In China, most directions of river flowing are from west to east. During historic period, since the water traffic played an important role, it was very important to form a cross-horizontal net of water carriage route....In China, most directions of river flowing are from west to east. During historic period, since the water traffic played an important role, it was very important to form a cross-horizontal net of water carriage route. Canals should be dug so as to make up the lack of north-south river. Tongji Grand Canal, dug in the first year of Daye (605 A.D.) in the Sui Dynasty, was the important component of north-south system of Grand Canals in China. It promoted economic and social development of the Sui, Tang and Song dynasties (605 A.D.-1279 A.D.). As Tongji Canal (i.e. Tongji Grand Canal) flowed across the Huaibei Plain, which is aggraded by abundant mud and sand deposit resulted from the Huanghe (Yellow) River flooding, many traces (such as old channel) and human culture heritages were buried under mud-sand. Tongji Canal was silted up, and disappeared in the Jin Dynasty (1115 A.D.-1234 A.D.). From then on, there were many different stories about the flowing route of the canal in historical literature. Based on space-bone and air-bone remote sensing imagery, we attempt to search the old channel of Tongji Canal, and supplement historical record. The paper discusses transformation process of Tongji Canal’s traffic function, and resumptively summarizes the reasons of the transformation, which results from synthetic function of physical geographical, political, economic, and social conditions.展开更多
Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformatio...In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.展开更多
Reliability allocation of computerized numerical controlled(CNC)lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate componen...Reliability allocation of computerized numerical controlled(CNC)lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis(FMEA)is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.展开更多
The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wave...The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.展开更多
To elucidate feasible routes of producing CO from CH 3 and unravel the eff ect of adsorbed O on CH x transformation, the reactivity of CH x ( x = 1-3) with and without the assistance of adsorbed atomic O on Ni(111) wa...To elucidate feasible routes of producing CO from CH 3 and unravel the eff ect of adsorbed O on CH x transformation, the reactivity of CH x ( x = 1-3) with and without the assistance of adsorbed atomic O on Ni(111) was explored using density functional theory calculations. The adsorption energies of CH x ( x = 0-3) were found to be signifi cantly reduced on an O-preadsorbed Ni(111) surface compared to a pure surface. Furthermore, O-assisted one-step dehydrogenation of CH x ( x = 1-3) features energy barriers and thus is diffi cult to proceed. In terms of energy, the direct dissociation of CH 3 is favorable, except for the last CH dehydrogenation, which is energy intensive. Interestingly, in O-assisted two-step CH transformation to CO via CHO intermediate, the barrier is dramatically lowered. The successive dehydrogenations of CH x O ( x = 1-3) were also found to be a route for CO formation. Finally, two possible pathways from CH 3 to CO are proposed:(a) CH 3 → CH 2 → CH → CHO → CO;(b) CH 3 → CH 3 O → CH 2 O → CHO → CO.展开更多
The Auto-Transformer Rectifier Unit（ATRU） is one preferred solution for high-power AC/DC power conversion in aircraft. This is mainly due to its simple structure, high reliability and reduced k VA ratings. Indeed, t...The Auto-Transformer Rectifier Unit（ATRU） is one preferred solution for high-power AC/DC power conversion in aircraft. This is mainly due to its simple structure, high reliability and reduced k VA ratings. Indeed, the ATRU has become a preferred AC/DC solution to supply power to the electric environment control system on-board future aircraft. In this paper, a general modelling method for ATRUs is introduced. The developed model is based on the fact that the DC voltage and current are strongly related to the voltage and current vectors at the AC terminals of ATRUs. In this paper, we carry on our research in modelling symmetric 18-pulse ATRUs and develop a generic modelling technique. The developed generic model can study not only symmetric but also asymmetric ATRUs. An 18-pulse asymmetric ATRU is used to demonstrate the accuracy and efficiency of the developed model by comparing with corresponding detailed switching SABER models provided by our industrial partner. The functional models also allow accelerated and accurate simulations and thus enable whole-scale more-electric aircraft electrical power system studies in the future.展开更多
In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a nove...In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.展开更多
The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential t...The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.展开更多
The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric a...The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.展开更多
This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates th...This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.展开更多
In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in term...In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.展开更多
The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual...The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.展开更多
Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spect...Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.展开更多
Power transformer insulation systems are subjected to many stresses during normal operation due to lightning and switching.If the spectrum of incoming surge voltage matches the winding one,the corresponding resonance ...Power transformer insulation systems are subjected to many stresses during normal operation due to lightning and switching.If the spectrum of incoming surge voltage matches the winding one,the corresponding resonance will be excited.Therefore external transients occurring in power systems might trigger internal overvoltages with large maximum value in transformer windings.Overvoltages having such characteristic have been the root cause of many power transformer failures.The paper presents an approach to the identification of sensitive zones in the transformer windings based on the measurements of overvoltages inside windings and frequency dependences of admittance of the power transformer.The frequency characteristic of the transformer winding may determine those regions in the frequency spectrum.The presented approach might be used both for design optimization and diagnostics of distribution and power transformers.展开更多
Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author ...Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense.展开更多
A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initi...A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.展开更多
基金Under the auspices of the National Natural Science Foundation of China (No.40571162), the Natural Science Foun-dation of Anhui Province (No.050450401), Natural Science Foundation of Anhui Provincal Education Department (No.2004kj65zd), Postdoctoral Foundation of University of Science and Technology of China
文摘In China, most directions of river flowing are from west to east. During historic period, since the water traffic played an important role, it was very important to form a cross-horizontal net of water carriage route. Canals should be dug so as to make up the lack of north-south river. Tongji Grand Canal, dug in the first year of Daye (605 A.D.) in the Sui Dynasty, was the important component of north-south system of Grand Canals in China. It promoted economic and social development of the Sui, Tang and Song dynasties (605 A.D.-1279 A.D.). As Tongji Canal (i.e. Tongji Grand Canal) flowed across the Huaibei Plain, which is aggraded by abundant mud and sand deposit resulted from the Huanghe (Yellow) River flooding, many traces (such as old channel) and human culture heritages were buried under mud-sand. Tongji Canal was silted up, and disappeared in the Jin Dynasty (1115 A.D.-1234 A.D.). From then on, there were many different stories about the flowing route of the canal in historical literature. Based on space-bone and air-bone remote sensing imagery, we attempt to search the old channel of Tongji Canal, and supplement historical record. The paper discusses transformation process of Tongji Canal’s traffic function, and resumptively summarizes the reasons of the transformation, which results from synthetic function of physical geographical, political, economic, and social conditions.
文摘Let and denote respectively the functionswhere λ≥1, The author discusses the similarity transformation of the regularizing functionals of these functions and the similar property of their Fourier transformation.
文摘In this paper, an extended functional transformation is given to solve some nonlinear evolution equations. This function, in fact, is a solution of the famous KdV equation, so this transformation gives a transformation between KdV equation and other soliton equations. Then many new exact solutions can be given by virtue of the solutions of KdV equation.
基金Supported by National Natural Science Foundation of China(Grant Nos.51135003,51205050,U1234208)Key National Science&Technology Special Project on"High-Grade CNC Machine Tools and Basic Manufacturing Equipments"(Grant No.2013ZX04011011)+1 种基金Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110042120020)Fundamental Research Funds for the Central
文摘Reliability allocation of computerized numerical controlled(CNC)lathes is very important in industry.Traditional allocation methods only focus on high-failure rate components rather than moderate failure rate components,which is not applicable in some conditions.Aiming at solving the problem of CNC lathes reliability allocating,a comprehensive reliability allocation method based on cubic transformed functions of failure modes and effects analysis(FMEA)is presented.Firstly,conventional reliability allocation methods are introduced.Then the limitations of direct combination of comprehensive allocation method with the exponential transformed FMEA method are investigated.Subsequently,a cubic transformed function is established in order to overcome these limitations.Properties of the new transformed functions are discussed by considering the failure severity and the failure occurrence.Designers can choose appropriate transform amplitudes according to their requirements.Finally,a CNC lathe and a spindle system are used as an example to verify the new allocation method.Seven criteria are considered to compare the results of the new method with traditional methods.The allocation results indicate that the new method is more flexible than traditional methods.By employing the new cubic transformed function,the method covers a wider range of problems in CNC reliability allocation without losing the advantages of traditional methods.
基金Supported by the National Natural Science Founda-tion of China (49771060)
文摘The theory of detecling ridges in the modulus of the continuous wavelet transform is presented as well as reconstructing signal by using information on ridges,To periodic signal we suppose Morlet wavelet as basic wavelet, and research the local extreme point and extrema of the wavelet transform on periodic function for the collection of signal＇ s instantaneous amplitude and period.
文摘To elucidate feasible routes of producing CO from CH 3 and unravel the eff ect of adsorbed O on CH x transformation, the reactivity of CH x ( x = 1-3) with and without the assistance of adsorbed atomic O on Ni(111) was explored using density functional theory calculations. The adsorption energies of CH x ( x = 0-3) were found to be signifi cantly reduced on an O-preadsorbed Ni(111) surface compared to a pure surface. Furthermore, O-assisted one-step dehydrogenation of CH x ( x = 1-3) features energy barriers and thus is diffi cult to proceed. In terms of energy, the direct dissociation of CH 3 is favorable, except for the last CH dehydrogenation, which is energy intensive. Interestingly, in O-assisted two-step CH transformation to CO via CHO intermediate, the barrier is dramatically lowered. The successive dehydrogenations of CH x O ( x = 1-3) were also found to be a route for CO formation. Finally, two possible pathways from CH 3 to CO are proposed:(a) CH 3 → CH 2 → CH → CHO → CO;(b) CH 3 → CH 3 O → CH 2 O → CHO → CO.
文摘The Auto-Transformer Rectifier Unit（ATRU） is one preferred solution for high-power AC/DC power conversion in aircraft. This is mainly due to its simple structure, high reliability and reduced k VA ratings. Indeed, the ATRU has become a preferred AC/DC solution to supply power to the electric environment control system on-board future aircraft. In this paper, a general modelling method for ATRUs is introduced. The developed model is based on the fact that the DC voltage and current are strongly related to the voltage and current vectors at the AC terminals of ATRUs. In this paper, we carry on our research in modelling symmetric 18-pulse ATRUs and develop a generic modelling technique. The developed generic model can study not only symmetric but also asymmetric ATRUs. An 18-pulse asymmetric ATRU is used to demonstrate the accuracy and efficiency of the developed model by comparing with corresponding detailed switching SABER models provided by our industrial partner. The functional models also allow accelerated and accurate simulations and thus enable whole-scale more-electric aircraft electrical power system studies in the future.
基金the National Natural Science Foundation of China (50677014)Hunan Provincial Natural Science Foundation of China (06JJ50114).
文摘In order to provide larger capacity of the hidden secret data while maintaining a good visual quality of stego-image, in accordance with the visual property that human eyes are less sensitive to strong texture, a novel steganographic method based on wavelet and modulus function is presented. First, an image is divided into blocks of prescribed size, and every block is decomposed into one-level wavelet. Then, the capacity of the hidden secret data is decided with the number of wavelet coefficients of larger magnitude. Finally, secret information is embedded by steganography based on modulus function. From the experimental results, the proposed method hides much more information and maintains a good visual quality of stego-image. Besides, the embedded data can be extracted from the stego-image without referencing the original image.
基金the National Natural Science Foundation of China under Grand No.549974011
文摘The theory of elastic wave scattering is a fundamental concept in the study of elastic dynamics and wave motion,and the wave function expansion technique has been widely used in many subjects.To supply the essential tools for solving wave scattering problems induced by an eccentric source or multi-sources as well as multi-scatters,a whole-space transform formula of cylindrical wave functions is presented and its applicability to some simple cases is demonstrated in this study.The transforms of wave functions in cylindrical coordinates can be classifi ed into two basic types: interior transform and exterior transform,and the existing Graf’s addition theorem is only suitable for the former.By performing a new replacement between the two coordinates,the exterior transform formula is fi rst deduced.It is then combined with Graf’s addition theorem to establish a whole-space transform formula.By using the whole-space transform formula,the scattering solutions by the sources outside and inside a cylindrical cavity are constructed as examples of its application.The effectiveness and advantages of the whole-space transform formula is illustrated by comparison with the approximate model based on a large cycle method.The whole-space transform formula presented herein can be used to perform the transform between two different cylindrical coordinates in the whole space.In addition,its concept and principle are universal and can be further extended to establish the coordinate transform formula of wave functions in other coordinate systems.
基金Supported by the Marine Engineering Equipment Scientific Research Project of Ministry of Industry and Information Technology of PRCthe National Science and Technology Major Project of China(Grant No.2016ZX05057020)National Natural Science Foundation of China(Grant No.51809067)
文摘The probability distributions of wave characteristics from three groups of sampled ocean data with different significant wave heights have been analyzed using two transformation functions estimated by non-parametric and parametric methods. The marginal wave characteristic distribution and the joint density of wave properties have been calculated using the two transformations, with the results and accuracy of both transformations presented here. The two transformations deviate slightly between each other for the calculation of the crest and trough height marginal wave distributions, as well as the joint densities of wave amplitude with other wave properties. The transformation methods for the calculation of the wave crest and trough height distributions are shown to provide good agreement with real ocean data. Our work will help in the determination of the most appropriate transformation procedure for the prediction of extreme values.
基金supported by the National Natural Science Foundation of China (Grant Nos 10775097 and 10874174)
文摘This paper proves a new theorem on the relationship between optical field Wigner function＇s two-parameter Radon transform and optical Fresnel transform of the field, i.e., when an input field ψ （x＇） propagates through an optical [D （-B） （-C） A] system, the energy density of the output field is equal to the Radon transform of the Wigner function of the input field, where the Radon transform parameters are D, B. It prove this theorem in both spatial-domain and frequency-domain, in the latter case the Radon transform parameters are A, C.
文摘In the present paper,we have considered the approximation of analytic functions represented by Laplace-Stieltjes transformations using sequence of definite integrals. We have characterized their order and type in terms of the rate of decrease of E;（F,β） where E;（F,β） is the error in approximating of the function F（s） by definite integral polynomials in the half plane Res≤β<α.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10171026, 60473114,and Anhui Provincial Natural Science Foundation under Grant No. 03046102.
文摘The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.
基金Foundation items:the National Development Programming of Key Fundamental Researches of China(G1999022103)Planed Item for Distinguished Teacher Invested by Minisny of Education PRC
文摘Some properties of the wavelet transform of trigonometric Junction, periodic function and nonstationary periodic function have been investigated. The results show that the peak height and width in wavelet energy spectrum of a periodic function are in proportion to its period. At the same time, a new equation, which can truly reconstruct a trigonometric function with only one scale wavelet coefficient, is presented. The reconstructed wave shape of a periodic function with the equation is better than any term of its Fourier series. And the reconstructed wave shape of a class of nonstationary periodic function with this equation agrees well with the function.
文摘Power transformer insulation systems are subjected to many stresses during normal operation due to lightning and switching.If the spectrum of incoming surge voltage matches the winding one,the corresponding resonance will be excited.Therefore external transients occurring in power systems might trigger internal overvoltages with large maximum value in transformer windings.Overvoltages having such characteristic have been the root cause of many power transformer failures.The paper presents an approach to the identification of sensitive zones in the transformer windings based on the measurements of overvoltages inside windings and frequency dependences of admittance of the power transformer.The frequency characteristic of the transformer winding may determine those regions in the frequency spectrum.The presented approach might be used both for design optimization and diagnostics of distribution and power transformers.
基金Funded by by Natural Science Foundation Project of CQ CSTC (Grant No: cstc2012jjA50018)the Basic Research of Chongqing Municipal Education Commission (Grant No:KJ120613)
文摘Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense.
基金National Nature Science Foundation of China (49974021).
文摘A new method for receiver function inversion by wavelet transformation is presented in this paper. Receiver func-tion is expanded to different scales with different resolution by wavelet transformation. After an initial model be-ing taken, a generalized least-squares inversion procedure is gradually carried out for receiver function from low to high scale, with the inversion result for low order receiver function as the initial model for high order. A neighborhood containing the global minimum is firstly searched from low scale receiver function, and will gradu-ally focus at the global minimum by introducing high scale information of receiver function. With the gradual ad-dition of high wave-number to smooth background velocity structure, wavelet transformation can keep the inver-sion result converge to the global minimum, reduce to certain extent the dependence of inversion result on the initial model, overcome the nonuniqueness of generalized least-squares inversion, and obtain reliable crustal and upper mantle velocity with high resolution.
