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.