True-amplitude wavefield separation using staggered-grid interpolation in the wavenumber domain

Wavefield separation of multicomponent seismic data to image subsurface structures can be realized in either the space domain or the wavenumber domain. However, as the particle velocity components used in the wavenumber-domain wavefield separation are not defined at the same grid point with the staggered-grid finite-difference method for elastic wavefield simulation, we propose the wavenumber-domain interpolation method to estimate the required values at the common grid points prior to the wavenumber-domain true-amplitude wavefield separation. Moreover, numerical experiments show that the wavenumber-domain interpolation method has high interpolation accuracy and the trueamplitude wavefield separation method shows good amplitude preservation. The application of the proposed methodology to elastic reverse-time migration can obtain good amplitudepreserved images even in the case of some velocity error.

Quantitative Rectangular Notch Detection of Laser-induced Lamb Waves in Aluminium Plates with Wavenumber Analysis

It is difficult to quantitatively detect defects by using the time domain or frequency domain features of Lamb wave signals due to their dispersion and multimodal characteristics.Therefore,it is important to discover an intrinsical parameter of Lamb waves that could be used as a damage sensitive feature.In this paper,quantitative defect detection in aluminium plates is carried out by means of wavenumber analysis approach.The wavenumber of excited Lamb wave mode is a fixed value,given a frequency,a thickness and material properties of the target plate.When Lamb waves propagate to the structural discontinuity,new wavenumber components are created by abrupt wavefield change.The new wavenumber components can be identified in the frequency-wavenumber domain.To estimate spatially dependent wavenumber values,a short-space two-dimensional Fourier transform(FT)method is presented for processing wavefield data of Lamb waves.The results can be used to determine the location,size and depth of rectangular notch.The analysis techniques are demonstrated using simulation examples of an aluminium plate with a rectangular notch.Then,the wavenumber analysis method is applied to simulation data that are obtained through a range of notch depths and widths.The results are analyzed and rules of the technique with regards to estimating notch depth are determined.Based on simulation results,guidelines for using the technique are developed.Finally,experimental wavefield data are obtained in aluminium plates with rectangular notches by a full noncontact transceiving method,i.e.,laser-laser method.Band-pass filtering combined with continuous wavelet transform is used to extract a certain frequency component from the full laser-induced wavefield with wide band.Shortspace two-dimensional FT method is used for further processing full wavefield data at a certain frequency to estimate spatially dependent wavenumber values.The consistency of simulation and experimental results shows the effectiveness of proposed wavenumber method for quantitative rectangular notch detection.

Analytical solution based on the wavenumber integration method for the acoustic field in a Pekeris waveguide

An exact solution based on the wavenumber integration method is proposed and implemented in a numerical model for the acoustic field in a Pekeris waveguide excited by either a point source in cylindrical geometry or a line source in plane geometry. Besides, an unconditionally stable numerical solution is also presented, which entirely resolves the stability problem in previous methods. Generally the branch line integral contributes to the total field only at short ranges, and hence is usually ignored in traditional normal mode models. However, for the special case where a mode lies near the branch cut, the branch line integral can contribute to the total field significantly at all ranges. The wavenumber integration method is well-suited for such problems. Numerical results are also provided, which show that the present model can serve as a benchmark for sound propagation in a Pekeris waveguide.

Wavenumber-4 spectral component extracted from TIMED/SABER observations

The wavenumber spectral components WN4 at the mesosphere and low thermosphere(MLT)altitudes(70–10 km)and in the latitude range between±45°are obtained from temperature data(T)observed by the Sounding of the Atmosphere using Broadband Emission Radiometry(SABER)instruments on board the National Aeronautics and Space Administration(NASA)’s Thermosphere–Ionosphere–Mesosphere Energetics and Dynamics(TIMED)spacecraft during the 11-year solar period from 2002 to 2012.We analyze in detail these spectral components WNk and obtain the main properties of their vertical profiles and global structures.We report that all of the wavenumber spectral components WNk occur mainly around 100 km altitude,and that the most prominent component is the wavenumber spectral component WN4 structure.Comparing these long duration temperature data with results of previous investigations,we have found that the yearly variation of spectral component WN4 is similar to that of the eastward propagating non-migrating diurnal tide with zonal wavenumber 3(DE3)at the low latitudes,and to that of the semi-diurnal tide with zonal wavenumber 2(SE2)at the mid-latitudes:the amplitudes of the A4 are larger during boreal summer and autumn at the low-latitudes;at the mid-latitudes the amplitudes have a weak peak in March.In addition,the amplitudes of component WN4 undergo a remarkable short period variation:significant day-to-day variation of the spectral amplitudes A4 occurs primarily in July and September at the low-latitudes.In summary,we conclude that the non-migrating tides DE3 and SE2 are likely to be the origins,at the low-latitudes and the mid-latitudes in the MLT region,respectively,of the observed wavenumber spectral component WN4.

Slope wavenumber spectrum models of capillary and capillary-gravity waves

Capillary and capillary-gravity waves possess a random character, and the slope wavenumber spectra of them can be used to represent mean distributions of wave energy with respect to spatial scale of variability. But simple and practical models of the slope wavenumber spectra have not been put forward so far. In this article, we address the accurate definition of the slope wavenumber spectra of water surface capillary and capillary-gravity waves. By combining the existing slope wavenumber models and using the dispersion relation of water surface waves, we derive the slope wavenumber spectrum models of capillary and capillary-gravity waves. Simultaneously, by using the slope wavenumber models, the dependence of the slope wavenumber spectrum on wind speed is analyzed using data obtained in an experiment which was performed in a laboratory wind wave tank. Generally speaking, the slope wavenumber spectra are influenced profoundly by the wind speed above water surface. The slope wavenumber spectrum increases with wind speed obviously and do not cross each other for different wind speeds. But, for the same wind speed, the slope wavenumber spectra are essentially identical, even though the capillary and capillary-gravity waves are excited at different times and locations. Furthermore, the slope wavenumber spectra obtained from the models agree quite well with experimental results as regards both the values and the shape of the curve.

Fast local wavenumber （FLW） method for the inversion of magnetic source parameters

The current local wavenumber methods for the interpretation of magnetic anomalies compute the locations of geological bodies by solving complex matrices. Presently, such methods require to know the structural index, which is a parameter that represents the source type. The structural index is hard to know in real data; consequently, the precision of current methods is low. We present the fast local wavenumber （FLW） method, and define the squared sum of the horizontal and vertical local wavenumbers as the cumulative local wavenumber. The FLW method is the linear combination of the umulative local wavenumberand other wavenumbers, and is used to compute the locations and structural index of the source without a priori information and matrix solution. We apply the FLW method to synthetic magnetic anomalies, and the results suggest that the FLW method is insensitive to background and oblique magnetization. Next, we apply the FLW method to real magnetic data to obtain the location and structural index of the source.

Linear stability theory with the equivalent spanwise wavenumber correction in 3D boundary layers

The prediction on small disturbance propagation in complex three-dimensional(3D) boundary layers is of great significance in transition prediction methodology, especially in the aircraft design. In this paper, the linear stability theory(LST) with the equivalent spanwise wavenumber correction(ESWC) is proposed in order to accurately predict the linear evolution of a disturbance in a kind of boundary layer flow with a vital variation in the spanwise direction. The LST with the ESWC takes not only the scale of the mean flow with the significant variation but also the wavenumber evolution of the disturbance itself. Compared with the conventional LST, the results obtained by the new method are in excellent agreement with those of the numerical simulations. The LST with the ESWC is an effective method on the prediction of the disturbance evolution in 3D boundary layers, which improves the prediction of the LST in the applications to complex 3D boundary layers greatly.

Three-dimensional numerical simulation of geothermal fi eld in space-wavenumber domain

Large-scale,fine,and efficient numerical simulation of a geothermal field plays an important role in geothermal energy development.Confronted with the problem of large computation and high storage requirements for complex underground models in a three-dimensional(3-D)numerical simulation of a geothermal fi eld,a mixed space-wavenumber domain 3-D numerical simulation algorithm is proposed in this paper.According to the superposition principle of temperature field,the geothermal field is decomposed into background and abnormal temperature fi elds for calculation.The uniform layered model is used to solve the background field.When the abnormal field is solved,the horizontal two-dimensional(2-D)Fourier transform is used to transform the 3-D diff erential equation satisfi ed by an abnormal field into a series of one-dimensional ordinary differential equations with diff erent wavenumbers,which greatly reduces the calculation and storage.The unit division of an ordinary diff erential equation is fl exible,and the calculation amount is small.The algorithm fully takes advantage of the effi ciency of the Fourier transform and the quickness of the catch-up method to solve linear equations with a fixed bandwidth,which effectively improves the computational efficiency.Compared with the COMSOL Multiphysics professional simulation finite element software,the time consumption and memory requirements of the algorithm proposed in this paper are reduced by multiple orders of magnitude in terms of ensuring accuracy and the same mesh division.The more the number of calculated nodes is,the more obvious is the advantage.We design models to study the thermal conductivity,heat fl ux boundary,regional tectonic morphology,and topographic relief of the geothermal fi eld distribution.A 3-D geophysical model is developed based on topographic elevation data,geothermal geology,and geophysical exploration data in the Qiabuqia area of Gonghe Basin,Qinghai Province,China.Numerical simulation of the geothermal fi eld in this area is realized,which shows that the algorithm is suitable for precise and effi cient simulation of an arbitrary complex terrain and geological conditions.

Wavenumber Selection by Bénard-Marangoni Convection at High Supercritical Number

Marangoni Benard convection, which is mainly driven by the thermocapillary （Marangoni） effect, occurs in a thin liquid layer heated uniformly from the bottom. The wavenumber of supercritical convection is studied experimentally in a 160×160-mm^2 cavity that ＆ heated from the bottom block. The convection pattern ＆ visualized by an infrared thermography camera. It is shown that the onset of the Benard cell is consistent with theoretical analysis. The wavenumber decreases obviously with increasing temperature, except for a slight increase near the onset. The wavenumber gradually approaches the minimum when the supercritical number e is larger than 10. Finally, a formula is devised to describe the wavenumber selection in supercritical convection.

Stable and Unstable Eigensolutions of Laplace's Tidal Equations for Zonal Wavenumber Zero

Laplace's tidal equations are of great importance in various fields of geophysics. Here, the special case of zonal symmetry (zonal wavenumber m = 0) is investigated, where degenerate sets of eigensolutions appear. New results are presented for the inclusion of dissipative processes and the case of unstable conditions. In both instances the (nonzero) eigenfrequencies are complex. In the latter case, additional stable (i.e. real) eigenfrequencies appear in the numerical results for the absolute value of the Lambparameter ε being larger than a critical value εc. Further, it is shown that any degeneracies are removed through the inclusion of dissipation. Moreover, asymptotic relations are derived employing the relation of Laplace's tidal equations for m = 0 to the spheroidal differential equation. The implications of these findings to numerical techniques are demonstrated and results of computations are presented.

Representation of microscale ocean wavenumber spectrum correct to the second order

In this paper, the analytical representations of four wave source functions in high-frequency spectrum range are given on the basis of ocean wave theory and dimensional analysis, and the perturbation method is used to solve the governing equations of ocean wave high-frequency spectrum on the basis of the temporally stationary and locally homogeneous scale relations of microscale wave. The microscale ocean wavenumber spectrum correct to the second order has an explicit structure, its first order part represents the equilibrium between dif- ferent source functions, and its second order part represents the contribution of microscale wave propagation.

Anisotropy of the horizontal velocity fluctuation field in the large wavenumber region

This paper utilizes meridional and zonal velocity data measured by chaff rockets at a high resolution of 25 m in the 67—96 km region during the MAC/SINE campaign to study the char-acteristics of the spectra of the meridional and zonal velocity fluctuations. Results suggest that the mean vertical wavenumber spectra have a forked point near vertical wavenumber k = 0.001 m-1. In the vertical wavenumber region smaller than the forked point, the spectra of the meridional and zonal velocities have approximately the same spectral slope, amplitude, and characteristic vertical wavelength, and agree well with the linear saturated spectral model. In the vertical wavenumber region larger than the forked point, however, the meridional and zonal spectra are inconsistent not only in both slope and amplitude, but also in spectral structure. The differences between the observed meridional and zonal spectra provide observational evidence of azimuthal anisotropy of the velocity fluctuation field in the large vertical wavenumber region in mean sense.

Raman wavenumbers calculated as a function of pressure from the mode Grüneisen parameter of PZT(x=0:48)ceramic close to the monoclinic-cubic transition

The isothermal mode Grüneisen parameterγTðPÞof some Raman modes in PbZr_(1-x)Ti_(x)O_(3)(PZT,x=0.48)were calculated as a function of pressure by means of the observed pressure-dependent volume data of PZT(x=0.48)crystal from the literature at room temperature of 298 K.Those calculated values ofγTðPÞwere then used to compute the pressure dependence of the Raman modes in PZT(x=0.48)ceramic studied here.The observed and calculated values of the Raman wavenumbers in PZT were in good agreement,which indicates that the isothermal mode Grüneisen parameter can also be used to predict the pressure-dependent wavenumbers of some other perovskite-type crystals.Additionally,the pressure dependence of the thermodynamic quantities such as isothermal compressibilityκT,thermal expansionαP and the specific heat C_(P)-C_(V) of PZT(x=0.48)ceramic were predicted at constant temperature of 298 K.Here,the experimentally measurable thermodynamic quantities calculated for PZT(x=0.48)ceramics provide theoretically a significant opportunity for testing.

The algorithm of 3D multi-scale volumetric curvature and its application

To fully extract and mine the multi-scale features of reservoirs and geologic structures in time/depth and space dimensions, a new 3D multi-scale volumetric curvature （MSVC） methodology is presented in this paper. We also propose a fast algorithm for computing 3D volumetric curvature. In comparison to conventional volumetric curvature attributes, its main improvements and key algorithms introduce multi-frequency components expansion in time-frequency domain and the corresponding multi-scale adaptive differential operator in the wavenumber domain, into the volumetric curvature calculation. This methodology can simultaneously depict seismic multi-scale features in both time and space. Additionally, we use data fusion of volumetric curvatures at various scales to take full advantage of the geologic features and anomalies extracted by curvature measurements at different scales. The 3D MSVC can highlight geologic anomalies and reduce noise at the same time. Thus, it improves the interpretation efficiency of curvature attributes analysis. The 3D MSVC is applied to both land and marine 3D seismic data. The results demonstrate that it can indicate the spatial distribution of reservoirs, detect faults and fracture zones, and identify their multi-scale properties.

Effect of Excited-state Substituent Constant on the UV Spectra of 1,4-disubstituted Benzenes

A correlation equation between the UV absorption wavenumbers of 1,4-disubstituted benzenes and the excited-state substituent constant was obtained. For 80 sorts of 1,4- disubstituted benzenes, the correlation coefficient was 0.9805, and the standard deviation was only 672.27 cm^-1. The results imply that the excited-state substituent constant can be used productively for research on UV energy of 1,4-disubstituted benzenes. The present method provides a new avenue to study the UV absorption spectra of aromatic systems with the excited-state substituent constant, and it is helpful to understand the effect of substituent electrostatic effects on the chemical and physical properties of conjugated compounds with multiple substituents in excited state.

Structures and Intermolecular Interactions in Dimethyl Sulfoxide-Water System Studied by All-atom Molecular Simulations

An all-atom dimethyl sulfoxide （DMSO） and water model have been used for molecular dynamics simulation. The NMR and IR spectra are also performed to study the structures and interactions in the DMSO-water system. And there are traditional strong hydrogen bonds and weak C-H- ~ ~ O contacts existing in the mixtures according to the analysis of the radial distribution functions. The insight structures in the DMSO-water mixtures can be classified into different regions by the analysis of the hydrogen-bonding network. Interestingly, the molar fraction of DMSO 0.35 is found to be a special concentration by the network. It is the transitional region which is from the water rich region to the DMSO rich region. The stable aggregates of （DMSO）m＇S=O…… HW-OW-（H20）n might play a key role in this region. Moreover, the simulation is compared with the chemical shifts in NMR and wavenumbers in IR with concentration dependence. And the statistical results of the average number hydrogen bonds in the MD simulations are in agreement with the experiment data in NMR and IR spectra.

Modal Wave Number Tomography for South China Sea Front

Monitoring of the South China Sea is always one of the focuses in the field of ocean engineering for its particular geographic position. The modal wave number tomography is proposed for monitoring the front and numerical simulation is performed for the front of the South China Sea. With the empirical orthonormal function (EOF) applied to reduce the parameter search space, the perturbation inversion method is used for inversing sound speed profiles. The 2-D ocean environment used for numerical simulation is selected from the ocean area, located in 20°N, 118°E～20°N, 125°E, near the Luzon Strait in the South China Sea. The ocean environment sound speed distribution in the ocean area under study is obtained from the assimilation of multi-source remote sensing data. The numerical simulation shows that the modal wave number tomography can inverse the average sound speed profile, therefore,it can be used to monitor ocean internal structures such as ocean fronts and eddies which affect sound speed distribution.

Circular SAR processing using an improved omega-k type algorithm

An improved circular synthetic aperture radar（CSAR） imaging algorithm of omega-k（ω-k） type mainly for reconstructing an image on a cylindrical surface is proposed.In the typical CSAR ω-k algorithm,the rage trajectory is approximated by Taylor series expansion to the quadratic terms,which limits the valid synthetic aperture length and the angular reconstruction range severely.Based on the model of the CSAR echo signal,the proposed algorithm directly transforms the signal to the two-dimensional（2D） wavenumber domain,not using approximation processing to the range trajectory.Based on form of the signal spectrum in the wavenumber domain,the formula for the wavenumber domain interpolation of the w-k algorithm is deduced,and the wavenumber spectrum of the reference point used for bulk compression is obtained from numerical method.The improved CSAR ω-k imaging algorithm increases the valid synthetic aperture length and the angular area greatly and hence improves the angular resolution of the cylindrical imaging.Additionally,the proposed algorithm can be repeated on different cylindrical surfaces to achieve three dimensional（3D） image reconstruction.The 3D spatial resolution of the CSAR system is discussed,and the simulation results validate the correctness of the analysis and the feasibility of the algorithm.

Three-dimensional transformation of magnetization direction and magnetic field component at low latitudes based on vertical relationship

The transformation of the magnetization direction and the magnetic fi eld component is one of the important methods in magnetic data processing and transformation,which can be conducted in both wavenumber and spatial domains.The transformation method in the wavenumber domain has simpler processing expression and higher processing effi ciency than in the spatial domain;however,they are unstable at low latitude.In this paper,the conclusion that the sum is 0 of two vertical magnetic fi eld components(magnetization inclinations are also perpendicular)in 2D is used for the 3D transformation of the magnetization direction and the magnetic field component.In addition,the transformation method at low latitudes based on vertical relationship(VMT)is proposed,which is an iterative algorithm that converts the transformation of the magnetization direction and the magnetic field component at the low latitude into the high latitude.This method restrains the instability of transformation of constant and variable magnetization direction and magnetic fi eld components in low latitudes.The accuracy,stability,and practicality are verifi ed from synthetic models and real data.