accurate results.

Dynamics of crustal compensation and its influences on crustal isostasy

Deviation from isostasy is commonly believed to be caused by the strength of the Earth's lithosphere. An analysis of crustal compensation dynamics suggests that the deviation may have a dynamic origin. The analysis is based on analytic models that assume that (1) the medium is incompressible and has a layered and linear viscoelastic rheology and (2) the amplitude of topography is small compared with its wavelength. The models can describe topographic relaxation of different density interfaces at both small (e.g., postglacial rebound) and large time‐scales. The models show that for a simple crust‐mantle system with topography at the Earth's surface and Moho representing the only mass anomalies, while the crust always approaches the isostatic state at long wavelengths (&gt;800 km), crustal isostasy may not be an asymptotic limit at short wavelengths, depending on crustal and lithospheric rheology. For a crust with viscosity smaller than lithospheric viscosity, at wavelengths comparable with widths of orogenic belts (i.e., &lt;300 km), the crust tends to approach a state with significant overcompensation (i.e., excess topography at the Moho) within a timescale of about 107 years, and this characteristic time depends on wavelengths and crustal viscosity. This overcompensation is greater for weaker crust and stronger lithosphere. A thicker crust or lithosphere also enhances this overcompensation. If crustal and lithospheric viscosities are both large and comparable, the asymptotic state for the crust displays a slight undercompensation. For an elastic and rigid upper crust, the crust eventually becomes undercompensated after a characteristic decay time of topography at the Moho. The characteristic time is dependent on viscosity and thickness of the lower crust. The deviation from isostasy arises because these viscosity structures result in a ratio of vertical velocity at the surface to vertical velocity at the Moho which in the asymptotic state for short wavelengths differs from the ratio of density contrast at the Moho to that at the surface.

New development in the MOCNESS, an apparatus for sampling zooplankton and micronekton

Four variants of the Multiple Opening/Closing Net and Environmental Sensing System (MOCNESS) have been constructed to sample a broad size spectrum of oceanic animals from microzooplankton to micronekton. The systems differ in mouth opening dimensions (ranging from 1/4 to 20 m2), the number of nets carried (from 5 to 20), and the mesh size of the netting (from 64 μm to 3.0 mm). A new electronics package enables an operator to send commands down a single conductor, armored cable to open/close the nets and provides 12-bit resolution for the environmental (temperature, depth, conductivity) and net operation data (flow, net-frame angle, net-bar release), which are transmitted up the cable to the deck unit at 2-s intervals. A microcomputer system, interfaced to the deck unit, calculates salinity, volume filtered by a net, net trajectory velocity, and vertical velocity. The data are printed out and stored on disc, and profiles of temperature and salinity versus depth are plotted during the course of the tow. Analysis of the relationship between the geometry of the MOCNESS under tow and the past and present methods used to estimate the water filtered by a net revealed that significant bias is introduced when the ascent or descent angle of a net is disregarded. The bias is a function of the ratio of vertical velocity to net trajectory velocity and results in an underestimate of volume filtered while shooting a net and an overestimate while hauling.

強風時の鉛直風速の大きさと水平相関

This paper deals with turbulent properties of vertical velocities and wind inclinations at height of 40m in strong winds. In the wind of sea trajectory, the intensity of turbulence was mostly in the range from 0.03-0.04. The ratio of vertical velocity to longitudinal one, that of vertical velocity to friction velocity, and non-dimensional frequency _??_m at which logarithmic power spectrum had a maximum were in good agreement with those by other investigators. The lateral correlation was small compared with that of longitudinal velocities. It vanished almost at the separation of 35m. When the square root of coherence was ex-pressed by an exponential function, the decay parameter scattered in a wide range but it was estimated from 14-16 on the average. The effect of averaging on peak values and scales of wind inclinations was discussed as engineering application. With increase of averaging time, peak values decreased and lateral scales increased, but the rate of increase was small compared with that of decrease of the peak values.