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The contributions to this book follow a topical trend. In several
geophysical fields evidence is accumulating concerning the
deviation of the earth's structure from radial symmetry. Seismology
provides the most adequate resolution for revealing the earth's
lateral inhomogeneity on a global to local scale. Lateral structure
in the density distribution is also manifest in the earth's gravity
field and in the geoid. Asphericity in physical parameters,
generally supposed only to vary with the vertical coordinate, has a
profound influence on geodynamics. The effects of these deviations
from spherical symmetry concern in particular convection theory,
post-glacial rebound and the dynamics of the lithosphere and upper
mantle in general. At the 16th International Conference on
Mathematical Geophysics which was held in Oosterbeek, the
Netherlands, in 1986, the need was felt to present the state of the
art. Several prospective authors were found interested to
contribute to the present book. This Oosterbeek conference was one
in a long series of topical conferences starting with the Upper
Mantle Project Symposia on Geophysical Theory and Computers in the
1960s, and thence their successors, the conferences on Mathematical
Geophysics, until the present.
Methods to eonstruet images of an objeet from "projeetions" of
x-rays, ultrasound or eleetromagnetie waves have found wide
applieations in eleetron mieroseopy, diagnostie medicine and radio
astronomy. Projeetions are measurable quantities that are a
funetiona- usually involving a line integral - of physieal
properties of an objeet. Convolutional methods, or iterative
algorithms to solve large systems of linear equations are used to
reeonstruet the objeet. In prineiple, there is no reasan why
similar image reeonstruetions ean not be made with seismie waves.
In praetiee, seismic tomography meets with a number of
diffieulties, and it is not until the last deeade that imaging of
transmitted seismie waves has found applicatian in the Earth
sciences. The most important differenee between global seismie
tomography and mare eonventional applieations in the laboratory is
the faet that the seismologist is eonfronted with the lack of
anything resembling a well-eontrolled experimental set-up. Apart
from a few nuelear tests, it is not in our power to locate or time
seismie events. Apart from a few seabattom seismographs, our
sensors are located on land -and even there the availability of
data depends on eultural and politieal factors. Even in exploratian
seismics, praetieal faetors such as the east of an experiment put
strong limitations on the eompleteness of the data set.
Methods to eonstruet images of an objeet from "projeetions" of
x-rays, ultrasound or eleetromagnetie waves have found wide
applieations in eleetron mieroseopy, diagnostie medicine and radio
astronomy. Projeetions are measurable quantities that are a
funetiona- usually involving a line integral - of physieal
properties of an objeet. Convolutional methods, or iterative
algorithms to solve large systems of linear equations are used to
reeonstruet the objeet. In prineiple, there is no reasan why
similar image reeonstruetions ean not be made with seismie waves.
In praetiee, seismic tomography meets with a number of
diffieulties, and it is not until the last deeade that imaging of
transmitted seismie waves has found applicatian in the Earth
sciences. The most important differenee between global seismie
tomography and mare eonventional applieations in the laboratory is
the faet that the seismologist is eonfronted with the lack of
anything resembling a well-eontrolled experimental set-up. Apart
from a few nuelear tests, it is not in our power to locate or time
seismie events. Apart from a few seabattom seismographs, our
sensors are located on land -and even there the availability of
data depends on eultural and politieal factors. Even in exploratian
seismics, praetieal faetors such as the east of an experiment put
strong limitations on the eompleteness of the data set.
The contributions to this book follow a topical trend. In several
geophysical fields evidence is accumulating concerning the
deviation of the earth's structure from radial symmetry. Seismology
provides the most adequate resolution for revealing the earth's
lateral inhomogeneity on a global to local scale. Lateral structure
in the density distribution is also manifest in the earth's gravity
field and in the geoid. Asphericity in physical parameters,
generally supposed only to vary with the vertical coordinate, has a
profound influence on geodynamics. The effects of these deviations
from spherical symmetry concern in particular convection theory,
post-glacial rebound and the dynamics of the lithosphere and upper
mantle in general. At the 16th International Conference on
Mathematical Geophysics which was held in Oosterbeek, the
Netherlands, in 1986, the need was felt to present the state of the
art. Several prospective authors were found interested to
contribute to the present book. This Oosterbeek conference was one
in a long series of topical conferences starting with the Upper
Mantle Project Symposia on Geophysical Theory and Computers in the
1960s, and thence their successors, the conferences on Mathematical
Geophysics, until the present.
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