Geophysical Inverse TheoryPrinceton University Press, 5 juin 1994 - 386 pages In many physical sciences, the most natural description of a system is with a function of position or time. In principle, infinitely many numbers are needed to specify that function, but in practice only finitely many measurements can be made. Inverse theory concerns the mathematical techniques that enable researchers to use the available information to build a model of the unknown system or to determine its essential properties. In Geophysical Inverse Theory, Robert Parker provides a systematic development of inverse theory at the graduate and professional level that emphasizes a rigorous yet practical solution of inverse problems, with examples from experimental observations in geomagnetism, seismology, gravity, electromagnetic sounding, and interpolation. Although illustrated with examples from geophysics, this book has broad implications for researchers in applied disciplines from materials science and engineering to astrophysics, oceanography, and meteorology. |
Table des matières
Mathematical Precursor | 3 |
102 Subspaces Linear Combinations and Linear Independence | 7 |
103 Bases and Dimension | 8 |
104 Functionals | 10 |
105 Norms | 12 |
106 Some Norms on FiniteDimensional Spaces | 13 |
107 Some Norms on InfiniteDimensional Spaces | 18 |
108 Convergence Cauchy Sequences and Completeness | 20 |
304 The Magnetic Anomaly Problem Revisited | 153 |
305 The Theory in Numerical Dress | 163 |
306 Return to the Seismic Dissipation Problem | 174 |
307 Large Numbers of Observations | 186 |
Resolution and Inference | 199 |
402 Resolution | 201 |
403 Bounding Linear Functionals in Hilbert Space | 214 |
404 Bounding Functionals in Practice | 226 |
109 Completion | 25 |
110 Inner Products | 27 |
111 Hilbert Space | 31 |
112 Two Simple Minimization Problems | 34 |
113 Numerical Aspects of Hilbert Space | 38 |
114 Lagrange Multipliers | 46 |
115 Convexity | 51 |
Linear Problems with Exact Data | 55 |
202 Linear Inverse Problems | 58 |
203 Existence of a Solution | 62 |
204 Uniqueness and Stability | 65 |
205 Some Special Solutions | 72 |
206 The Magnetic Anomaly Profile | 79 |
207 Interpolation | 88 |
208 Seismic Dissipation in the Mantle | 104 |
Linear Problems with Uncertain Data | 119 |
302 Fitting within the Tolerance | 131 |
303 The Spectral Approach | 144 |
405 Ideal Bodies | 241 |
406 Linear and Quadratic Programming | 253 |
407 Examples using LP and QP | 268 |
408 A Statistical Theory | 278 |
Nonlinear Problems | 293 |
502 Two Examples | 295 |
503 Functional Differentiation | 304 |
504 Constructing Models | 308 |
505 The Gravity Profile | 319 |
506 The Magnetotelluric Problem I | 333 |
507 Resolution in Nonlinear Problems | 345 |
508 The Magnetotelluric Problem II | 351 |
509 Coda | 368 |
The Dilogarithm Function | 371 |
Table for 1norm Misfits | 373 |
References | 375 |
381 | |