Traditional two-dimensional(2D) complex resistivity forward modeling is based on Poisson's equation but spectral induced polarization(SIP) data are the coproducts of the induced polarization(IP) and the electro...Traditional two-dimensional(2D) complex resistivity forward modeling is based on Poisson's equation but spectral induced polarization(SIP) data are the coproducts of the induced polarization(IP) and the electromagnetic induction(EMI) effects.This is especially true under high frequencies,where the EMI effect can exceed the IP effect.2D inversion that only considers the IP effect reduces the reliability of the inversion data.In this paper,we derive differential equations using Maxwell's equations.With the introduction of the Cole-Cole model,we use the finite-element method to conduct2 D SIP forward modeling that considers the EMI and IP effects simultaneously.The data-space Occam method,in which different constraints to the model smoothness and parametric boundaries are introduced,is then used to simultaneously obtain the four parameters of the Cole-Cole model using multi-array electric field data.This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity.To improve the computational efficiency,message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion.Synthetic datasets were tested using both serial and parallel algorithms,and the tests suggest that the proposed parallel algorithm is robust and efficient.展开更多
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
To monitor growth and predict the yield of rice over a large area, the chlorophyll contents in the rice canopy were estimated using the unmanned aerial vehicle(UAV) remote sensing technology. In this work, multi-spect...To monitor growth and predict the yield of rice over a large area, the chlorophyll contents in the rice canopy were estimated using the unmanned aerial vehicle(UAV) remote sensing technology. In this work, multi-spectral image information of the rice crop was obtained using a 6-channel multi-spectral camera mounted on a fixed wing UAV, which was flown 600 m above the ground, between 11: 00-14: 00 on a sunny day in summer. The measured chlorophyll values were collected as sample sets. The s-REP index was screened out to estimate chlorophyll contents through the analysis of six kinds of spectral indexes of chlorophyll estimated capacity. An inversion model of the chlorophyll contents was then built using the least square support vector regression(LS-SVR)algorithm, with calibration and prediction R-square values of 0.89 and 0.83, respectively. Finally, remote sensing mapping for a UAV image of the Fangzheng County Dexter Rice Planting Park was accomplished using the inversion model. The inversion and measured values were then compared using regression fitting. R-square and root-mean-square error of the fitting model were 0.79 and 2.39,respectively. The results demonstrated that accurate estimation of rice-canopy chlorophyll contents was feasible using the LS-SVR inversion model developed using the s-REP vegetation index.展开更多
In this paper, signal distortions caused by spectral inverters which are used in 10Gb/s optical fiber communication systems with mid span spectrum inversion in terms of dispersion shift fibers are analyed numerically....In this paper, signal distortions caused by spectral inverters which are used in 10Gb/s optical fiber communication systems with mid span spectrum inversion in terms of dispersion shift fibers are analyed numerically. It is shown that there exist the optimal input signal power, fiber length and fiblter bandwidth for the spectral in verters. System transmission penalty can be minimized by optimizing these parameters.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
Operation safety and stability of the train mainly depend on the interaction between the wheel and rail.Knowledge of wheel/rail contact force is important for vehicle control systems that aim to enhance vehicle stabil...Operation safety and stability of the train mainly depend on the interaction between the wheel and rail.Knowledge of wheel/rail contact force is important for vehicle control systems that aim to enhance vehicle stability and passenger safety.Since wheel/rail contact forces of high-speed train are very difficult to measure directly,a new estimation process for wheel/rail contact forces was introduced in this work.Based on the state space equation,dynamic programming methods and the Bellman principle of optimality,the main theoretical derivation of the inversion mathematical model was given.The new method overcomes the weakness of large fluctuations which exist in current inverse techniques.High-speed vehicle was chosen as the research object,accelerations of axle box as input conditions,10 degrees of freedom vertical vibration model and 17 degrees of freedom lateral vibration model were established,respectively.Under 250 km/h,the vertical and lateral wheel/rail forces were identified.From the time domain and frequency domain,the comparison of the results between inverse and SIMPACK models were given.The results show that the inverse mathematical model has high precision for inversing the wheel/rail contact forces of an operation high-speed vehicle.展开更多
Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient m...Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.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
In order to obtain stable interval Q factor, by analyzing the spectrum of monitoring wavelet and down-going wavelet of zero-offset VSP data and referring the spectrum expression of Ricker wavelet, we propose a new exp...In order to obtain stable interval Q factor, by analyzing the spectrum of monitoring wavelet and down-going wavelet of zero-offset VSP data and referring the spectrum expression of Ricker wavelet, we propose a new expression of source wavelet spectrum. Basing on the new expression, we present improved amplitude spectral fitting and spectral ratio methods for interval Q inversion based on zero-offset VSP data, and the sequence for processing the zero-offset VSP data. Subsequently, we apply the proposed methods to real zero-offset VSP data, and carry out prestack inverse Q filtering to zero-offset VSP data and surface seismic data for amplitude compensation with the estimated Q value.展开更多
In this study,we focused on a novel parallel mechanism for utilizing the motion simulator of a high-speed boat(HSB).First,we expressed the real behavior of the HSB based on a seakeeping trial.For this purpose,we recor...In this study,we focused on a novel parallel mechanism for utilizing the motion simulator of a high-speed boat(HSB).First,we expressed the real behavior of the HSB based on a seakeeping trial.For this purpose,we recorded the motion parameters of the HSB by gyroscope and accelerometer sensors,while using a special data acquisition technique.Additionally,a Chebychev highpass filter was applied as a noise filter to the accelerometer sensor.Then,a novel 3 degrees of freedom(DoF)parallel mechanism(1T2R)with prismatic actuators is proposed and analyses were performed on its inverse kinematics,velocity,and acceleration.Finally,the inverse dynamic analysis is presented by the principle of virtual work,and the validation of the analytical equations was compared by the ADAMS simulation software package.Additionally,according to the recorded experimental data of the HSB,the feasibility of the proposed novel parallel mechanism motion simulator of the HSB,as well as the necessity of using of the washout filters,was explored.展开更多
An important application of spectral decomposition(SD)is to identify subsurface geological anomalies such as channels and karst caves,which may be buried in full-band seismic data.However,the classical SD methods incl...An important application of spectral decomposition(SD)is to identify subsurface geological anomalies such as channels and karst caves,which may be buried in full-band seismic data.However,the classical SD methods including the wavelet transform(WT)are often limited by relatively low time-frequency resolution,which is responsible for false high horizonassociated space resolution probably indicating more geological structures,especially when close geological anomalies exist.To address this issue,we impose a constraint of minimizing an lp(0<p<1)norm of time-frequency spectral coefficients on the misfit derived by using the inverse WT and apply the generalized iterated shrinkage algorithm to invert for the optimal coefficients.Compared with the WT and inverse SD(ISD)using a typical l1-norm constraint,the modified ISD(MISD)using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features.We design a 3 D synthetic dataset involving frequency-close thin geological anomalies and the other3 D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD.The application of 4 D spectrum on a 3 D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.展开更多
Research on quantitative models of suspended sediment concentration (SSC) using remote sensing technology is very important to understand the scouting and siltation variation in harbors and water channels. Based onl...Research on quantitative models of suspended sediment concentration (SSC) using remote sensing technology is very important to understand the scouting and siltation variation in harbors and water channels. Based onlaboratory study of the relationship between different suspended sediment concentrations and reflectance spectra measured synchronously, quantitative inversion models of SSC based on single factor, band ratio and sediment parameter were developed, which provides an effective method to retrieve the SSC from satellite images. Results show that the bl (430-500nm) and b3 (670-735nm) are the optimal wavelengths for the estimation of lower SSC and the b4 (780-835nm) is the optimal wavelength to estimate the higher SSC. Furthermore the band ratio B2/B3 can be used to simulate the variation of lower SSC better and the B4/B1 to estimate the higher SSC accurately. Also the inversion models developed by sediment parameters of higher and lower SSCs can get a relatively higher accuracy than the single factor and band ratio models.展开更多
If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses cons...If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.展开更多
基金jointly sponsored by the National Natural Science Foundation of China(Grant No.41374078)the Geological Survey Projects of the Ministry of Land and Resources of China(Grant Nos.12120113086100 and 12120113101300)Beijing Higher Education Young Elite Teacher Project
文摘Traditional two-dimensional(2D) complex resistivity forward modeling is based on Poisson's equation but spectral induced polarization(SIP) data are the coproducts of the induced polarization(IP) and the electromagnetic induction(EMI) effects.This is especially true under high frequencies,where the EMI effect can exceed the IP effect.2D inversion that only considers the IP effect reduces the reliability of the inversion data.In this paper,we derive differential equations using Maxwell's equations.With the introduction of the Cole-Cole model,we use the finite-element method to conduct2 D SIP forward modeling that considers the EMI and IP effects simultaneously.The data-space Occam method,in which different constraints to the model smoothness and parametric boundaries are introduced,is then used to simultaneously obtain the four parameters of the Cole-Cole model using multi-array electric field data.This approach not only improves the stability of the inversion but also significantly reduces the solution ambiguity.To improve the computational efficiency,message passing interface programming was used to accelerate the 2D SIP forward modeling and inversion.Synthetic datasets were tested using both serial and parallel algorithms,and the tests suggest that the proposed parallel algorithm is robust and efficient.
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 the National Key R&D Program of China(2016YFD0300610)
文摘To monitor growth and predict the yield of rice over a large area, the chlorophyll contents in the rice canopy were estimated using the unmanned aerial vehicle(UAV) remote sensing technology. In this work, multi-spectral image information of the rice crop was obtained using a 6-channel multi-spectral camera mounted on a fixed wing UAV, which was flown 600 m above the ground, between 11: 00-14: 00 on a sunny day in summer. The measured chlorophyll values were collected as sample sets. The s-REP index was screened out to estimate chlorophyll contents through the analysis of six kinds of spectral indexes of chlorophyll estimated capacity. An inversion model of the chlorophyll contents was then built using the least square support vector regression(LS-SVR)algorithm, with calibration and prediction R-square values of 0.89 and 0.83, respectively. Finally, remote sensing mapping for a UAV image of the Fangzheng County Dexter Rice Planting Park was accomplished using the inversion model. The inversion and measured values were then compared using regression fitting. R-square and root-mean-square error of the fitting model were 0.79 and 2.39,respectively. The results demonstrated that accurate estimation of rice-canopy chlorophyll contents was feasible using the LS-SVR inversion model developed using the s-REP vegetation index.
文摘In this paper, signal distortions caused by spectral inverters which are used in 10Gb/s optical fiber communication systems with mid span spectrum inversion in terms of dispersion shift fibers are analyed numerically. It is shown that there exist the optimal input signal power, fiber length and fiblter bandwidth for the spectral in verters. System transmission penalty can be minimized by optimizing these parameters.
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Project(2009BAG12A04-A11)supported by the National Key Technology R&D Program in the"11-th Five-year Plan"of ChinaProjects(51275432,51005190)supported by the National Natural Science Foundation of ChinaProject(SWJTU09ZT23)supported by University Doctor Academics Particularly Science Research Fund,China
文摘Operation safety and stability of the train mainly depend on the interaction between the wheel and rail.Knowledge of wheel/rail contact force is important for vehicle control systems that aim to enhance vehicle stability and passenger safety.Since wheel/rail contact forces of high-speed train are very difficult to measure directly,a new estimation process for wheel/rail contact forces was introduced in this work.Based on the state space equation,dynamic programming methods and the Bellman principle of optimality,the main theoretical derivation of the inversion mathematical model was given.The new method overcomes the weakness of large fluctuations which exist in current inverse techniques.High-speed vehicle was chosen as the research object,accelerations of axle box as input conditions,10 degrees of freedom vertical vibration model and 17 degrees of freedom lateral vibration model were established,respectively.Under 250 km/h,the vertical and lateral wheel/rail forces were identified.From the time domain and frequency domain,the comparison of the results between inverse and SIMPACK models were given.The results show that the inverse mathematical model has high precision for inversing the wheel/rail contact forces of an operation high-speed vehicle.
文摘Spectral conjugate gradient method is an algorithm obtained by combination of spectral gradient method and conjugate gradient method,which is characterized with global convergence and simplicity of spectral gradient method,and small storage of conjugate gradient method.Besides,the spectral conjugate gradient method was proved that the search direction at each iteration is a descent direction of objective function even without relying on any line search method.Spectral conjugate gradient method is applied to full waveform inversion for numerical tests on Marmousi model.The authors give a comparison on numerical results obtained by steepest descent method,conjugate gradient method and spectral conjugate gradient method,which shows that the spectral conjugate gradient method is superior to the other two methods.
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sponsored by the National Nature Science Foundation of China(Nos.41174114 and 41274128)
文摘In order to obtain stable interval Q factor, by analyzing the spectrum of monitoring wavelet and down-going wavelet of zero-offset VSP data and referring the spectrum expression of Ricker wavelet, we propose a new expression of source wavelet spectrum. Basing on the new expression, we present improved amplitude spectral fitting and spectral ratio methods for interval Q inversion based on zero-offset VSP data, and the sequence for processing the zero-offset VSP data. Subsequently, we apply the proposed methods to real zero-offset VSP data, and carry out prestack inverse Q filtering to zero-offset VSP data and surface seismic data for amplitude compensation with the estimated Q value.
文摘In this study,we focused on a novel parallel mechanism for utilizing the motion simulator of a high-speed boat(HSB).First,we expressed the real behavior of the HSB based on a seakeeping trial.For this purpose,we recorded the motion parameters of the HSB by gyroscope and accelerometer sensors,while using a special data acquisition technique.Additionally,a Chebychev highpass filter was applied as a noise filter to the accelerometer sensor.Then,a novel 3 degrees of freedom(DoF)parallel mechanism(1T2R)with prismatic actuators is proposed and analyses were performed on its inverse kinematics,velocity,and acceleration.Finally,the inverse dynamic analysis is presented by the principle of virtual work,and the validation of the analytical equations was compared by the ADAMS simulation software package.Additionally,according to the recorded experimental data of the HSB,the feasibility of the proposed novel parallel mechanism motion simulator of the HSB,as well as the necessity of using of the washout filters,was explored.
基金financially supported by the National Key R&D Program of China(2018YFA0702504)the Fundamental Research Funds for the Central Universities(2462019QNXZ03)+2 种基金the Scientific Research and Technology Development Project of China National Petroleum Corporation(2017D-3504)the Major Scientific Research Program of Petrochina Science and Technology Management Department"Comprehensive Seismic Prediction Technology and Software Development of Natural Gas"(2019B-0607)the National Science and Technology Major Project(2017ZX05005-004)。
文摘An important application of spectral decomposition(SD)is to identify subsurface geological anomalies such as channels and karst caves,which may be buried in full-band seismic data.However,the classical SD methods including the wavelet transform(WT)are often limited by relatively low time-frequency resolution,which is responsible for false high horizonassociated space resolution probably indicating more geological structures,especially when close geological anomalies exist.To address this issue,we impose a constraint of minimizing an lp(0<p<1)norm of time-frequency spectral coefficients on the misfit derived by using the inverse WT and apply the generalized iterated shrinkage algorithm to invert for the optimal coefficients.Compared with the WT and inverse SD(ISD)using a typical l1-norm constraint,the modified ISD(MISD)using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features.We design a 3 D synthetic dataset involving frequency-close thin geological anomalies and the other3 D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD.The application of 4 D spectrum on a 3 D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.
基金Under the auspices of the Key Program of National Natural Science Foundation of China(No.50339010)Huaihe Valley Open Fund Projects(No.Hx2007)
文摘Research on quantitative models of suspended sediment concentration (SSC) using remote sensing technology is very important to understand the scouting and siltation variation in harbors and water channels. Based onlaboratory study of the relationship between different suspended sediment concentrations and reflectance spectra measured synchronously, quantitative inversion models of SSC based on single factor, band ratio and sediment parameter were developed, which provides an effective method to retrieve the SSC from satellite images. Results show that the bl (430-500nm) and b3 (670-735nm) are the optimal wavelengths for the estimation of lower SSC and the b4 (780-835nm) is the optimal wavelength to estimate the higher SSC. Furthermore the band ratio B2/B3 can be used to simulate the variation of lower SSC better and the B4/B1 to estimate the higher SSC accurately. Also the inversion models developed by sediment parameters of higher and lower SSCs can get a relatively higher accuracy than the single factor and band ratio models.
文摘If an operator is not invertible, we are interested if there is a subspace such that the reduction of the operator to that subspace is invertible. In this paper we give a spectral approach to generalized inverses considering the subspace determined by the range of the spectral projection associated with an operator and a spectral set containing the point 0. We compare the cases, 0 is a simple pole of the resolvent function, 0 is a pole of order n of the resolvent function, 0 is an isolated point of the spectrum, and 0 is contained in a circularly isolated spectral set.