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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