Analytical model test of methods to find the geometry and velocity of magnetic structures
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摘要
It is important to determine the dimensionality and velocity information in the study of spatial magnetic structures. Many data analysis theories/techniques are based on the assumption of one or two dimensions. For example, the Grad-Shafranov(GS)reconstruction method assumes a dimensionality of two or less. The Minimum Direction Derivative(MDD) method provides an indication of the dimensionality. For the structure velocity, the components in each dimensionality can be calculated by SpatioTemporal Difference analysis(STD). In order to improve the convenience of use of MDD method, a new parameter Dm quantifying the dimensionality based on MDD eigenvalues is introduced in this paper. The influences of noise/turbulence,separation distance and tetrahedron configuration on MDD and the evaluation of Dmare systematically tested using two analytical models for magnetic structures, representing a magnetic mirror and magnetic flux rope. We tested and gave the threshold values of three quality indicators for MDD results using the flux rope model. We also show that the error induced by turbulence is comparable to that of random noise when the turbulence scales are less than the spacecraft separation. Besides, the accuracy of STD velocity estimation will also be influenced by turbulence for cases with excessively high data time resolution.By using Dm, we show that an ideal model of a mirror-like structure can be divided into one dimension(1-D) and three dimension(3-D) regions. This restricts the applicability of the GS method in mirror-like structures. For example, in a given reconstruction range, the GS error increased from less than 7% to more than 15% by using the data along trajectories in 1-D and 3-D regions as predicated by Dm. Thus, it is important to estimate the structure dimensionality, which can be further used to estimate the reliability of the GS reconstruction map.
It is important to determine the dimensionality and velocity information in the study of spatial magnetic structures. Many data analysis theories/techniques are based on the assumption of one or two dimensions. For example, the Grad-Shafranov(GS)reconstruction method assumes a dimensionality of two or less. The Minimum Direction Derivative(MDD) method provides an indication of the dimensionality. For the structure velocity, the components in each dimensionality can be calculated by SpatioTemporal Difference analysis(STD). In order to improve the convenience of use of MDD method, a new parameter Dm quantifying the dimensionality based on MDD eigenvalues is introduced in this paper. The influences of noise/turbulence,separation distance and tetrahedron configuration on MDD and the evaluation of Dmare systematically tested using two analytical models for magnetic structures, representing a magnetic mirror and magnetic flux rope. We tested and gave the threshold values of three quality indicators for MDD results using the flux rope model. We also show that the error induced by turbulence is comparable to that of random noise when the turbulence scales are less than the spacecraft separation. Besides, the accuracy of STD velocity estimation will also be influenced by turbulence for cases with excessively high data time resolution.By using Dm, we show that an ideal model of a mirror-like structure can be divided into one dimension(1-D) and three dimension(3-D) regions. This restricts the applicability of the GS method in mirror-like structures. For example, in a given reconstruction range, the GS error increased from less than 7% to more than 15% by using the data along trajectories in 1-D and 3-D regions as predicated by Dm. Thus, it is important to estimate the structure dimensionality, which can be further used to estimate the reliability of the GS reconstruction map.
It is important to determine the dimensionality and velocity information in the study of spatial magnetic structures. Many data analysis theories/techniques are based on the assumption of one or two dimensions. For example, the Grad-Shafranov(GS)reconstruction method assumes a dimensionality of two or less. The Minimum Direction Derivative(MDD) method provides an indication of the dimensionality. For the structure velocity, the components in each dimensionality can be calculated by SpatioTemporal Difference analysis(STD). In order to improve the convenience of use of MDD method, a new parameter Dm quantifying the dimensionality based on MDD eigenvalues is introduced in this paper. The influences of noise/turbulence,separation distance and tetrahedron configuration on MDD and the evaluation of Dmare systematically tested using two analytical models for magnetic structures, representing a magnetic mirror and magnetic flux rope. We tested and gave the threshold values of three quality indicators for MDD results using the flux rope model. We also show that the error induced by turbulence is comparable to that of random noise when the turbulence scales are less than the spacecraft separation. Besides, the accuracy of STD velocity estimation will also be influenced by turbulence for cases with excessively high data time resolution.By using Dm, we show that an ideal model of a mirror-like structure can be divided into one dimension(1-D) and three dimension(3-D) regions. This restricts the applicability of the GS method in mirror-like structures. For example, in a given reconstruction range, the GS error increased from less than 7% to more than 15% by using the data along trajectories in 1-D and 3-D regions as predicated by Dm. Thus, it is important to estimate the structure dimensionality, which can be further used to estimate the reliability of the GS reconstruction map.
引文
1 Russell C T,Mellott M M,Smith E J,et al.Multiple spacecraft observations of interplanetary shocks:Four Spacecraft determination of shock normals.J Geophys Res,1983,88:4739-4748
2 Schwartz Steven J.Shock and discontinuity normals,mach numbers,and related parameters.In:Analysis Methods for Multi Spacecraft Data.edited by:Paschmann G Daly P W,eds.Noordwijk:European Space Agency(ESA)Communications,1998.249-270
3 Haaland S E,Sonnerup B U?,Dunlop M W,et al.Four-spacecraft determination of magnetopause orientation,motion and thickness:Comparison with results from single-spacecraft methods.Ann Geophys,2004,22:1347-1365
4 Sonnerup B U?,Haaland S E,Paschmann G.Discontinuity orientation,motion,and thickness.In:Multi-Spacecraft Analysis Methods Revisited.Paschmann G,Daly P,eds.Noordwijk:European Space Agency(ESA)Communications,2008.1-15
5 Hau L N,Sonnerup B U?.Two-dimensional coherent structures in the magnetopause:Recovery of static equilibria from single-spacecraft data.J Geophys Res,1999,104:6899-6917
6 Hu Q.Reconstruction of magnetic clouds in the solar wind:Orientations and configurations.J Geophys Res,2002,107:1142
7 Hasegawa H,Nakamura R,Fujimoto M,et al.Reconstruction of a bipolar magnetic signature in an earthward jet in the tail:Flux rope or3D guide-field reconnection?J Geophys Res,2007,112:A11206
8 Sonnerup B U?,Scheible M.Minimum and maximum variance analysis.In:Analysis Methods for Multi-spacecraft Data.Paschmann G,Daly P,eds.ISSI/ESA,Netherlands,1998.185-220
9 Zhou X Z,Pu Z Y,Zong Q G,et al.On the error estimation of multispacecraft timing method.Ann Geophys,2009,27:3949-3955
10 Sonnerup B U?.Orientation and motion of two-dimensional structures in a space plasma.J Geophys Res,2005,110:A06208
11 Sonnerup B U?,Hasegawa H,Teh W L,et al.Grad-Shafranov reconstruction:An overview.J Geophys Res,2006,111:A09204
12 Tian A M,Zong Q G,Wang Y F,et al.A series of plasma flow vortices in the tail plasma sheet associated with solar wind pressure enhancement.J Geophys Res,2010,115:A09204
13 Tian A M,Shi Q Q,Zong Q G,et al.Analysis of magnetotail flux rope events by ARTEMIS observations.Sci China Technol Sci,2014,57:1010-1019
14 Sonnerup B U?,Guo M.Magnetopause transects.Geophys Res Lett,1996,23:3679-3682
15 Escoubet C P,Schmidt R,Goldstein M L.Cluster-science and mission overview.Space Sci Rev,1997,79:11-32
16 Burch J L,Moore T E,Torbert R B,et al.Magnetospheric Multiscale overview and science objectives.Space Sci Rev,2016,199:5-21
17 Shi Q Q,Shen C,Pu Z Y,et al.Dimensional analysis of observed structures using multipoint magnetic field measurements:Application to Cluster.Geophys Res Lett,2005,32:L12105
18 Pu Z Y,Zong Q G,Fritz T A,et al.Multipule flux rope events at the high-latitude magnetopause:Cluster/rapid observation on January 26,2001.In:The Magnetospheric Cusps:Structure and Dynamics.Fritz TA,Fung S F,eds.Dordrecht:Springer,Netherlands,2005.191-212
19 Shi Q Q,Shen C,Dunlop M W,et al.Motion of observed structures calculated from multi-point magnetic field measurements:Application to cluster.Geophys Res Lett,2006,33:L08109
20 Shi Q Q,Pu Z Y,Soucek J,et al.Spatial structures of magnetic depression in the Earth’s high-altitude cusp:Cluster multipoint observations.J Geophys Res,2009,114:A10202
21 Shi Q Q,Zong Q G,Zhang H,et al.Cluster observations of the entry layer equatorward of the cusp under northward interplanetary magnetic field.J Geophys Res,2009,114:A12219
22 Yao S T,Shi Q Q,Li Z Y,et al.Propagation of small size magnetic holes in the magnetospheric plasma sheet.J Geophys Res Space Phys,2016,121:5510-5519
23 Yao S T,Shi Q Q,Guo R L,et al.Magnetospheric multiscale observations of electron scale magnetic peak.Geophys Res Lett,2018,45:527-537
24 Hasegawa H,Sonnerup B U?,Denton R E,et al.Reconstruction of the electron diffusion region observed by the Magnetospheric Multiscale spacecraft:First results.Geophys Res Lett,2017,44:4566-4574
25 Hasegawa H,Sonnerup B U?,Klecker B,et al.Optimal reconstruction of magnetopause structures from cluster data.Ann Geophys,2005,23:973-982
26 Hasegawa H,Sonnerup B U?,Owen C J,et al.The structure of flux transfer events recovered from cluster data.Ann Geophys,2006,24:603-618
27 Zhou X Z,Zong Q G,Pu Z Y,et al.Multiple triangulation analysis:Another approach to determine the orientation of magnetic flux ropes.Ann Geophys,2006,24:1759-1765
28 Zhou X Z,Zong Q G,Wang J,et al.Multiple triangulation analysis:Application to determine the velocity of 2-D structures.Ann Geophys,2006,24:3173-3177
29 Denton R E,Sonnerup B U?,Birn J,et al.Test of methods to infer the magnetic reconnection geometry from spacecraft data.J Geophys Res,2010,115:A10242
30 Denton R E,Sonnerup B U?,Swisdak M,et al.Test of Shi et al.method to infer the magnetic reconnection geometry from spacecraft data:MHD simulation with guide field and antiparallel kinetic simulation.J Geophys Res,2012,117:A09201
31 Russell C T,Anderson B J,Baumjohann W,et al.The Magnetospheric Multiscale magnetometers.Space Sci Rev,2016,199:189-256
32 Huang S Y,Zhou M,Sahraoui F,et al.Observations of turbulence within reconnection jet in the presence of guide field.Geophys Res Lett,2012,39:L11104
33 Tao X.A numerical study of chorus generation and the related variation of wave intensity using the DAWN code.J Geophys Res Space Phys,2014,119:3362-3372
34 Xiao C J,Pu Z Y,Ma Z W,et al.Inferring of flux rope orientation with the minimum variance analysis technique.J Geophys Res,2004,109:A11218
35 Robert P,Dunlop M W,Roux A,et al.Accuracy of Current Density Determination.In:Analysis Methods for Multi Spacecraft Data.Paschmann G,Daly P W,eds.Noordwijk:European Space Agency(ESA)Communications,1998.395-418
36 Fu H S,Vaivads A,Khotyaintsev Y V,et al.How to find magnetic nulls and reconstruct field topology with MMS data?J Geophys Res Space Phys,2015,120:3758-3782
37 Olshevsky V,Divin A,Eriksson E,et al.Energy dissipation in magnetic null points at kinetic scales.Astrophys J,2015,807:155
38 Dunlop M W,Southwood D J,Glassmeier K H,et al.Analysis of multipoint magnetometer data.Adv Space Res,1988,8:273-277
39 Huang S Y,Sahraoui F,Retino A,et al.MMS observations of ionscale magnetic island in the magnetosheath plasma.Geophys Res Lett,2016,43:7850-7858
2 Schwartz Steven J.Shock and discontinuity normals,mach numbers,and related parameters.In:Analysis Methods for Multi Spacecraft Data.edited by:Paschmann G Daly P W,eds.Noordwijk:European Space Agency(ESA)Communications,1998.249-270
3 Haaland S E,Sonnerup B U?,Dunlop M W,et al.Four-spacecraft determination of magnetopause orientation,motion and thickness:Comparison with results from single-spacecraft methods.Ann Geophys,2004,22:1347-1365
4 Sonnerup B U?,Haaland S E,Paschmann G.Discontinuity orientation,motion,and thickness.In:Multi-Spacecraft Analysis Methods Revisited.Paschmann G,Daly P,eds.Noordwijk:European Space Agency(ESA)Communications,2008.1-15
5 Hau L N,Sonnerup B U?.Two-dimensional coherent structures in the magnetopause:Recovery of static equilibria from single-spacecraft data.J Geophys Res,1999,104:6899-6917
6 Hu Q.Reconstruction of magnetic clouds in the solar wind:Orientations and configurations.J Geophys Res,2002,107:1142
7 Hasegawa H,Nakamura R,Fujimoto M,et al.Reconstruction of a bipolar magnetic signature in an earthward jet in the tail:Flux rope or3D guide-field reconnection?J Geophys Res,2007,112:A11206
8 Sonnerup B U?,Scheible M.Minimum and maximum variance analysis.In:Analysis Methods for Multi-spacecraft Data.Paschmann G,Daly P,eds.ISSI/ESA,Netherlands,1998.185-220
9 Zhou X Z,Pu Z Y,Zong Q G,et al.On the error estimation of multispacecraft timing method.Ann Geophys,2009,27:3949-3955
10 Sonnerup B U?.Orientation and motion of two-dimensional structures in a space plasma.J Geophys Res,2005,110:A06208
11 Sonnerup B U?,Hasegawa H,Teh W L,et al.Grad-Shafranov reconstruction:An overview.J Geophys Res,2006,111:A09204
12 Tian A M,Zong Q G,Wang Y F,et al.A series of plasma flow vortices in the tail plasma sheet associated with solar wind pressure enhancement.J Geophys Res,2010,115:A09204
13 Tian A M,Shi Q Q,Zong Q G,et al.Analysis of magnetotail flux rope events by ARTEMIS observations.Sci China Technol Sci,2014,57:1010-1019
14 Sonnerup B U?,Guo M.Magnetopause transects.Geophys Res Lett,1996,23:3679-3682
15 Escoubet C P,Schmidt R,Goldstein M L.Cluster-science and mission overview.Space Sci Rev,1997,79:11-32
16 Burch J L,Moore T E,Torbert R B,et al.Magnetospheric Multiscale overview and science objectives.Space Sci Rev,2016,199:5-21
17 Shi Q Q,Shen C,Pu Z Y,et al.Dimensional analysis of observed structures using multipoint magnetic field measurements:Application to Cluster.Geophys Res Lett,2005,32:L12105
18 Pu Z Y,Zong Q G,Fritz T A,et al.Multipule flux rope events at the high-latitude magnetopause:Cluster/rapid observation on January 26,2001.In:The Magnetospheric Cusps:Structure and Dynamics.Fritz TA,Fung S F,eds.Dordrecht:Springer,Netherlands,2005.191-212
19 Shi Q Q,Shen C,Dunlop M W,et al.Motion of observed structures calculated from multi-point magnetic field measurements:Application to cluster.Geophys Res Lett,2006,33:L08109
20 Shi Q Q,Pu Z Y,Soucek J,et al.Spatial structures of magnetic depression in the Earth’s high-altitude cusp:Cluster multipoint observations.J Geophys Res,2009,114:A10202
21 Shi Q Q,Zong Q G,Zhang H,et al.Cluster observations of the entry layer equatorward of the cusp under northward interplanetary magnetic field.J Geophys Res,2009,114:A12219
22 Yao S T,Shi Q Q,Li Z Y,et al.Propagation of small size magnetic holes in the magnetospheric plasma sheet.J Geophys Res Space Phys,2016,121:5510-5519
23 Yao S T,Shi Q Q,Guo R L,et al.Magnetospheric multiscale observations of electron scale magnetic peak.Geophys Res Lett,2018,45:527-537
24 Hasegawa H,Sonnerup B U?,Denton R E,et al.Reconstruction of the electron diffusion region observed by the Magnetospheric Multiscale spacecraft:First results.Geophys Res Lett,2017,44:4566-4574
25 Hasegawa H,Sonnerup B U?,Klecker B,et al.Optimal reconstruction of magnetopause structures from cluster data.Ann Geophys,2005,23:973-982
26 Hasegawa H,Sonnerup B U?,Owen C J,et al.The structure of flux transfer events recovered from cluster data.Ann Geophys,2006,24:603-618
27 Zhou X Z,Zong Q G,Pu Z Y,et al.Multiple triangulation analysis:Another approach to determine the orientation of magnetic flux ropes.Ann Geophys,2006,24:1759-1765
28 Zhou X Z,Zong Q G,Wang J,et al.Multiple triangulation analysis:Application to determine the velocity of 2-D structures.Ann Geophys,2006,24:3173-3177
29 Denton R E,Sonnerup B U?,Birn J,et al.Test of methods to infer the magnetic reconnection geometry from spacecraft data.J Geophys Res,2010,115:A10242
30 Denton R E,Sonnerup B U?,Swisdak M,et al.Test of Shi et al.method to infer the magnetic reconnection geometry from spacecraft data:MHD simulation with guide field and antiparallel kinetic simulation.J Geophys Res,2012,117:A09201
31 Russell C T,Anderson B J,Baumjohann W,et al.The Magnetospheric Multiscale magnetometers.Space Sci Rev,2016,199:189-256
32 Huang S Y,Zhou M,Sahraoui F,et al.Observations of turbulence within reconnection jet in the presence of guide field.Geophys Res Lett,2012,39:L11104
33 Tao X.A numerical study of chorus generation and the related variation of wave intensity using the DAWN code.J Geophys Res Space Phys,2014,119:3362-3372
34 Xiao C J,Pu Z Y,Ma Z W,et al.Inferring of flux rope orientation with the minimum variance analysis technique.J Geophys Res,2004,109:A11218
35 Robert P,Dunlop M W,Roux A,et al.Accuracy of Current Density Determination.In:Analysis Methods for Multi Spacecraft Data.Paschmann G,Daly P W,eds.Noordwijk:European Space Agency(ESA)Communications,1998.395-418
36 Fu H S,Vaivads A,Khotyaintsev Y V,et al.How to find magnetic nulls and reconstruct field topology with MMS data?J Geophys Res Space Phys,2015,120:3758-3782
37 Olshevsky V,Divin A,Eriksson E,et al.Energy dissipation in magnetic null points at kinetic scales.Astrophys J,2015,807:155
38 Dunlop M W,Southwood D J,Glassmeier K H,et al.Analysis of multipoint magnetometer data.Adv Space Res,1988,8:273-277
39 Huang S Y,Sahraoui F,Retino A,et al.MMS observations of ionscale magnetic island in the magnetosheath plasma.Geophys Res Lett,2016,43:7850-7858