Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, convened wave data is charac...Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, convened wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution convened wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.展开更多
This paper introduces the mid-span spectral inversion by four-wave mixing in a commercially available semiconductor optical amplifier （SOA） with a length of about 1.5 mm to optical label switching network based on c...This paper introduces the mid-span spectral inversion by four-wave mixing in a commercially available semiconductor optical amplifier （SOA） with a length of about 1.5 mm to optical label switching network based on combined frequency shift keying （FSK）-intensiy modulation （IM）/optical label-packet modulation to overcome the dispersion limitation of fiber. The 155 Mb/s-10 Gb/s combined FSK/IM signal is experimentally transmitted over a 100 km standard single mode fiber. 10^-10 and 10^-9 BER （bit error ratio）, or even better, is achieved for the FSK label and IM packet, respectively. The -19 dB power conversion efficiency is obtained for -1 nm wavelength detuning.展开更多
We present new quantitative model describing the pressure dependence of acoustic P-and S-wave velocities.Assuming that a variety of individual mechanisms or defects(such as cracks,pore collapse and grain crushing)can ...We present new quantitative model describing the pressure dependence of acoustic P-and S-wave velocities.Assuming that a variety of individual mechanisms or defects(such as cracks,pore collapse and grain crushing)can contribute to the pressure-dependent change of the wave velocity,we order a characteristic pressure to all of them and allow a series of exponential terms in the description of the(Pand S-waves)velocity-pressure function.We estimate the parameters of the multi-exponential rock physical model in inversion procedures using laboratory measured P-and S-wave velocity data.As is known,the conventional damped least squares method gives acceptable results only when one or two individual mechanisms are assumed.Increasing the number of exponential terms leads to highly nonlinear ill-posed inverse problem.Due to this reason,we develop the spectral inversion method(SIM)in which the velocity amplitudes(the spectral lines in the characteristic pressure spectrum)are only considered as unknowns.The characteristic pressures(belonging to the velocity amplitudes)are excluded from the set of inversion unknowns,instead,they are defined in a set of fixed positions equidistantly distributed in the actual interval of the independent variable(pressure).Through this novel linear inversion method,we estimate the parameters of the multi-exponential rock physical model using laboratory measured P-and S-wave velocity data.The characteristic pressures are related to the closing pressures of cracks which are described by well-known rock mechanical relationships depending on the aspect ratio of elliptical cracks.This gives the possibility to estimate the aspect ratios in terms of the characteristic pressures.展开更多
A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic moments (M0) and source corner frequencies (fc) of several Jiashi (Xinjiang, China) earthquakes, as well...A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic moments (M0) and source corner frequencies (fc) of several Jiashi (Xinjiang, China) earthquakes, as well as the apparent Lg Q models for the paths from Jiashi to eight seismic stations (WMQ, AAK, TLG, MAKZ, KUR, VOS, ZRN and CHK) in Central Asia. The resultant seismic moments correlate well with the M0 values obtained by Harvard University using the centroid moment tensor (CMT) inversion and the surface-wave magnitudes as well. After the correction by a typical value of average radiation coefficient for regional SV waves, the M0 values from Lg spectral inversion are still close to the corresponding values obtained from CMT inversion. The obtained ap- parent Q0Lg values (Lg Q at 1 Hz) are consistent with the tectonic features of corresponding propagation paths. The Q0Lg values are 351±87, 349±86 and 300±27 for the paths from Jiashi to AAK, TLG and MAKZ, respectively. They are smaller than Q0Lg values for the paths to KUR, VOS, ZRN and CHK, which are 553±72, 569±58, 550±57 and 603±65, respectively. These results agree with the condition that the paths to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area where relatively strong seismic activities and large variations of topography are exhibited, while the paths to KUR, VOS, ZRN and CHK mainly propagate through the stable area of Kazak platform. The Q0Lg value for the path to WMQ is 462±56. This is also in agreement with the condition that the path to WMQ is basically along the border area between Tianshan Mountain and Tarim Basin, and along this path the variations of topography and crustal thickness are moderate in comparison with that along the path to MAKZ.展开更多
Thin reservoirs prediction method such as spectral inversion has drawn considerable attention in recent years. In order to avoid extracting wavelets within the whole field area purposeless and to make the filtered dat...Thin reservoirs prediction method such as spectral inversion has drawn considerable attention in recent years. In order to avoid extracting wavelets within the whole field area purposeless and to make the filtered data has preferable fidelity as well as signal-to-noise ratio, an effective structural constrained thin reservoir description method which combines spectral inversion and wide-band Ricker wavelet filtering technology has been proposed in this paper. The method given here is more credible and is suitable for the prediction of middle-deep thin reservoirs. We take LD-A structure within Bohai Bay Basin as an example to show the implement of our method. Several sets of thin sand layers which are hardly to recognize originally have been finally identified. Also, with the application of this method, a high-production thin reservoir of LD-B structure has been identified accurately, which provides credible information for subsequent fine oil exploration and development.展开更多
Sturm-Liouville operators on a finite interval with discontinuities are considered. We give a uniqueness theorem for determining the potential and the parameters in boundary and under discontinuous conditions from a p...Sturm-Liouville operators on a finite interval with discontinuities are considered. We give a uniqueness theorem for determining the potential and the parameters in boundary and under discontinuous conditions from a particular set of eigenvalues, and provide corresponding reconstruction algorithm, which can be applicable to McLaughlin-Rundell＇s uniqueness theorem （see J. Math. Phys. 28, 1987）.展开更多
In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’...In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation.Based on solving the ■ equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.展开更多
In this paper,we consider the recovery of third-order differential operators from two spectra,as well as fourth-order or fifth-order differential operators from three spectra,where these differential operators are end...In this paper,we consider the recovery of third-order differential operators from two spectra,as well as fourth-order or fifth-order differential operators from three spectra,where these differential operators are endowed with complex-valued distributional coefficients.For the case of multiple spectra,we first establish the relationship between spectra and the Weyl–Yurko matrix.Secondly,we prove the uniqueness theorem for the solution of the inverse problems.Our approach allows us to obtain results for the general case of complex-valued distributional coefficients.展开更多
For the generalized Dirichlet–Regge problem with complex coefficients,we prove the local solvability and stability for the inverse spectral problem,which indicates an improved result of the previous work([Journal of ...For the generalized Dirichlet–Regge problem with complex coefficients,we prove the local solvability and stability for the inverse spectral problem,which indicates an improved result of the previous work([Journal of Geometry and Physics,159,103936(2021)]).展开更多
The partial inverse problem for differential pencils on a star-shaped graph is studied from mixed spectral data.More precisely,we show that if the potentials on all edges on the star-shaped graph but one are known a p...The partial inverse problem for differential pencils on a star-shaped graph is studied from mixed spectral data.More precisely,we show that if the potentials on all edges on the star-shaped graph but one are known a priori then the unknown potential on the remaining edge can be uniquely determined by partial information on the potential and a part of eigenvalues.展开更多
This paper revisits the classical problem“Can we hear the density of a string?”,which can be formulated as an inverse spectral problem for a Sturm-Liouville operator.Instead of inverting the map from density to spec...This paper revisits the classical problem“Can we hear the density of a string?”,which can be formulated as an inverse spectral problem for a Sturm-Liouville operator.Instead of inverting the map from density to spectral data directly,we propose a novel method to reconstruct the density based on inverting a sequence of trace formulas which bridge the density and its spectral data clearly in terms of a series of nonlinear integral equations.Numerical experiments are presented to verify the validity and effectiveness of the proposed numerical algorithm.The impact of different parameters involved in the algorithm is also discussed.展开更多
The inverse spectral problem for the Dirac operators defined on the interval[0, π] with self-adjoint separated boundary conditions is considered. Some uniqueness results are obtained, which imply that the pair of pot...The inverse spectral problem for the Dirac operators defined on the interval[0, π] with self-adjoint separated boundary conditions is considered. Some uniqueness results are obtained, which imply that the pair of potentials(p(x), r(x)) and a boundary condition are uniquely determined even if only partial information is given on(p(x), r(x))together with partial information on the spectral data, consisting of either one full spectrum and a subset of norming constants, or a subset of pairs of eigenvalues and the corresponding norming constants. Moreover, the authors are also concerned with the situation where both p(x) and r(x) are C n-smoothness at some given point.展开更多
We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable selfadjoint matrix potential.The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators,which a...We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable selfadjoint matrix potential.The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators,which are subject to separation boundary conditions or periodic(semi-periodic)boundary conditions,and some analogs of Ambarzumyan's theorem are obtained.The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators,which are the second power of Dirac operators.展开更多
We study inverse spectral problems for radial Schrodinger operators in L^(2)(0,1).It is well known that for a radial Schrodinger operator,two spectra for the different boundary conditions can uniquely determine the po...We study inverse spectral problems for radial Schrodinger operators in L^(2)(0,1).It is well known that for a radial Schrodinger operator,two spectra for the different boundary conditions can uniquely determine the potential.However,if the spectra corresponding to the radial Schrodinger operators with the two potential functions miss a finite number of eigenvalues,what is the relationship between the two potential functions?Inspired by Hochstadt(1973)'s work,which handled the Sturm-Liouville operator with the potential q∈L^(1)(0,1),we give a corresponding result for radial Schrodinger operators with a larger class of potentials than L^(1)(0,1).When q∈L^(1)(0,1),we also consider the case where the spectra corresponding to the radial Schrodinger operators with the two potential functions miss an infinite number of eigenvalues and the eigenvalues are close in some sense.展开更多
The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x...The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree graphs.We prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.展开更多
基金supported by the China National Petroleum Corporation Scientific research and technology development project(Nos.2013E-38-08)
文摘Multi-wave exploration is an effective means for improving precision in the exploration and development of complex oil and gas reservoirs that are dense and have low permeability. However, convened wave data is characterized by a low signal-to-noise ratio and low resolution, because the conventional deconvolution technology is easily affected by the frequency range limits, and there is limited scope for improving its resolution. The spectral inversion techniques is used to identify λ/8 thin layers and its breakthrough regarding band range limits has greatly improved the seismic resolution. The difficulty associated with this technology is how to use the stable inversion algorithm to obtain a high-precision reflection coefficient, and then to use this reflection coefficient to reconstruct broadband data for processing. In this paper, we focus on how to improve the vertical resolution of the converted PS-wave for multi-wave data processing. Based on previous research, we propose a least squares inversion algorithm with a total variation constraint, in which we uses the total variance as a priori information to solve under-determined problems, thereby improving the accuracy and stability of the inversion. Here, we simulate the Gaussian fitting amplitude spectrum to obtain broadband wavelet data, which we then process to obtain a higher resolution converted wave. We successfully apply the proposed inversion technology in the processing of high-resolution data from the Penglai region to obtain higher resolution convened wave data, which we then verify in a theoretical test. Improving the resolution of converted PS-wave data will provide more accurate data for subsequent velocity inversion and the extraction of reservoir reflection information.
基金supported by National Natural Science Foundation of China (Grant No 60677004)National High Technology 863 Research and Development Program of China (Grant Nos 2007AA01Z260,2007AA03Z447 and 2009AA01Z220)+4 种基金Key Project of the Chinese Ministry of Education (Grant No 107011)Key Laboratory of Broadband Optical Fiber Transmission and Communication Networks (UESTC) (Ministry of Education)Teaching and Scientific Research Foundation for the Returned Overseas Chinese Scholars (State Education Ministry)the Corporative Building Project of Beijing Educational Committee (Grant NoXK100130737)Program for New Century Excellent Talents in University of China (Grant No NECT-07-0111)
文摘This paper introduces the mid-span spectral inversion by four-wave mixing in a commercially available semiconductor optical amplifier （SOA） with a length of about 1.5 mm to optical label switching network based on combined frequency shift keying （FSK）-intensiy modulation （IM）/optical label-packet modulation to overcome the dispersion limitation of fiber. The 155 Mb/s-10 Gb/s combined FSK/IM signal is experimentally transmitted over a 100 km standard single mode fiber. 10^-10 and 10^-9 BER （bit error ratio）, or even better, is achieved for the FSK label and IM packet, respectively. The -19 dB power conversion efficiency is obtained for -1 nm wavelength detuning.
基金supported by the European Union,co-financed by the European Social Fund and the GINOP-2.315-2016-00010"Development of enhanced engineering methods with the aim at utilization of subterranean energy resources"project in the framework of the Szechenyi 2020 Plan,funded by the European Union,co-financed by the European Structural and Investment Funds。
文摘We present new quantitative model describing the pressure dependence of acoustic P-and S-wave velocities.Assuming that a variety of individual mechanisms or defects(such as cracks,pore collapse and grain crushing)can contribute to the pressure-dependent change of the wave velocity,we order a characteristic pressure to all of them and allow a series of exponential terms in the description of the(Pand S-waves)velocity-pressure function.We estimate the parameters of the multi-exponential rock physical model in inversion procedures using laboratory measured P-and S-wave velocity data.As is known,the conventional damped least squares method gives acceptable results only when one or two individual mechanisms are assumed.Increasing the number of exponential terms leads to highly nonlinear ill-posed inverse problem.Due to this reason,we develop the spectral inversion method(SIM)in which the velocity amplitudes(the spectral lines in the characteristic pressure spectrum)are only considered as unknowns.The characteristic pressures(belonging to the velocity amplitudes)are excluded from the set of inversion unknowns,instead,they are defined in a set of fixed positions equidistantly distributed in the actual interval of the independent variable(pressure).Through this novel linear inversion method,we estimate the parameters of the multi-exponential rock physical model using laboratory measured P-and S-wave velocity data.The characteristic pressures are related to the closing pressures of cracks which are described by well-known rock mechanical relationships depending on the aspect ratio of elliptical cracks.This gives the possibility to estimate the aspect ratios in terms of the characteristic pressures.
基金Foundation of Verification Researches for Army Control Technology (413290102).
文摘A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic moments (M0) and source corner frequencies (fc) of several Jiashi (Xinjiang, China) earthquakes, as well as the apparent Lg Q models for the paths from Jiashi to eight seismic stations (WMQ, AAK, TLG, MAKZ, KUR, VOS, ZRN and CHK) in Central Asia. The resultant seismic moments correlate well with the M0 values obtained by Harvard University using the centroid moment tensor (CMT) inversion and the surface-wave magnitudes as well. After the correction by a typical value of average radiation coefficient for regional SV waves, the M0 values from Lg spectral inversion are still close to the corresponding values obtained from CMT inversion. The obtained ap- parent Q0Lg values (Lg Q at 1 Hz) are consistent with the tectonic features of corresponding propagation paths. The Q0Lg values are 351±87, 349±86 and 300±27 for the paths from Jiashi to AAK, TLG and MAKZ, respectively. They are smaller than Q0Lg values for the paths to KUR, VOS, ZRN and CHK, which are 553±72, 569±58, 550±57 and 603±65, respectively. These results agree with the condition that the paths to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area where relatively strong seismic activities and large variations of topography are exhibited, while the paths to KUR, VOS, ZRN and CHK mainly propagate through the stable area of Kazak platform. The Q0Lg value for the path to WMQ is 462±56. This is also in agreement with the condition that the path to WMQ is basically along the border area between Tianshan Mountain and Tarim Basin, and along this path the variations of topography and crustal thickness are moderate in comparison with that along the path to MAKZ.
文摘Thin reservoirs prediction method such as spectral inversion has drawn considerable attention in recent years. In order to avoid extracting wavelets within the whole field area purposeless and to make the filtered data has preferable fidelity as well as signal-to-noise ratio, an effective structural constrained thin reservoir description method which combines spectral inversion and wide-band Ricker wavelet filtering technology has been proposed in this paper. The method given here is more credible and is suitable for the prediction of middle-deep thin reservoirs. We take LD-A structure within Bohai Bay Basin as an example to show the implement of our method. Several sets of thin sand layers which are hardly to recognize originally have been finally identified. Also, with the application of this method, a high-production thin reservoir of LD-B structure has been identified accurately, which provides credible information for subsequent fine oil exploration and development.
基金supported in part by the National Natural Science Foundation of China(11611530682,11171152 and 91538108)Natural Science Foundation of Jiangsu Province of China(BK 20141392)supported by the China Scholarship Fund(201706840062)
文摘Sturm-Liouville operators on a finite interval with discontinuities are considered. We give a uniqueness theorem for determining the potential and the parameters in boundary and under discontinuous conditions from a particular set of eigenvalues, and provide corresponding reconstruction algorithm, which can be applicable to McLaughlin-Rundell＇s uniqueness theorem （see J. Math. Phys. 28, 1987）.
基金supported by National Natural Science Foundation of China under Grant Nos.12175111,11975131K C Wong Magna Fund in Ningbo University。
文摘In this work,the(2+1)-dimensional Date–Jimbo–Kashiwara–Miwa(DJKM)equation is studied by means of the ■-dressing method.A new ■ problem has been constructed by analyzing the characteristic function and the Green’s function of its Lax representation.Based on solving the ■ equation and choosing the proper spectral transformation,the solution of the DJKM equation is constructed.Furthermore,the more general solution of the DJKM equation can be also obtained by ensuring the evolution of the time spectral data.
基金Supported by the National Natural Science Foundation of China(Grant No.11871031)by the Natural Science Foundation of the Jiangsu Province of China(Grant No.BK 20201303)the Graduate Education and Teaching Reform Project of Nanjing University of Science and Technology(Grant No.KT2024_B08)。
文摘In this paper,we consider the recovery of third-order differential operators from two spectra,as well as fourth-order or fifth-order differential operators from three spectra,where these differential operators are endowed with complex-valued distributional coefficients.For the case of multiple spectra,we first establish the relationship between spectra and the Weyl–Yurko matrix.Secondly,we prove the uniqueness theorem for the solution of the inverse problems.Our approach allows us to obtain results for the general case of complex-valued distributional coefficients.
基金Supported by NSFC(Grant No.11901304)Russian Foundation for Basic Research(Grant Nos.20-31-70005 and 19-01-00102)。
文摘For the generalized Dirichlet–Regge problem with complex coefficients,we prove the local solvability and stability for the inverse spectral problem,which indicates an improved result of the previous work([Journal of Geometry and Physics,159,103936(2021)]).
基金supported by the Russian Ministry of Education and Science(Grant No.1.1660.2017/4.6)。
文摘The partial inverse problem for differential pencils on a star-shaped graph is studied from mixed spectral data.More precisely,we show that if the potentials on all edges on the star-shaped graph but one are known a priori then the unknown potential on the remaining edge can be uniquely determined by partial information on the potential and a part of eigenvalues.
基金partly supported by NSFC grant No.11621101,12071430the Fundamental Research Funds for the Central Universitiespartially supported by Research Grant Council of Hong Kong,China(GRF grailt 16305018).
文摘This paper revisits the classical problem“Can we hear the density of a string?”,which can be formulated as an inverse spectral problem for a Sturm-Liouville operator.Instead of inverting the map from density to spectral data directly,we propose a novel method to reconstruct the density based on inverting a sequence of trace formulas which bridge the density and its spectral data clearly in terms of a series of nonlinear integral equations.Numerical experiments are presented to verify the validity and effectiveness of the proposed numerical algorithm.The impact of different parameters involved in the algorithm is also discussed.
基金supported by the National Natural Science Foundation of China(No.11171198)the Scientific Research Program Funded by Shaanxi Provincial Education Department(No.2013JK0563)
文摘The inverse spectral problem for the Dirac operators defined on the interval[0, π] with self-adjoint separated boundary conditions is considered. Some uniqueness results are obtained, which imply that the pair of potentials(p(x), r(x)) and a boundary condition are uniquely determined even if only partial information is given on(p(x), r(x))together with partial information on the spectral data, consisting of either one full spectrum and a subset of norming constants, or a subset of pairs of eigenvalues and the corresponding norming constants. Moreover, the authors are also concerned with the situation where both p(x) and r(x) are C n-smoothness at some given point.
基金supported in part by the National Natural Science Foundation of China(11871031)by the Natural Science Foundation of the Jiangsu Province of China(BK 20201303)。
文摘We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable selfadjoint matrix potential.The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators,which are subject to separation boundary conditions or periodic(semi-periodic)boundary conditions,and some analogs of Ambarzumyan's theorem are obtained.The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators,which are the second power of Dirac operators.
基金supported by National Natural Science Foundation of China (Grant No.11871031)the Natural Science Foundation of Jiangsu Province of China (Grant No.BK 20201303)。
文摘We study inverse spectral problems for radial Schrodinger operators in L^(2)(0,1).It is well known that for a radial Schrodinger operator,two spectra for the different boundary conditions can uniquely determine the potential.However,if the spectra corresponding to the radial Schrodinger operators with the two potential functions miss a finite number of eigenvalues,what is the relationship between the two potential functions?Inspired by Hochstadt(1973)'s work,which handled the Sturm-Liouville operator with the potential q∈L^(1)(0,1),we give a corresponding result for radial Schrodinger operators with a larger class of potentials than L^(1)(0,1).When q∈L^(1)(0,1),we also consider the case where the spectra corresponding to the radial Schrodinger operators with the two potential functions miss an infinite number of eigenvalues and the eigenvalues are close in some sense.
基金supported by the National Natural Science Foundation of China(No.11871031)the Natural Science Foundation of the Jiangsu Province of China(No.BK 20201303).
文摘The classical Ambarzumyan’s theorem states that if the Neumann eigenvalues of the Sturm-Liouville operator-d^(2)/dx^(2)+q with an integrable real-valued potential q on[0,π] are {n^(2):n≥0},then q=0 for almost all x∈[0,π].In this work,the classical Ambarzumyan’s theorem is extended to the Dirac operator on equilateral tree graphs.We prove that if the spectrum of the Dirac operator on graphs coincides with the unperturbed case,then the potential is identically zero.
