This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering a...This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.展开更多
The quality factor Q, which reflects the energy attenuation of seismic waves in subsurface media, is a diagnostic tool for hydrocarbon detection and reservoir characterization. In this paper, we propose a new Q extrac...The quality factor Q, which reflects the energy attenuation of seismic waves in subsurface media, is a diagnostic tool for hydrocarbon detection and reservoir characterization. In this paper, we propose a new Q extraction method based on the energy ratio before and after the wavelet attenuation, named the energy-ratio method（ERM）. The proposed method uses multipoint signal data in the time domain to estimate the wavelet energy without invoking the source wavelet spectrum, which is necessary in conventional Q extraction methods, and is applicable to any source wavelet spectrum; however, it requires high-precision seismic data. Forward zero-offset VSP modeling suggests that the ERM can be used for reliable Q inversion after nonintrinsic attenuation（geometric dispersion, refl ection, and transmission loss） compensation. The application to real zero-offset VSP data shows that the Q values extracted by the ERM and spectral ratio methods are identical, which proves the reliability of the new method.展开更多
The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a m...The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.展开更多
By integrating deep neural networks with reinforcement learning,the Double Deep Q Network(DDQN)algorithm overcomes the limitations of Q-learning in handling continuous spaces and is widely applied in the path planning...By integrating deep neural networks with reinforcement learning,the Double Deep Q Network(DDQN)algorithm overcomes the limitations of Q-learning in handling continuous spaces and is widely applied in the path planning of mobile robots.However,the traditional DDQN algorithm suffers from sparse rewards and inefficient utilization of high-quality data.Targeting those problems,an improved DDQN algorithm based on average Q-value estimation and reward redistribution was proposed.First,to enhance the precision of the target Q-value,the average of multiple previously learned Q-values from the target Q network is used to replace the single Q-value from the current target Q network.Next,a reward redistribution mechanism is designed to overcome the sparse reward problem by adjusting the final reward of each action using the round reward from trajectory information.Additionally,a reward-prioritized experience selection method is introduced,which ranks experience samples according to reward values to ensure frequent utilization of high-quality data.Finally,simulation experiments are conducted to verify the effectiveness of the proposed algorithm in fixed-position scenario and random environments.The experimental results show that compared to the traditional DDQN algorithm,the proposed algorithm achieves shorter average running time,higher average return and fewer average steps.The performance of the proposed algorithm is improved by 11.43%in the fixed scenario and 8.33%in random environments.It not only plans economic and safe paths but also significantly improves efficiency and generalization in path planning,making it suitable for widespread application in autonomous navigation and industrial automation.展开更多
Determination of Fe^(2+)/Fe^(3+) ratios from metallogenic belts to explore controlling physical and chemical conditions of rock formation is of great significance.In order to explore magnetite Fe^(2+)/Fe^(3+) ratios o...Determination of Fe^(2+)/Fe^(3+) ratios from metallogenic belts to explore controlling physical and chemical conditions of rock formation is of great significance.In order to explore magnetite Fe^(2+)/Fe^(3+) ratios of the Qimantag metallogenic belt,part of the Eastern Kunlun orogenic belt in the northeastern margin of the Qinghai–Tibetan plateau,western Central Orogenic Belt of China,and overcome the limitation of the traditional electronic probe,five different measurement methods are proposed and their respective advantages and disadvantages evaluated,with the composition data of the magnetite obtained using electron probe microanalysis(EPMA).The direct oxygen measurement method has a significant impact on the determination results of FeO and Fe2O3,but the accuracy and uniformity of the results are low.The valence method(Flank method)based on the spectral intensity ratio of Lαto Lβfor iron is also unreliable for FeO and Fe_(2)O^(3) measurements because it is difficult to establish a relationship between Lβ/Lα,the spectral intensity ratio,and the Fe^(2+)/Fe^(3+) content ratio.In comparison,the charge difference method,the surplus-oxygen method and the Mössbauer spectrum method are still the most favorable.Mössbauer spectroscopy,with its isomer movement particularly sensitive to the oxidation state of iron,yields results closer to 0.5,which is relatively reliable.Earlier magnetite deposits are located in intrusions or contact zones and formed by magmatic fluids with high Fe2+/Fe3+ratios,whereas later magnetite deposits are farther away from intrusions and have low Fe^(2+)/Fe^(3+) ratios.The transformation mechanism of hematite and magnetite in the Qimantage metallogenic belt is also studied.No large volume changes,such as pore filling and shrinkage fracture,were detected in the metallogenic belt,and the transformation mechanism is more similar to a reoxidation and reduction mechanism.展开更多
In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is...In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.展开更多
A computational code is developed to help identify metal absorption lines in high resolution QSO spectra, especially in the Lyα forest. The input to the code includes a list of line central wavelengths, column densit...A computational code is developed to help identify metal absorption lines in high resolution QSO spectra, especially in the Lyα forest. The input to the code includes a list of line central wavelengths, column densities and Doppler widths. The code then searches for candidate metal absorption systems and assesses the probability that each system could be real. The framework of the strategy we employ is described in detail and we discuss how to estimate the errors in line profile fitting that are essential to identification. A series of artificial spectra is constructed to calibrate the performance of the code. Due to the effects of blending and noise on Voigt profile fitting, the completeness of the identification depends on the column density of absorbers. For intermediate and strong artificial metal absorbers, more than 90% could be confirmed by the code. The results of applying the code to the real spectra of QSOs HS0757＋5218 and Q0100＋1300 are also presented.展开更多
This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the erro...This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.展开更多
In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton ...In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.展开更多
The estimation of the quality factor Q plays a fundamental role in enhancing seismic resolution via absorption compensation in the near-surface layer.We present a new geometry that can be used to acquire field data by...The estimation of the quality factor Q plays a fundamental role in enhancing seismic resolution via absorption compensation in the near-surface layer.We present a new geometry that can be used to acquire field data by combining surface and cross-hole surveys to decrease the effect of geophone coupling on Q estimation.In this study,we drilled number of receiver holes around the source hole,each hole has different depth and each geophone is placed geophones into the bottom of each receiver hole to avoid the effect of geophone coupling with the borehole wall on Q estimation in conventional cross-hole seismic surveys.We also propose a novel tomographic inversion of the Q factor without the effect of the source signature,and examine its stability and reliability using synthetic data.We estimate the Q factors of the near-surface layer in two different frequency bands using field data acquired in the Dagang Oilfield.The results show that seismic absorption in the nearsurface layer is much greater than that in the subsurface strata.Thus,it is of critical practical importance to enhance the seismic solution by compensating for near-surface absorption.In addition,we derive different Q factors from two frequency bands,which can be treated,to some extent,as evidence of a frequency-dependent Q.展开更多
The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, e...The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.展开更多
基金funded by the National Key Research and Development Program of China(No.2021YFB2600704)the National Natural Science Foundation of China(No.52171272)the Significant Science and Technology Project of the Ministry of Water Resources of China(No.SKS-2022112).
文摘This paper presents an efficient numerical technique for solving multi-term linear systems of fractional ordinary differential equations(FODEs)which have been widely used in modeling various phenomena in engineering and science.An approximate solution of the system is sought in the formof the finite series over the Müntz polynomials.By using the collocation procedure in the time interval,one gets the linear algebraic system for the coefficient of the expansion which can be easily solved numerically by a standard procedure.This technique also serves as the basis for solving the time-fractional partial differential equations(PDEs).The modified radial basis functions are used for spatial approximation of the solution.The collocation in the solution domain transforms the equation into a system of fractional ordinary differential equations similar to the one mentioned above.Several examples have verified the performance of the proposed novel technique with high accuracy and efficiency.
基金supported by the Major Project of the Ministry of Science and Technology of China(No.2011ZX05024-001-01)National Nature Science Foundation of China(No.41140033)
文摘The quality factor Q, which reflects the energy attenuation of seismic waves in subsurface media, is a diagnostic tool for hydrocarbon detection and reservoir characterization. In this paper, we propose a new Q extraction method based on the energy ratio before and after the wavelet attenuation, named the energy-ratio method（ERM）. The proposed method uses multipoint signal data in the time domain to estimate the wavelet energy without invoking the source wavelet spectrum, which is necessary in conventional Q extraction methods, and is applicable to any source wavelet spectrum; however, it requires high-precision seismic data. Forward zero-offset VSP modeling suggests that the ERM can be used for reliable Q inversion after nonintrinsic attenuation（geometric dispersion, refl ection, and transmission loss） compensation. The application to real zero-offset VSP data shows that the Q values extracted by the ERM and spectral ratio methods are identical, which proves the reliability of the new method.
基金supported by The National Key Research and Development Program Plane(No.2017YFC0601505)National Natural Science Foundation(No.41672325)Science&Technology Department of Sichuan Province Technology Project(No.2017GZ0393)
文摘The attenuation factor or quality factor(Q-factor or Q) has been used to measure the energy attenuation of seismic waves propagating in underground media. Many methods are used to estimate the Q-factor. We propose a method to calculate the Q-factor based on the prestack Q-factor inversion and the generalized S-transform. The proposed method specifies a standard primary wavelet and calculates the cumulative Q-factors; then, it finds the interlaminar Q-factors using the relation between Q and offset(QVO) and the Dix formula. The proposed method is alternative to methods that calculate interlaminar Q-factors after horizon picking. Because the frequency spectrum of each horizon can be extracted continuously on a 2D time–frequency spectrum, the method is called the continuous spectral ratio slope(CSRS) method. Compared with the other Q-inversion methods, the method offers nearly effortless computations and stability, and has mathematical and physical significance. We use numerical modeling to verify the feasibility of the method and apply it to real data from an oilfield in Ahdeb, Iraq. The results suggest that the resolution and spatial stability of the Q-profile are optimal and contain abundant interlaminar information that is extremely helpful in making lithology and fluid predictions.
基金funded by National Natural Science Foundation of China(No.62063006)Guangxi Science and Technology Major Program(No.2022AA05002)+1 种基金Key Laboratory of AI and Information Processing(Hechi University),Education Department of Guangxi Zhuang Autonomous Region(No.2022GXZDSY003)Central Leading Local Science and Technology Development Fund Project of Wuzhou(No.202201001).
文摘By integrating deep neural networks with reinforcement learning,the Double Deep Q Network(DDQN)algorithm overcomes the limitations of Q-learning in handling continuous spaces and is widely applied in the path planning of mobile robots.However,the traditional DDQN algorithm suffers from sparse rewards and inefficient utilization of high-quality data.Targeting those problems,an improved DDQN algorithm based on average Q-value estimation and reward redistribution was proposed.First,to enhance the precision of the target Q-value,the average of multiple previously learned Q-values from the target Q network is used to replace the single Q-value from the current target Q network.Next,a reward redistribution mechanism is designed to overcome the sparse reward problem by adjusting the final reward of each action using the round reward from trajectory information.Additionally,a reward-prioritized experience selection method is introduced,which ranks experience samples according to reward values to ensure frequent utilization of high-quality data.Finally,simulation experiments are conducted to verify the effectiveness of the proposed algorithm in fixed-position scenario and random environments.The experimental results show that compared to the traditional DDQN algorithm,the proposed algorithm achieves shorter average running time,higher average return and fewer average steps.The performance of the proposed algorithm is improved by 11.43%in the fixed scenario and 8.33%in random environments.It not only plans economic and safe paths but also significantly improves efficiency and generalization in path planning,making it suitable for widespread application in autonomous navigation and industrial automation.
基金obtained grants from the National Key Research and Development Program Project"Enhanced Bioremediation Technology and Equipment for Chromium Residuation Site",the Scientific Research Project of Hunan Provincial Department of Education(Grant No.19C1178)the Construction Program for the First-Class Disciplines(Geography)of Hunan Province,China.The anonymous reviewers and editors are thanked for constructive suggestions on improving the quality of the manuscript.
文摘Determination of Fe^(2+)/Fe^(3+) ratios from metallogenic belts to explore controlling physical and chemical conditions of rock formation is of great significance.In order to explore magnetite Fe^(2+)/Fe^(3+) ratios of the Qimantag metallogenic belt,part of the Eastern Kunlun orogenic belt in the northeastern margin of the Qinghai–Tibetan plateau,western Central Orogenic Belt of China,and overcome the limitation of the traditional electronic probe,five different measurement methods are proposed and their respective advantages and disadvantages evaluated,with the composition data of the magnetite obtained using electron probe microanalysis(EPMA).The direct oxygen measurement method has a significant impact on the determination results of FeO and Fe2O3,but the accuracy and uniformity of the results are low.The valence method(Flank method)based on the spectral intensity ratio of Lαto Lβfor iron is also unreliable for FeO and Fe_(2)O^(3) measurements because it is difficult to establish a relationship between Lβ/Lα,the spectral intensity ratio,and the Fe^(2+)/Fe^(3+) content ratio.In comparison,the charge difference method,the surplus-oxygen method and the Mössbauer spectrum method are still the most favorable.Mössbauer spectroscopy,with its isomer movement particularly sensitive to the oxidation state of iron,yields results closer to 0.5,which is relatively reliable.Earlier magnetite deposits are located in intrusions or contact zones and formed by magmatic fluids with high Fe2+/Fe3+ratios,whereas later magnetite deposits are farther away from intrusions and have low Fe^(2+)/Fe^(3+) ratios.The transformation mechanism of hematite and magnetite in the Qimantage metallogenic belt is also studied.No large volume changes,such as pore filling and shrinkage fracture,were detected in the metallogenic belt,and the transformation mechanism is more similar to a reoxidation and reduction mechanism.
文摘In this paper, a modified Newton type iterative method is considered for ap- proximately solving ill-posed nonlinear operator equations involving m-accretive mappings in Banach space. Convergence rate of the method is obtained based on an a priori choice of the regularization parameter. Our analysis is not based on the sequential continuity of the normalized duality mapping.
基金supported in part by the US NSF grants AST0507717 and AST0808168the National Natural Science Foundation of China(Grant No.10573028)+3 种基金the Key Project(No.10833005)the Group Innovation Project(No.10821302)the National Basic Research Program of China(973 ProgramNo.2007CB815402)
文摘A computational code is developed to help identify metal absorption lines in high resolution QSO spectra, especially in the Lyα forest. The input to the code includes a list of line central wavelengths, column densities and Doppler widths. The code then searches for candidate metal absorption systems and assesses the probability that each system could be real. The framework of the strategy we employ is described in detail and we discuss how to estimate the errors in line profile fitting that are essential to identification. A series of artificial spectra is constructed to calibrate the performance of the code. Due to the effects of blending and noise on Voigt profile fitting, the completeness of the identification depends on the column density of absorbers. For intermediate and strong artificial metal absorbers, more than 90% could be confirmed by the code. The results of applying the code to the real spectra of QSOs HS0757＋5218 and Q0100＋1300 are also presented.
文摘This paper deals with the inertial manifold and the approximate inertialmanifold concepts of the Navier-Stokes equations with nonhomogeneous boundary conditions and inertial algorithm. Furtheremore,we provide the error estimates of the approximate solutions of the Navier-Stokes Equations.
文摘In this paper, the evolutionary behavior of N-solitons for a (2 + 1)-dimensional Konopelchenko-Dubrovsky equations is studied by using the Hirota bilinear method and the long wave limit method. Based on the N-soliton solution, we first study the evolution from N-soliton to T-order (T=1,2) breather wave solutions via the paired-complexification of parameters, and then we get the N-order rational solutions, M-order (M=1,2) lump solutions, and the hybrid behavior between a variety of different types of solitons combined with the parameter limit technique and the paired-complexification of parameters. Meanwhile, we also provide a large number of three-dimensional figures in order to better show the degeneration of the N-soliton and the interaction behavior between different N-solitons.
基金supported by the National Natural Science Foundation of China(Grant No.41174117 and 41474109)the National Key Basic Research Development Program of China(Grant No.2013CB228606)
文摘The estimation of the quality factor Q plays a fundamental role in enhancing seismic resolution via absorption compensation in the near-surface layer.We present a new geometry that can be used to acquire field data by combining surface and cross-hole surveys to decrease the effect of geophone coupling on Q estimation.In this study,we drilled number of receiver holes around the source hole,each hole has different depth and each geophone is placed geophones into the bottom of each receiver hole to avoid the effect of geophone coupling with the borehole wall on Q estimation in conventional cross-hole seismic surveys.We also propose a novel tomographic inversion of the Q factor without the effect of the source signature,and examine its stability and reliability using synthetic data.We estimate the Q factors of the near-surface layer in two different frequency bands using field data acquired in the Dagang Oilfield.The results show that seismic absorption in the nearsurface layer is much greater than that in the subsurface strata.Thus,it is of critical practical importance to enhance the seismic solution by compensating for near-surface absorption.In addition,we derive different Q factors from two frequency bands,which can be treated,to some extent,as evidence of a frequency-dependent Q.
基金financially supported by the Key Program of National Natural Science Foundation of China(No.41530320)China Natural Science Foundation for Young Scientists(No.41404093)+1 种基金Key National Research Project of China(Nos2016YFC0303100 and 2017YFC0601900)China Natural Science Foundation(No.41774125)
文摘The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.
