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Boundary-Value Problems for Gravimetric Determination of a Precise Geoid 1998 ed. [Pehme köide]

  • Formaat: Paperback / softback, 228 pages, kõrgus x laius: 235x155 mm, kaal: 379 g, 6 Illustrations, black and white; XII, 228 p. 6 illus., 1 Paperback / softback
  • Sari: Lecture Notes in Earth Sciences 73
  • Ilmumisaeg: 20-Aug-1998
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540644628
  • ISBN-13: 9783540644620
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Boundary-Value Problems for Gravimetric Determination of a Precise Geoid 1998 ed.Suurem pilt
  • Formaat: Paperback / softback, 228 pages, kõrgus x laius: 235x155 mm, kaal: 379 g, 6 Illustrations, black and white; XII, 228 p. 6 illus., 1 Paperback / softback
  • Sari: Lecture Notes in Earth Sciences 73
  • Ilmumisaeg: 20-Aug-1998
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540644628
  • ISBN-13: 9783540644620
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783540644620.html
Märksõnad:
This book offers a simultaneous treatment of the theory and numerical application of boundary-value problems related to the determination of a precise geoid from gravimetric data. The following subjects are discussed: topographical effects and their computations in precise gravimetric geoid determination, the downward continuation of a harmonic function, Stokes' problem formulated on an ellipsoid of revolution, spherical Stokes' problem with ellipsoidal corrections involved in boundary conditions for an anomalous potential, and the altimetry-gravimetry boundary-value problem. The answer to a number of scientific problems, raised and discussed in geodetic literature over the past years, can be found here. The book is intended for scientists and advanced graduate students.

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List of symbols
ix(3)
Acknowledgements xii
Introduction 1(5)
1 The Stokes two-boundary-value problem for geoid determination
6(22)
1.1 Formulation of the boundary-value problem
6(1)
1.2 Compensation of topographical masses
7(2)
1.3 Anomalous potential
9(1)
1.4 Bruns's formula
10(1)
1.5 Linearization of the boundary condition
11(2)
1.6 The first-degree spherical harmonics
13(2)
1.7 Numerical investigations
15(8)
1.7.1 An example: constant height
16(3)
1.7.2 Axisymmetric geometry
19(4)
1.8 Different approximations leading to the fundamental equation of physical geodesy
23(3)
1.9 Conclusion
26(2)
2 The Zeroth-and first-degree spherical harmonics in the Helmert 2nd condensation technique
28(6)
2.1 Principle of mass conservation
28(3)
2.2 Principle of mass-center conservation
31(1)
2.3 Conclusion
32(2)
3 Topographical effects
34(16)
3.1 Approximations used for DeltaV
34(1)
3.2 A weak singularity of the Newton kernel
35(2)
3.3 The Pratt-Hayford and the Airy-Heiskanen isostatic compensation models
37(2)
3.4 Helmert's condensation layer
39(1)
3.5 The direct topographical effect on gravity
40(2)
3.6 The primary indirect topographical effect on potential
42(2)
3.7 The secondary indirect topographical effect on gravity
44(1)
3.8 Analytical expressions for integration kernels of Newton's type
44(2)
3.8.1 The singularity of the kernel L(-1)(r,Psi,r') at the point Psi=0
45(1)
3.9 Numerical tests
46(4)
4 Planar approximation
50(6)
4.1 Constant density of topographical masses
50(1)
4.2 Restricted integration
51(1)
4.3 Planar approximation of distances
51(2)
4.4 The difference between spherical and planar approximation of topographical effects
53(1)
4.5 Conclusion
54(2)
5 Taylor series expansion of the Newton kernel
56(16)
5.1 The problem of the convergence of Taylor series expansion
57(2)
5.2 The Taylor expansion of the terrain roughness term
59(1)
5.3 Numerical computations
60(4)
5.3.1 The Taylor kernels Ki
60(2)
5.3.2 The primary indirect topographical effect on potential
62(2)
5.4 Conclusion
64(1)
A.5 Integration kernels Mi(r,Psi,R)
65(7)
A.5.1 Spectral form
65(1)
A.5.2 Recurrence formula
66(1)
A.5.3 Spatial form
66(1)
A.5.4 Singularity at the point Psi=0
67(1)
A.5.5 Angular integrals
68(1)
A.5.6 Proofs of eqns.(A.5.11) and (A.5.12)
69(3)
6 The effect of anomalous density of topographical masses
72(12)
6.1 Topographical effects
73(1)
6.2 One particular example: a lake
74(3)
6.3 Numerical results for the lake Superior
77(3)
6.4 Another example: the Purcell Mountains
80(2)
6.5 conclusion
82(2)
7 Formulation of the Stokes two-boundary-value problem with a higher-degree reference field
84(15)
7.1 A higher-degree reference gravitational potential
85(2)
7.2 Reference gravity anomaly
87(1)
7.3 Formulation of the two-boundary-value problem
88(3)
7.4 Numerical results for V(t,i)(jm) - V(t,e)(jm)
91(4)
7.5 Conclusion
95(1)
A.7 Spherical harmonic representation of PsiV
96(3)
8 A discrete downward continuation problem for geoid determination
99(33)
8.1 Formulation of the boundary-value problem
102(1)
8.2 Poisson's integral
103(2)
8.3 A continuous downward continuation problem
105(1)
8.4 Discretization
106(2)
8.5 Jacobi's iterations
108(1)
8.6 Numerical tests
109(14)
8.6.1 Analysis of conditionality
109(5)
8.6.2 Analysis of convergency
114(2)
8.6.3 Power spectrum analysis of gravity anomalies
116(1)
8.6.4 Downward continuation of gravity anomalies
117(6)
8.7 Conclusion
123(2)
A.8 Spherical radius of the near-zone integration cap
125(1)
B.8 Poisson's integration over near- and far-zones
126(6)
B.8.1 Near-zone contribution
127(2)
B.8.2 Truncation coefficients
129(2)
B.8.3 Far-zone contribution
131(1)
B.8.4 Summary
131(1)
9 The Stokes boundary-value problem on an ellipsoid of revoluation
132(23)
9.1 Formulation of the boundary-value problem
133(2)
9.2 The zero-degree harmonic of T
135(1)
9.3 Solution on the reference ellipsoid of revolution
136(1)
9.4 The derivative of teh Legendre function of the 2nd kind
137(1)
9.5 The uniqueness of the solution
138(1)
9.6 The approximation up to O(e2\0)
139(3)
9.7 The ellipsoidal Stokes function
142(1)
9.8 Spatial forms of functions Ki(cos X)
143(4)
9.9 Conclusion
147(1)
A.9 Power series expansion of the Legendre functions
148(2)
B.9 Sum of the series (9.49)
150(5)
10 The external Dirichlet boundary-value problem for the Laplace equation on an ellipsoid of revolution
155(15)
10.1 Formulation of the boundary-value problem
156(1)
10.2 Power series representation of the integral kernel
157(3)
10.3 The approximation up to 0 (e 2/0)
160(2)
10.4 The ellipsoidal Poisson kernel
162(2)
10.5 Residuals R(i)(t, x)
164(2)
10.6 The behaviour at the singularity
166(1)
10.7 Conclusion
167(1)
A.10 Some sums of infinite series of Legendre polynomials
168(1)
B.10 Program KERL
169(1)
11 The Stokes boundary-value problem with ellipsoidal corrections in boundary condition
170(22)
11.1 Formulation of the boundary-value problem
172(2)
11.2 The 0 (e 2/0) -approximation
174(3)
11.3 The 'spherical-ellipsoidal' Stokes function
177(2)
11.4 Spatial forms of functions Mi(cos Psi)
179(4)
11.5 Conclusion
183(1)
A.11 Spectral form of ellipsoidal corrections
183(2)
B.11 an approximate solution to tridiagonal system of equations
185(1)
C.11 Different forms of the addition theorem for spherical harmonics
186(6)
12 The least-squares solution to the discrete altimetry-gravimetry boundary-value problem for determination of the global gravity model
192(18)
12.1 Formulation of the boundary-value problem
194(3)
12.2 Parametrization and discretization
197(1)
12.3 A least-squares estimation
198(1)
12.4 The axisymmetric geometry
199(6)
12.5 Overdetermination
205(2)
12.6 Numerical examples
207(1)
12.7 Conclusion
208(2)
Summary 210(3)
References 213(8)
Index 221