With the 2008 Ms6.1 Panzhihua earthquake as a case study, we demonstrate that the focal depth of the main shock can be well constrained with two approaches: (1) using the depth phase sPL and (2) using full wavefo...With the 2008 Ms6.1 Panzhihua earthquake as a case study, we demonstrate that the focal depth of the main shock can be well constrained with two approaches: (1) using the depth phase sPL and (2) using full waveform inversion of local and teleseismic data. We also show that focal depths can be well constrained using the depth phase sPL with single broadband seismic station. Our study indicates that the main shock is located at a depth of ii kin, much shallower than those from other studies, confirming that the earthquake occurs in upper crust. Aftershocks are located in the depth range of 11 16 kin, which is consistent with a ruptured near vertical fault whose width is about 10 km, as expected for an Ms6.1 earthquake.展开更多
We use interferometric synthetic aperture radar (InSAR) and broadband seismic waveform data to estimate a source model of the 11th July, 2004 M W 6.2 Zhongba earthquake, Tibet of China. This event occurred within th...We use interferometric synthetic aperture radar (InSAR) and broadband seismic waveform data to estimate a source model of the 11th July, 2004 M W 6.2 Zhongba earthquake, Tibet of China. This event occurred within the seismically active zone of southwestern Tibetan Plateau where the east-west extension of the upper crust is observed. Because of limitations in one pair of InSAR data available, there are trade-offs among centroid depth, rupture area and amount of slip. Available seismic data tightly constrain the focal mechanism and centroid depth of the earthquake but not the horizontal location. Together, two complementary data sets can be used to identify the actual fault plane, better constrain the slip model and event location. We first use regional seismic waveform to estimate point source mechanism, then InSAR data is used to obtain better location. Finally, a joint inversion of teleseismic P-waves and InSAR data is performed to obtain a distributed model. Our preferred point source mechanism indicates a seismic moment of ~2.2×10 18 N·m (~M W 6.2), a fault plane solution of 171° (342 ° )/42 ° (48 ° )/-83 ° (-97 ° ), corresponding to strike/dip/rake, and a depth of 11 km. The fault plane with strike of 171 ? and dip of 42° is identified as the ruptured fault with the aid of InSAR data. The preferred source model features compact area of slips between depth of 5–11 km and 10 km along strike with maximum slip amplitude of about 1.5 m.展开更多
The long-term reclamation-induced ground subsidence in Macao, a coastal city of southern China was investigated. Persistent scatterer interferometry (PSI) technique was applied to retrieve the deformation rate in Maca...The long-term reclamation-induced ground subsidence in Macao, a coastal city of southern China was investigated. Persistent scatterer interferometry (PSI) technique was applied to retrieve the deformation rate in Macao during the period from April 2003 to August 2010 with a total of 41 scenes of descending ASAR data sets. The PSI-retrieved results show a relatively stable pattern in Macao Peninsula, Taipa Island and Coloane Island, with an average subsidence velocity of -3 mm/a. In contrast, relatively large subsidence rates are highlighted in Cotai area, a new reclamation land in 1990s, in which an average subsidence velocity is about -10 mm/a. A consistent relationship between the PSI results and the leveling measurements indicate that this PSI technique is an effective tool to monitor the reclamation-induced ground subsidence with a high accuracy and adequate spatial details. Accordingly, the valuable ground subsidence results generated by PSI can be used not only for early detection and remedial activities of potential settlement of building, but also for helping the local government to formulate regional sustainable development planning and decision-making in disaster prevention and mitigation.展开更多
By using 11 global ocean tide models and tidal gauge data obtained in the East China Sea and South China Sea, the influence of the ocean loading on gravity field in China and its neighbor area is calculated in this pa...By using 11 global ocean tide models and tidal gauge data obtained in the East China Sea and South China Sea, the influence of the ocean loading on gravity field in China and its neighbor area is calculated in this paper. Furthermore, the differences between the results from original global models and modified models with local tides are discussed based on above calculation. The comparison shows that the differences at the position near the sea are so large that the local tides must be taken into account in the calculation. When the global ocean tide models of CSR4.0, FES02, GOT00, NAO99 and ORI96 are chosen, the local effect for M2 is less than 0.10 × 10-8 m·s-2 over the area far away from sea. And the local effect for O1 is less than 0.05 × 10-8 m·s-2 over that area when choosing AG95 or CSR3.0 models. This numerical result demonstrates that the choice of model is a complex problem because of the inconsistent accuracy of the models over the areas of East and South China Seas.展开更多
Geodesy is among the oldest branches of Earth science with historical record of geodesy study by Thales of Miletus more than 2000 years. Originally geodesy was defined as the science of measuring and portraying of the...Geodesy is among the oldest branches of Earth science with historical record of geodesy study by Thales of Miletus more than 2000 years. Originally geodesy was defined as the science of measuring and portraying of the Earth's surface, i.e., assuming that the Earth is展开更多
In this paper we give a review of several previously published papers on anomalous tremors observed before the 2008 Ms8.0 Weuchuan earthquake. Based on the observed time and frequency shifts between coastal and inland...In this paper we give a review of several previously published papers on anomalous tremors observed before the 2008 Ms8.0 Weuchuan earthquake. Based on the observed time and frequency shifts between coastal and inland stations, we discussed some methods to distinguish different kinds of microseisms, and speculated that a pre-earthquake typhoon might have caused a "mainland-originated microseism" which in turn trig- gered the earthquake.展开更多
Estimated Green’s function (EGF) between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical der...Estimated Green’s function (EGF) between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical derivations assuming diffusive wave field, equi-partition of modes or random sources on an enclosed surface. This method provides a new approach to study the crust and mantle structure at regional scale, continental scale and global scale. Following the achievements with seismometer records, the records of infrasonic station, hydrophone and microphone were also used to obtain the EGFs of different wave fields. Since superconducting gravimeter is a better long period instrument than regular seismometer, EGF at longer period is expected to be obtained with the cross correlation of gravity data. In this paper, we will show the EGFs extracted by cross-correlations between the superconducting gravimeters and the seismometers. Both the travel times and dispersion curves obtained from different data types are consistent. The result shows that it is possible to retrieve the deep structure by the cross correlation of gravity data.展开更多
The uppermost mantle is the key area for exchange of heat flux and material convection between the crust and lithospheric mantle. Spatial variations of lithospheric thinning and dynamic processes in the North China Cr...The uppermost mantle is the key area for exchange of heat flux and material convection between the crust and lithospheric mantle. Spatial variations of lithospheric thinning and dynamic processes in the North China Craton could inevitably induce the velocity heterogeneity in the uppermost mantle.In this study,we used Pn arrivals from permanent seismic stations in North China and surrounding regions to construct a tomographic image of the North China Craton.The tomographic method with Pn travel time difference data were used to study the velocity variations in the uppermost mantle.Pn velocities in the uppermost mantle varied significantly in the Eastern,Central and Western blocks of the North China Craton.This suggests that the lithosphere beneath different blocks of the North China Craton have experienced distinct tectonic evolutions and dynamic processes since the Paleo- zoic.The current uppermost mantle has been imprinted by these tectonic and dynamic processes.Fast Pn velocities are prominent beneath the Bohai Bay Basin in the Eastern Block of the North China Craton,suggesting residuals of the Archean lithospheric mantle.Beneath the Tanlu Fault Zone and Bohai Sea,slow Pn velocities are present in the uppermost mantle,which can be attributed to significant lithospheric thinning and asthenospheric upwelling.The newly formed lithospheric mantle beneath Yanshan Mountain may be the dominant reason for the existence of slow Pn velocities in this region.Conversely,the ancient lower crust and lithospheric mantle already have been delaminated.In the Central Block,significant slow Pn velocities are present in Taihangshan Mountain,which also extends northward to the Yinchuan-Hetao Rift on the northern margin of the Ordos Block and Yinshan Orogen.This characteristic probably is a result of hot asthenospheric upwelling along the active tectonic boundary on the margin of the Western Block.The protracted thermal erosion and underplating of hot asthenospheric upwelling may induce lithospheric thinning and significant slow velocities in the uppermost mantle.Fast velocities beneath the Western Block suggest that the thick,cold and refractory Archean lithospheric keel of craton still is retained without apparent destruction.展开更多
As a deepening and extension of Theory of Unified Representation of Gravitational Field^([1]), this paper covers two aspects as follows: in theory, we go into the fundamental structure of the internal problem and put ...As a deepening and extension of Theory of Unified Representation of Gravitational Field^([1]), this paper covers two aspects as follows: in theory, we go into the fundamental structure of the internal problem and put emphasis on seeking the solution of the disturbing potential in spectral domain and establishing a spectral structure form of anomalous density; and in application, according to the given form we try to take a look at the distribution charateristics of anomalous densities of lithosphere about 30—40 km deep in the continent of China in illustration of evaluating practical trustworthiness of the present theory. Calculations done here are based on earth gravity model DQM84D^([2]) and show that this theory seems to be convincing.展开更多
On May 12,2008,a magnitude 7.9 earthquake ruptured the Longmenshan fault system in Sichuan Province,China,collapsing buildings and killing tens of thousands people.As predicted,aftershocks may last for at least one ye...On May 12,2008,a magnitude 7.9 earthquake ruptured the Longmenshan fault system in Sichuan Province,China,collapsing buildings and killing tens of thousands people.As predicted,aftershocks may last for at least one year,and moreover,large aftershocks are likely to occur.Therefore,it is critical to outline the areas with potential aftershocks before reconstruction and resettling people as to avoid future disasters.It is demonstrated that the redistribution of stress induced by an earthquake should trigger successive seismic activity.Based on static stress triggering theory,we calculated the coseismic stress changes on major faults induced by the Wenchuan earthquake,with elastic dislocation the-ory and the multilayered crustal model.We also discuss the stress distribution and its significance for future seismic activity under the impact of the Wenchuan earthquake.It is shown that coulomb failure stress(CFS) increases obviously on the Daofu-Kangding segment of the Xianshuihe Fault,the Maqu and Nanping segment of the Eastern Kunlun Fault,the Qingchuan Fault,southern segment of the Min-jiang Fault,Pengxian-Guanxian Fault,Jiangyou-Guangyuan Fault,and Jiangyou-Guanxian Fault.The increased stress raises the probability of earthquake occurrence on these faults.Since these areas are highly populated,earthquake monitoring and early disaster alarm system are needed.CFS increases with a magnitude of 0.03―0.06 MPa on the Qingchuan Fault,which is close to the northern end of the rapture of Wenchuan earthquake.The occurrence of some strong aftershocks,including three events with magnitude higher than 5.0,indicates that the seismic activities have been triggered by the main shock.Aftershocks seem to migrate northwards.Since the CFS change on the Lueyang-Mianxian Fault located on the NEE of the Qingchuan Fault is rather small(±0.01 MPa),the migration of aftershocks might be terminated in the area near Hanzhong City.The CFS change on the western Qinling Fault is around 10 Pa,and the impact of static triggering can be neglected.The increment of CFS on the Pengxian-Guanxian Fault and Beichuan-Yingxiu Fault southwest to the main rupture is 0.005―0.015 MPa,which would facilitate earthquake triggering in these areas.Very few aftershocks in these areas indicate that the accumulated stress has not been released sufficiently.High seismic risk is predicated in these areas due to coseismic CFS loading.The Wenchuan earthquake released the accumulated CFS on the Fubianhe Fault,the Huya Fault,the Ha'nan-Qingshanwan Fault,and the Diebu-Bailongjiang Fault.The decrement of CFS changes on the Longquanshan Fault east to Chengdu City is about 0.002 MPa.The seismic activity will be depressed by decrement of CFS on these faults.展开更多
A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathe...A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.展开更多
The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step o...The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.展开更多
基金financial supported by Joint Seismological Science Foundation of China (No.200808078)National Natural Science Foundation of China (Nos.40821160549 and 41074032)
文摘With the 2008 Ms6.1 Panzhihua earthquake as a case study, we demonstrate that the focal depth of the main shock can be well constrained with two approaches: (1) using the depth phase sPL and (2) using full waveform inversion of local and teleseismic data. We also show that focal depths can be well constrained using the depth phase sPL with single broadband seismic station. Our study indicates that the main shock is located at a depth of ii kin, much shallower than those from other studies, confirming that the earthquake occurs in upper crust. Aftershocks are located in the depth range of 11 16 kin, which is consistent with a ruptured near vertical fault whose width is about 10 km, as expected for an Ms6.1 earthquake.
基金study was supported jointly by National Natural Science Foundation of China (Nos.40821160549 and 41074032)CAS Knowledge Innovation Program (No. KZCX2-YW-116-1)Joint Seismological Science Fundation of China(Nos.200808078 and 200708035)
文摘We use interferometric synthetic aperture radar (InSAR) and broadband seismic waveform data to estimate a source model of the 11th July, 2004 M W 6.2 Zhongba earthquake, Tibet of China. This event occurred within the seismically active zone of southwestern Tibetan Plateau where the east-west extension of the upper crust is observed. Because of limitations in one pair of InSAR data available, there are trade-offs among centroid depth, rupture area and amount of slip. Available seismic data tightly constrain the focal mechanism and centroid depth of the earthquake but not the horizontal location. Together, two complementary data sets can be used to identify the actual fault plane, better constrain the slip model and event location. We first use regional seismic waveform to estimate point source mechanism, then InSAR data is used to obtain better location. Finally, a joint inversion of teleseismic P-waves and InSAR data is performed to obtain a distributed model. Our preferred point source mechanism indicates a seismic moment of ~2.2×10 18 N·m (~M W 6.2), a fault plane solution of 171° (342 ° )/42 ° (48 ° )/-83 ° (-97 ° ), corresponding to strike/dip/rake, and a depth of 11 km. The fault plane with strike of 171 ? and dip of 42° is identified as the ruptured fault with the aid of InSAR data. The preferred source model features compact area of slips between depth of 5–11 km and 10 km along strike with maximum slip amplitude of about 1.5 m.
基金Projects(41204012, 41274026, 41274024, 40825012, 41021003, 41174016) supported by the National Natural Science Foundation of China
文摘The long-term reclamation-induced ground subsidence in Macao, a coastal city of southern China was investigated. Persistent scatterer interferometry (PSI) technique was applied to retrieve the deformation rate in Macao during the period from April 2003 to August 2010 with a total of 41 scenes of descending ASAR data sets. The PSI-retrieved results show a relatively stable pattern in Macao Peninsula, Taipa Island and Coloane Island, with an average subsidence velocity of -3 mm/a. In contrast, relatively large subsidence rates are highlighted in Cotai area, a new reclamation land in 1990s, in which an average subsidence velocity is about -10 mm/a. A consistent relationship between the PSI results and the leveling measurements indicate that this PSI technique is an effective tool to monitor the reclamation-induced ground subsidence with a high accuracy and adequate spatial details. Accordingly, the valuable ground subsidence results generated by PSI can be used not only for early detection and remedial activities of potential settlement of building, but also for helping the local government to formulate regional sustainable development planning and decision-making in disaster prevention and mitigation.
基金The Key Knowledge Innovation Project (KZCX3-SW-131), the Hundred Talents Program of Chinese Academy of Sciences and the National Natural Science Foundation of China (40374029)
文摘By using 11 global ocean tide models and tidal gauge data obtained in the East China Sea and South China Sea, the influence of the ocean loading on gravity field in China and its neighbor area is calculated in this paper. Furthermore, the differences between the results from original global models and modified models with local tides are discussed based on above calculation. The comparison shows that the differences at the position near the sea are so large that the local tides must be taken into account in the calculation. When the global ocean tide models of CSR4.0, FES02, GOT00, NAO99 and ORI96 are chosen, the local effect for M2 is less than 0.10 × 10-8 m·s-2 over the area far away from sea. And the local effect for O1 is less than 0.05 × 10-8 m·s-2 over that area when choosing AG95 or CSR3.0 models. This numerical result demonstrates that the choice of model is a complex problem because of the inconsistent accuracy of the models over the areas of East and South China Seas.
文摘Geodesy is among the oldest branches of Earth science with historical record of geodesy study by Thales of Miletus more than 2000 years. Originally geodesy was defined as the science of measuring and portraying of the Earth's surface, i.e., assuming that the Earth is
基金supported by the National Natural Science Foundation of China(90814009)Quality Control’s Special Funds for Scientific Researchon Public Causes(10-215)National Key Technology Research and Development Program(2008BAC35B05)
文摘In this paper we give a review of several previously published papers on anomalous tremors observed before the 2008 Ms8.0 Weuchuan earthquake. Based on the observed time and frequency shifts between coastal and inland stations, we discussed some methods to distinguish different kinds of microseisms, and speculated that a pre-earthquake typhoon might have caused a "mainland-originated microseism" which in turn trig- gered the earthquake.
基金supported jointly by Chinese Academy of Sciences Fund (No. KZCX-YW-116-1)Joint Seismological Science Foundation of China (Nos. 20080818 and 200708035)
文摘Estimated Green’s function (EGF) between stations has been extracted from ambient seismic noise, direct surface wave and coda waves. It is also confirmed by laboratory experiments on ultrasonics and theoretical derivations assuming diffusive wave field, equi-partition of modes or random sources on an enclosed surface. This method provides a new approach to study the crust and mantle structure at regional scale, continental scale and global scale. Following the achievements with seismometer records, the records of infrasonic station, hydrophone and microphone were also used to obtain the EGFs of different wave fields. Since superconducting gravimeter is a better long period instrument than regular seismometer, EGF at longer period is expected to be obtained with the cross correlation of gravity data. In this paper, we will show the EGFs extracted by cross-correlations between the superconducting gravimeters and the seismometers. Both the travel times and dispersion curves obtained from different data types are consistent. The result shows that it is possible to retrieve the deep structure by the cross correlation of gravity data.
基金supported by the National Natural ScienceFoundation of China (90814011)Open Fund of Key Laboratory of Geodetection (China University of Geosciences, Beijing),Ministry of Education (GDL0905)+1 种基金Fund of China Geological Survey (GZH200900504)the China Postdoctoral Science Foundation (20090460511)
文摘The uppermost mantle is the key area for exchange of heat flux and material convection between the crust and lithospheric mantle. Spatial variations of lithospheric thinning and dynamic processes in the North China Craton could inevitably induce the velocity heterogeneity in the uppermost mantle.In this study,we used Pn arrivals from permanent seismic stations in North China and surrounding regions to construct a tomographic image of the North China Craton.The tomographic method with Pn travel time difference data were used to study the velocity variations in the uppermost mantle.Pn velocities in the uppermost mantle varied significantly in the Eastern,Central and Western blocks of the North China Craton.This suggests that the lithosphere beneath different blocks of the North China Craton have experienced distinct tectonic evolutions and dynamic processes since the Paleo- zoic.The current uppermost mantle has been imprinted by these tectonic and dynamic processes.Fast Pn velocities are prominent beneath the Bohai Bay Basin in the Eastern Block of the North China Craton,suggesting residuals of the Archean lithospheric mantle.Beneath the Tanlu Fault Zone and Bohai Sea,slow Pn velocities are present in the uppermost mantle,which can be attributed to significant lithospheric thinning and asthenospheric upwelling.The newly formed lithospheric mantle beneath Yanshan Mountain may be the dominant reason for the existence of slow Pn velocities in this region.Conversely,the ancient lower crust and lithospheric mantle already have been delaminated.In the Central Block,significant slow Pn velocities are present in Taihangshan Mountain,which also extends northward to the Yinchuan-Hetao Rift on the northern margin of the Ordos Block and Yinshan Orogen.This characteristic probably is a result of hot asthenospheric upwelling along the active tectonic boundary on the margin of the Western Block.The protracted thermal erosion and underplating of hot asthenospheric upwelling may induce lithospheric thinning and significant slow velocities in the uppermost mantle.Fast velocities beneath the Western Block suggest that the thick,cold and refractory Archean lithospheric keel of craton still is retained without apparent destruction.
基金Project supported by National Natural Science foundation of China
文摘As a deepening and extension of Theory of Unified Representation of Gravitational Field^([1]), this paper covers two aspects as follows: in theory, we go into the fundamental structure of the internal problem and put emphasis on seeking the solution of the disturbing potential in spectral domain and establishing a spectral structure form of anomalous density; and in application, according to the given form we try to take a look at the distribution charateristics of anomalous densities of lithosphere about 30—40 km deep in the continent of China in illustration of evaluating practical trustworthiness of the present theory. Calculations done here are based on earth gravity model DQM84D^([2]) and show that this theory seems to be convincing.
基金Supported by Knowledge Innovation Program of Chinese Academy of Sciences (Grant No. KZCX-SW-153)National Natural Science Foundation of China (Grant Nos. 40574011 and 40474028)
文摘On May 12,2008,a magnitude 7.9 earthquake ruptured the Longmenshan fault system in Sichuan Province,China,collapsing buildings and killing tens of thousands people.As predicted,aftershocks may last for at least one year,and moreover,large aftershocks are likely to occur.Therefore,it is critical to outline the areas with potential aftershocks before reconstruction and resettling people as to avoid future disasters.It is demonstrated that the redistribution of stress induced by an earthquake should trigger successive seismic activity.Based on static stress triggering theory,we calculated the coseismic stress changes on major faults induced by the Wenchuan earthquake,with elastic dislocation the-ory and the multilayered crustal model.We also discuss the stress distribution and its significance for future seismic activity under the impact of the Wenchuan earthquake.It is shown that coulomb failure stress(CFS) increases obviously on the Daofu-Kangding segment of the Xianshuihe Fault,the Maqu and Nanping segment of the Eastern Kunlun Fault,the Qingchuan Fault,southern segment of the Min-jiang Fault,Pengxian-Guanxian Fault,Jiangyou-Guangyuan Fault,and Jiangyou-Guanxian Fault.The increased stress raises the probability of earthquake occurrence on these faults.Since these areas are highly populated,earthquake monitoring and early disaster alarm system are needed.CFS increases with a magnitude of 0.03―0.06 MPa on the Qingchuan Fault,which is close to the northern end of the rapture of Wenchuan earthquake.The occurrence of some strong aftershocks,including three events with magnitude higher than 5.0,indicates that the seismic activities have been triggered by the main shock.Aftershocks seem to migrate northwards.Since the CFS change on the Lueyang-Mianxian Fault located on the NEE of the Qingchuan Fault is rather small(±0.01 MPa),the migration of aftershocks might be terminated in the area near Hanzhong City.The CFS change on the western Qinling Fault is around 10 Pa,and the impact of static triggering can be neglected.The increment of CFS on the Pengxian-Guanxian Fault and Beichuan-Yingxiu Fault southwest to the main rupture is 0.005―0.015 MPa,which would facilitate earthquake triggering in these areas.Very few aftershocks in these areas indicate that the accumulated stress has not been released sufficiently.High seismic risk is predicated in these areas due to coseismic CFS loading.The Wenchuan earthquake released the accumulated CFS on the Fubianhe Fault,the Huya Fault,the Ha'nan-Qingshanwan Fault,and the Diebu-Bailongjiang Fault.The decrement of CFS changes on the Longquanshan Fault east to Chengdu City is about 0.002 MPa.The seismic activity will be depressed by decrement of CFS on these faults.
基金Project supported by the National Natural Science Foundation of China.
文摘A higher step of study on the GOBVPs (geodetic overdetermined boundary value problems) is reached in this paper, which covers the proposal of new concept of pseudo-solutionon the GOBVPs, its strict definition of mathematics and solving principle. The so-called pseudosolution is a harmonical function having the property of optimum approximating the given boundary values in the sense of a relevant norm. Analytical expressions of the pseudo-solutions of two typical OBVPs for biboundary surfaces in physical geodesy, the problems S—D and S—N, are obtained, which is elegant and concise in form and convenient for practice, by using the derived formulas of norms of fractional exponential Sobolev's spaces in the case of spherical biboundary. The pseudo-solution is composed of two parts: the major is the solution of classical Stokes' problem, playing control role in field representation; the minor is correction term, serving the function of synergist and precision of the gravity field. Besides, a general case of the GOBVP is also dealt with.
基金Project supported by the National Natural Science Foundaion of China.
文摘The properly-posedness of the nonlinear fixed gravimetric boundary value problem is shown with the help of nonlinear functional analysis and a new iterative method to solve the problem is also given, where each step of the iterative program is reduced to solving one and the same kind of oblique derivative boundary value problem with the same type. Furthermore, the convergence of the iterative program is proved with Schauder estimate of elliptic differential equation.