Choosing appropriate background field data is crucial for gravity field matching navigation.Current research mainly uses gravity anomaly data or gravity gradient data as background fields.However,using gravity gradien...Choosing appropriate background field data is crucial for gravity field matching navigation.Current research mainly uses gravity anomaly data or gravity gradient data as background fields.However,using gravity gradient invariants in existing research is seldom a concern.The gravity gradient tensor has three invariants,named as I_(1),I_(2)and I_(3).I_(1) is a Laplace operator outside the Earth and a Poison operator inside the Earth.The focus of this study is to discuss the performance of the other two invariants of gravity gradients in matching navigation based on the Iterative Closest Contour Point(ICCP)algorithm and compare the matching results with that of the gravity gradient Tzz.The results show that they have almost the same performance when there is no noise,and the background data noises have a large impact on the matching results.There are differences in the anti-interference ability of observation noises for the different components.Under the same random noises in the observations,I2performs a little better than the other two components in terms of position error standard deviation.According to the investigations,since attitude errors can not be avoided and influence the positioning based on Tzz,we recommend adopting invariants of gravity gradients,especially I2,for matching navigation in actual cases.展开更多
The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mappin...The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.展开更多
In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are...In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high- frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.展开更多
We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are...We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ＂Y＂ type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.展开更多
In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance grav...In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance gravity anomalies and gravity gradient tensors. We discuss the effect of Gaussian white noise on the improved small sub-domain filtering method, as well as analyze the effect of window size on geological body edge recognition at different extension directions. Model experiments show that the improved small sub-domain filtering method is less affected by noise, filter window size, and geological body edge direction so it can more accurately depict geological body edges than the conventional small sub-domain filtering method. It also shows that deeply buried body edges can be well delineated through increasing the filter window size. In application, the enhanced gravity anomalies and calculated gravity gradient tensors of the Hulin basin show that the improved small sub-domain filtering can recognize more horizontal fault locations than the conventional method.展开更多
We developed a three-dimensional（3D） conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotel...We developed a three-dimensional（3D） conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion,synthetic data were inverted using the 3D conjugate gradient inversion,and the inversion results were compared and analyzed.The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in inversions to obtain better inversion results when there are no enough data sites to recover the target resistivity structure.These examples show that lots of information about 3D structure is also contained in the diagonal components;as a result,diagonal components should be in-cluded in 3D inversions.The inversion algorithm was also used to invert the impedance tensor data ac-quired in the Kayabe area in Japan.Inversions with the synthetic and real data demonstrated the va-lidity and practicability of the inversion algorithm.展开更多
Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tens...Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object（2.44 Am^2@1 kHz） can be increased from（0.45 m, 0.75 m）,（0？, 25？） to（0.30 m, 0.80 m）,（0？,80？）, respectively.展开更多
We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much ...We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.展开更多
Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the mag...Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the magnetic gradient tensor is not easily interfered from the tilting magnetization,but it can infer the range of the fi eld source more accurately.However,the analytic signal strength decays faster with depth,making it diffi cult to identify deep fi eld sources.Balanced-boundary recognition can eff ectively overcome this disadvantage.We present here a balanced-boundary identifi cation technique based on the normalization of three-directional analytic signals from aeromagnetic gradient tensor data.This method can eff ectively prevent the fast attenuation of analytic signals.We also derive an Euler inversion algorithm of three-directional analytic signal derivative.By combining magnetic-anomaly model testing with the traditional magnetic anomaly interpretation method,we show that the boundary-recognition technology based on a magnetic gradient tensor analytic signal has a greater advantage in identifying the boundaries of the geological body and can better refl ect shallow anomalies.The characteristics of the Euler equation based on the magnetic anomaly direction to resolve the signal derivative have better convergence,and the obtained solution is more concentrated,which can obtain the depth and horizontal range information of the geological body more accurately.Applying the above method to the measured magneticanomaly gradient data from Baoding area,more accurate fi eld source information is obtained,which shows the feasibility of applying this method to geological interpretations.展开更多
Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy f...Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on(1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and(2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.展开更多
The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations...The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.展开更多
Diffusion tensor imaging (DTI) is mainly applied to white matter fiber tracking in human brain, but there is still a debate on how many diffusion gradient directions should be used to get the best results. In this pap...Diffusion tensor imaging (DTI) is mainly applied to white matter fiber tracking in human brain, but there is still a debate on how many diffusion gradient directions should be used to get the best results. In this paper, the performance of 7 protocols corresponding to 6, 9, 12, 15, 20, 25, and 30 noncollinear number of diffusion gradi-ent directions (NDGD) were discussed by com-paring signal-noise ratio (SNR) of tensor- de-rived measurement maps and fractional ani-sotropy (FA) values. All DTI data (eight healthy volunteers) were downloaded from the website of Johns Hopkins Medical Institute Laboratory of Brain Anatomi-cal MRI with permission. FA, apparent diffusion constant mean (ADC-mean), the largest eigen-value (LEV), and eigenvector orientation (EVO) maps associated with LEV of all subjects were calculated derived from tensor in the 7 proto-cols via DTI Studio. A method to estimate the variance was presented to calculate SNR of these tensor-derived maps. Mean ±standard deviation of the SNR and FA values within re-gion of interest (ROI) selected in the white mat-ter were compared among the 7 protocols. The SNR were improved significantly with NDGD increasing from 6 to 20 (P<0.05). From 20 to 30, SNR were improved significantly for LEV and EVO maps (P<0.05), but no significant dif-ferences for FA and ADC-mean maps (P>0.05). There were no significant variances in FA val-ues within ROI between any two protocols (P>0.05). The SNR could be improved with NDGD in-creasing, but an optimum protocol is needed because of clinical limitations.展开更多
Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we dire...Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.展开更多
Full tensor magnetic gradient measurements are available nowadays. These are essential for determining magnetization parameters in deep layers. Using full or partial tensor magnetic gradient measurements to determine ...Full tensor magnetic gradient measurements are available nowadays. These are essential for determining magnetization parameters in deep layers. Using full or partial tensor magnetic gradient measurements to determine the subsurface properties, e.g., magnetic susceptibility, is an inverse problem. Inversion using total magnetic intensity data is a traditional way.Because of di culty in obtaining the practical full tensor magnetic gradient data, the corresponding inversion results are not so widely reported. With the development of superconducting quantum interference devices(SQUIDs), we can acquire the full tensor magnetic gradient data through field measurements. In this paper, we study the inverse problem of retrieving magnetic susceptibility with the field data using our designed low-temperature SQUIDs. The solving methodology based on sparse regularization and an alternating directions method of multipliers is established. Numerical and field data experiments are performed to show the feasibility of our algorithm.展开更多
Airborne gravity gradient data contain additional short-wavelength information about the buried geological bodies.This study develops a fast interpretation method based on the gravity gradient data for the sources’sp...Airborne gravity gradient data contain additional short-wavelength information about the buried geological bodies.This study develops a fast interpretation method based on the gravity gradient data for the sources’spatial location and physical property parameters.This study analyzes the advantages of the source parameter inversion method based on tensor invariants.It proposes a normalized fast-imaging method based on tensor invariants to quickly estimate the spatial location parameters of sources through the local maximum value position of the imaging results.First,the tensor invariant characteristics and the imaging method’s effect in a simple model are analyzed using a theoretical model.Second,to analyze the imaging method’s application effect in complex model conditions,the method’s applicability is quantitatively analyzed using the data added with noise,superimposed anomalies of adjacent sources,and anomalies of deep and shallow geological bodies.The theoretical model’s simulation results show that the model’s imaging results in this study have satisfactory performance on the spatial position estimation of the sources.Finally,the method is applied to the gravity anomaly data corresponding to the Humble salt dome.The imaging results can effectively estimate the distribution of the salt dome’s horizontal and depths,verifying the practicability of the method.展开更多
We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations b...We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations between calculated and observed data. We also use the depth weighting function based on the eigenvector of gravity gradient tensor to eliminate undesired effects owing to the fast attenuation of the position function. Model data suggest that the extrapolated Tikhonov regularization in conjunction with the depth weighting function can effectively recover the 3D distribution of density anomalies. We conduct density inversion of gravity gradient data from the Australia Kauring test site and compare the inversion results with the published research results. The proposed inversion method can be used to obtain the 3D density distribution of underground anomalies.展开更多
基金funded by the Key Laboratory of Smart Earth(No.KF2023YB01-12)the National Natural Science Foundation of China(No.42074017)+1 种基金the Key Laboratory Fund Project for Simulation of Complex Electronic Systems(614201004022210)the Chinese Academy of Sciences Youth Innovation Promotion Association(2022126)。
文摘Choosing appropriate background field data is crucial for gravity field matching navigation.Current research mainly uses gravity anomaly data or gravity gradient data as background fields.However,using gravity gradient invariants in existing research is seldom a concern.The gravity gradient tensor has three invariants,named as I_(1),I_(2)and I_(3).I_(1) is a Laplace operator outside the Earth and a Poison operator inside the Earth.The focus of this study is to discuss the performance of the other two invariants of gravity gradients in matching navigation based on the Iterative Closest Contour Point(ICCP)algorithm and compare the matching results with that of the gravity gradient Tzz.The results show that they have almost the same performance when there is no noise,and the background data noises have a large impact on the matching results.There are differences in the anti-interference ability of observation noises for the different components.Under the same random noises in the observations,I2performs a little better than the other two components in terms of position error standard deviation.According to the investigations,since attitude errors can not be avoided and influence the positioning based on Tzz,we recommend adopting invariants of gravity gradients,especially I2,for matching navigation in actual cases.
基金supported by the National High Technology Research and Development Program of China(863 Program)(No.2013AA063901 and No.2006AA06A201)
文摘The full magnetic gradient tensor （MGT） refers to the spatial change rate of the three field components of the geomagnetic field vector along three mutually orthogonal axes. The tensor is of use to geological mapping, resources exploration, magnetic navigation, and others. However, it is very difficult to measure the full magnetic tensor gradient using existing engineering technology. We present a method to use triaxial aeromagnetic gradient measurements for deriving the full MGT. The method uses the triaxial gradient data and makes full use of the variation of the magnetic anomaly modulus in three dimensions to obtain a self-consistent magnetic tensor gradient. Numerical simulations show that the full MGT data obtained with the proposed method are of high precision and satisfy the requirements of data processing. We selected triaxial aeromagnetic gradient data from the Hebei Province for calculating the full MGT. Data processing shows that using triaxial tensor gradient data allows to take advantage of the spatial rate of change of the total field in three dimensions and suppresses part of the independent noise in the aeromagnetic gradient. The calculated tensor components have improved resolution, and the transformed full tensor gradient satisfies the requirement of geological mapping and interpretation.
基金financially supported by the SinoProbe-09-01(201011078)
文摘In oil and mineral exploration, gravity gradient tensor data include higher- frequency signals than gravity data, which can be used to delineate small-scale anomalies. However, full-tensor gradiometry （FTG） data are contaminated by high-frequency random noise. The separation of noise from high-frequency signals is one of the most challenging tasks in processing of gravity gradient tensor data. We first derive the Cartesian equations of gravity gradient tensors under the constraint of the Laplace equation and the expression for the gravitational potential, and then we use the Cartesian equations to fit the measured gradient tensor data by using optimal linear inversion and remove the noise from the measured data. Based on model tests, we confirm that not only this method removes the high- frequency random noise but also enhances the weak anomaly signals masked by the noise. Compared with traditional low-pass filtering methods, this method avoids removing noise by sacrificing resolution. Finally, we apply our method to real gravity gradient tensor data acquired by Bell Geospace for the Vinton Dome at the Texas-Louisiana border.
基金supported by the Scientific Research Starting Foundation of HoHai University,China(2084/40801136)the Fundamental Research Funds for the Central Universities(No.2009B12514)
文摘We present a method to calculate the full gravity gradient tensors from pre-existing vertical gravity data using the cosine transform technique and discuss the calculated tensor accuracy when the gravity anomalies are contaminated by noise. Gravity gradient tensors computation on 2D infinite horizontal cylinder and 3D ＂Y＂ type dyke models show that the results computed with the DCT technique are more accurate than the FFT technique regardless if the gravity anomalies are contaminated by noise or not. The DCT precision has increased 2 to 3 times from the standard deviation. In application, the gravity gradient tensors of the Hulin basin calculated by DCT and FFT show that the two results are consistent with each other. However, the DCT results are smoother than results computed with FFT. This shows that the proposed method is less affected by noise and can better reflect the fault distribution.
基金supported by the Scientific Research Starting Foundation of HoHai University, China (No. 2084/40801136)the Fundamental Research Funds for the Central Universities (No.2009B12514).
文摘In order to enhance geological body boundary visual effects in images and improve interpretation accuracy using gravity and magnetic field data, we propose an improved small sub-domain filtering method to enhance gravity anomalies and gravity gradient tensors. We discuss the effect of Gaussian white noise on the improved small sub-domain filtering method, as well as analyze the effect of window size on geological body edge recognition at different extension directions. Model experiments show that the improved small sub-domain filtering method is less affected by noise, filter window size, and geological body edge direction so it can more accurately depict geological body edges than the conventional small sub-domain filtering method. It also shows that deeply buried body edges can be well delineated through increasing the filter window size. In application, the enhanced gravity anomalies and calculated gravity gradient tensors of the Hulin basin show that the improved small sub-domain filtering can recognize more horizontal fault locations than the conventional method.
基金supported by the National Natural Science Foundation of China (Nos. 40774029, 41004028)the Special Fund for Basic Scientific Research of Central Colleges (No. 2010ZY53)the Program for New Century Excellent Talents in University (NCET)
文摘We developed a three-dimensional（3D） conjugate gradient inversion algorithm for in-verting magnetotelluric impedance tensor measurements.In order to show the importance of including diagonal components of magnetotelluric impedance tensor in 3D inversion,synthetic data were inverted using the 3D conjugate gradient inversion,and the inversion results were compared and analyzed.The results from the 3D inversion of synthetic data indicate that both the off-diagonal and the diagonal components are required in inversions to obtain better inversion results when there are no enough data sites to recover the target resistivity structure.These examples show that lots of information about 3D structure is also contained in the diagonal components;as a result,diagonal components should be in-cluded in 3D inversions.The inversion algorithm was also used to invert the impedance tensor data ac-quired in the Kayabe area in Japan.Inversions with the synthetic and real data demonstrated the va-lidity and practicability of the inversion algorithm.
基金supported by the National Natural Science Foundation of China(61473023)
文摘Magnetic field gradient tensor measurement is an important technique to obtain position information of magnetic objects. When using magnetic field sensors to measure magnetic field gradient as the coefficients of tensor, field differentiation is generally approximated by field difference. As a result, magnetic objects positioning by magnetic field gradient tensor measurement always involves an inherent error caused by sensor sizes, leading to a reduction in detectable distance and detectable angle. In this paper, the inherent positioning error caused by magnetic field gradient tensor measurement is calculated and corrected by iterations based on the systematic position error distribution patterns. The results show that, the detectable distance range and the angle range of an ac magnetic object（2.44 Am^2@1 kHz） can be increased from（0.45 m, 0.75 m）,（0？, 25？） to（0.30 m, 0.80 m）,（0？,80？）, respectively.
基金supported by National Natural Science Foundation of China(11301191)supported by MOST(MOST107-2115-M-110-007-MY2)
文摘We show that closed shrinking gradient Ricci solitons with positive Ricci curvature and sufficiently pinched Weyl tensor are Einstein. When Weyl tensor vanishes, this has been proved before but our proof here is much simpler.
基金supported by the National Key R&D Program of China (No. 2017YFC0602204)。
文摘Compared to conventional magnetic data,magnetic gradient tensor data contain more high-frequency signal components,which can better describe the features of geological bodies.The directional analytic signal of the magnetic gradient tensor is not easily interfered from the tilting magnetization,but it can infer the range of the fi eld source more accurately.However,the analytic signal strength decays faster with depth,making it diffi cult to identify deep fi eld sources.Balanced-boundary recognition can eff ectively overcome this disadvantage.We present here a balanced-boundary identifi cation technique based on the normalization of three-directional analytic signals from aeromagnetic gradient tensor data.This method can eff ectively prevent the fast attenuation of analytic signals.We also derive an Euler inversion algorithm of three-directional analytic signal derivative.By combining magnetic-anomaly model testing with the traditional magnetic anomaly interpretation method,we show that the boundary-recognition technology based on a magnetic gradient tensor analytic signal has a greater advantage in identifying the boundaries of the geological body and can better refl ect shallow anomalies.The characteristics of the Euler equation based on the magnetic anomaly direction to resolve the signal derivative have better convergence,and the obtained solution is more concentrated,which can obtain the depth and horizontal range information of the geological body more accurately.Applying the above method to the measured magneticanomaly gradient data from Baoding area,more accurate fi eld source information is obtained,which shows the feasibility of applying this method to geological interpretations.
基金supported by the National Special Plan for the 13th Five-Year Plan of China(No.2017YFC0602204-10)Independent Exploration of the Innovation Project for Graduate Students at Central South University(No.2017zzts176)+3 种基金National Natural Science Foundation of China(Nos.41574127,41404106,and 41674075)Postdoctoral Fund Projects of China(No.2017M622608)National Key R&D Program of China(No.2018YFC0603602)Natural Science Youth Fund Project of the Hunan Province,China(No.2018JJ3642)
文摘Magnetic field gradient tensor technique provides abundant data for delicate inversion of subsurface magnetic susceptibility distribution. Large scale magnetic data inversion imaging requires high speed and accuracy for forward modeling. For arbitrarily distributed susceptibility data on an undulated surface, we propose a fast 3D forward modeling method in the wavenumber domain based on(1) the wavenumber-domain expression of the prism combination model and the Gauss–FFT algorithm and(2) cubic spline interpolation. We apply the proposed 3D forward modeling method to synthetic data and use weighting coefficients in the wavenumber domain to improve the modeling for multiple observation surfaces, and also demonstrate the accuracy and efficiency of the proposed method.
基金Project supported by the National Natural Science Foundation of China(Nos.11872186 and11272126)the Fundamental Research Funds for the Central Universities(No.HUST:2016JCTD114)
文摘The definitions of the third-order elastic,piezoelectric,and dielectric constants and the properties of the associated tensors are discussed.Based on the energy conservation and coordinate transformation,the relations among the third-order constants are obtained.Furthermore,the relations among the third-order elastic,piezoelectric,and dielectric constants of the seven crystal systems and isotropic materials are listed in detail.These third-order constants relations play an important role in solving nonlinear problems of elastic and piezoelectric materials.It is further found that all third-order piezoelectric constants are 0 for 15 kinds of point groups,while all third-order dielectric constants are 0 for 16 kinds of point groups as well as isotropic material.The reason is that some of the point groups are centrally symmetric,and the other point groups are high symmetry.These results provide the foundation to measure these constants,to choose material,and to research nonlinear problems.Moreover,these results are helpful not only for the study of nonlinear elastic and piezoelectric problems,but also for the research on flexoelectric effects and size effects.
文摘Diffusion tensor imaging (DTI) is mainly applied to white matter fiber tracking in human brain, but there is still a debate on how many diffusion gradient directions should be used to get the best results. In this paper, the performance of 7 protocols corresponding to 6, 9, 12, 15, 20, 25, and 30 noncollinear number of diffusion gradi-ent directions (NDGD) were discussed by com-paring signal-noise ratio (SNR) of tensor- de-rived measurement maps and fractional ani-sotropy (FA) values. All DTI data (eight healthy volunteers) were downloaded from the website of Johns Hopkins Medical Institute Laboratory of Brain Anatomi-cal MRI with permission. FA, apparent diffusion constant mean (ADC-mean), the largest eigen-value (LEV), and eigenvector orientation (EVO) maps associated with LEV of all subjects were calculated derived from tensor in the 7 proto-cols via DTI Studio. A method to estimate the variance was presented to calculate SNR of these tensor-derived maps. Mean ±standard deviation of the SNR and FA values within re-gion of interest (ROI) selected in the white mat-ter were compared among the 7 protocols. The SNR were improved significantly with NDGD increasing from 6 to 20 (P<0.05). From 20 to 30, SNR were improved significantly for LEV and EVO maps (P<0.05), but no significant dif-ferences for FA and ADC-mean maps (P>0.05). There were no significant variances in FA val-ues within ROI between any two protocols (P>0.05). The SNR could be improved with NDGD in-creasing, but an optimum protocol is needed because of clinical limitations.
基金supported by the National Natural Science Foundation of China (Grant No. 10872060)the Fundamental Research Funds for the Central Universities (Grant No. HIT.BRET2.2010008)
文摘Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.
基金supported by National Natural Science Foundation of China(Grant Nos.91630202,41611530693&1181101259)R&D of Key Instruments and Technologies for Deep Resources Prospecting(Grant No.ZDYZ2012-1-02-04)+1 种基金National Key R&D Program(Grant No.2018YFC0603500)Russian Foundation for Basic Research(Grant No.17-51-53002)
文摘Full tensor magnetic gradient measurements are available nowadays. These are essential for determining magnetization parameters in deep layers. Using full or partial tensor magnetic gradient measurements to determine the subsurface properties, e.g., magnetic susceptibility, is an inverse problem. Inversion using total magnetic intensity data is a traditional way.Because of di culty in obtaining the practical full tensor magnetic gradient data, the corresponding inversion results are not so widely reported. With the development of superconducting quantum interference devices(SQUIDs), we can acquire the full tensor magnetic gradient data through field measurements. In this paper, we study the inverse problem of retrieving magnetic susceptibility with the field data using our designed low-temperature SQUIDs. The solving methodology based on sparse regularization and an alternating directions method of multipliers is established. Numerical and field data experiments are performed to show the feasibility of our algorithm.
基金supported by the National Key R&D Program of China(No.2020YFE0201300)Natural Science Foundation of Jilin Province(No.20210508033RQ)Fundamental Research Funds for the Central Universities and Geological Survey Project(No.DD20190129).
文摘Airborne gravity gradient data contain additional short-wavelength information about the buried geological bodies.This study develops a fast interpretation method based on the gravity gradient data for the sources’spatial location and physical property parameters.This study analyzes the advantages of the source parameter inversion method based on tensor invariants.It proposes a normalized fast-imaging method based on tensor invariants to quickly estimate the spatial location parameters of sources through the local maximum value position of the imaging results.First,the tensor invariant characteristics and the imaging method’s effect in a simple model are analyzed using a theoretical model.Second,to analyze the imaging method’s application effect in complex model conditions,the method’s applicability is quantitatively analyzed using the data added with noise,superimposed anomalies of adjacent sources,and anomalies of deep and shallow geological bodies.The theoretical model’s simulation results show that the model’s imaging results in this study have satisfactory performance on the spatial position estimation of the sources.Finally,the method is applied to the gravity anomaly data corresponding to the Humble salt dome.The imaging results can effectively estimate the distribution of the salt dome’s horizontal and depths,verifying the practicability of the method.
基金supported by National major special equipment development(No.2011YQ120045)The National Natural Science Fund(No.41074050 and 41304023)
文摘We use the extrapolated Tikhonov regularization to deal with the ill-posed problem of 3D density inversion of gravity gradient data. The use of regularization parameters in the proposed method reduces the deviations between calculated and observed data. We also use the depth weighting function based on the eigenvector of gravity gradient tensor to eliminate undesired effects owing to the fast attenuation of the position function. Model data suggest that the extrapolated Tikhonov regularization in conjunction with the depth weighting function can effectively recover the 3D distribution of density anomalies. We conduct density inversion of gravity gradient data from the Australia Kauring test site and compare the inversion results with the published research results. The proposed inversion method can be used to obtain the 3D density distribution of underground anomalies.
