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Geophysical inverse theory

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Princeton University Press, 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.

Parker's approach is to avoid artificial statistical constructs and to emphasize instead the reasonable assumptions researchers must make to reduce the ambiguity that inevitably arises in complex problems. The structure of the book follows a natural division in the subject into linear theory, in which the measured quantities are linear functionals of the unknown models, and nonlinear theory, which covers all other systems but is not nearly so well understood. The book covers model selection as well as techniques for drawing firm conclusions about the earth independent of any particular model.

  

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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
Index
381
Droits d'auteur

Expressions et termes fréquents

approximation basis bound calculations Cauchy sequence chapter coefficients complete components condition number constant constraint converge corresponding curve defined density depth dimensional eigenvalues elements Euclidean norm exact exactly example expansion factorization finite finite-dimensional forward problem Fre'chet derivative frequency func Gaussian geophysical Gram matrix gravity Hilbert space ideal body inequality inner product inner product space integral interpolation interval inverse problem iterative Lagrange multiplier linear combination linear functional linear system linear vector space linearly independent magnetic anomaly magnetic field magnetotelluric mantle mathematical measurements minimum misfit nonlinear norm minimization normed space normed vector space observations obtained optimization orthogonal parameters predictions random reader real numbers representers result satisfying scalars seismic seminorm seminorm minimization shown in figure smallest norm smooth solution solve spectral spherical harmonic subspace surface Theorem tion transform uniform norm variables zero

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Références issues de pages Web

Geophysical Inverse Theory
Geophysical Inverse Theory. EASA-610, Saint Louis University, Spring 2004. Instructor: Dr. Keith Koper, koper@eas.slu.edu, 977-3197 ...
www.eas.slu.edu/ People/ KKoper/ Teaching/ EASA-610/

Inverse Theory Resources
A growing list of recommended textbooks and helpful papers, Q&A list, related web links, and lecture notes, all on aspects of geophysical inverse theory. ...
staff.washington.edu/ aganse/ invresources/ index.html

Free Books > Science > Earth Sciences > General > Geophysical ...
Geophysical Inverse Theory. by John Scales And Martin Smith ... In Geophysical Inverse Theory, Robert Parker provides a systematic development of inverse ...
2020ok.com/ books/ 64/ geophysical-inverse-theory-36264.htm

Introductory Geophysical Inverse Theory
Introductory Geophysical Inverse Theory. John A. Scales, Martin L. Smith and Sven Treitel. Samizdat Press. Golden · White River Junction ...
mesoscopic.mines.edu/ ~jscales/ gp605/ snapshot.pdf

Classic Texts
Geophysical Inverse Theory. Berryman, jg, Lecture Notes on Nonlinear Inversion and ... Scales, J., M. Smith, and S. Treitel, Geophysical Inverse Theory . ...
cgiss.boisestate.edu/ ~billc/ important_texts.html

GEOS 657
Madden, T., Lecture Notes on Geophysical Inverse Theory, MIT, 1986. ... Scales, ja, and ml Smith, Introductory Geophysical Inverse Theory, SAMIZDAT Press, ...
web.ics.purdue.edu/ ~nowack/ geos657/ books.657.html

Parker, rl: Geophysical Inverse Theory.
Description of the book Geophysical Inverse Theory by Parker, RL, published by Princeton University Press.
press.princeton.edu/ titles/ 5527.html

Final Report Geoid Recovery using Geophysical Inverse Theory ...
Final Report. Geoid Recovery. using Geophysical. Inverse. Theory. Applied. to Satellite. to Satellite. Tracking. Data. NASA Contract. NAS5-99123. Principal ...
ntrs.nasa.gov/ archive/ nasa/ casi.ntrs.nasa.gov/ 20020091591_2002153272.pdf

A Reading List in Inverse Problems
Geophysical Inverse Theory. Princeton University. Press, Princeton, NJ, 1994. ... DRAFT: Geophysical inverse theory. http://landau.Mines. ...
www.ees.nmt.edu/ Geop/ Classes/ GEOP529/ Docs/ biblio.pdf

"Moment-tensor inversion references"
Least-Squares Modeling and Geophysical Inverse Theory ... Parker, rl, Geophysical Inverse Theory, Princeton University Press, Princeton, NJ, 386 pages, ...
eqseis.geosc.psu.edu/ ~cammon/ HTML/ MTinvDocs/ mtref01.html

À propos de l'auteur (1994)

University of Miami

Informations bibliographiques

QR code for Geophysical inverse theory
TitreGeophysical inverse theory
Princeton series in geophysics
AuteurRobert Ladislav Parker
Éditionillustrée
ÉditeurPrinceton University Press, 1994
ISBN0691036349, 9780691036342
Longueur386 pages
  
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