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
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
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
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
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
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
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
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 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.
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 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 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 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.
