Abstract
More than a decade ago the method of seismic delay time tomography was introduced in
geophysics by Alci et al. (1974, 1977). In the 1977 paper the inverse problem is formulated
of retrieving the three-dimensional seismic velocity structure of the Earth's interior from a
finite number of data (delay times). Originally the method
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aimed at imaging the seismic
structure of the lithosphere using a simple plane wave approximation for the incident
seismic waves which illuminated a three dimensional block model of the lithosphere.
Concurrently, papers dealing with mantle tomography on a global scale were presented by
Sengupta and Toksoz (1976) and Dziewonski et al. (1977) also using a block division of
the Earth's interior.
In the early days of seismic tomography the computer hardware and inversion
algorithms limited the applications of delay time tomography to using only a few hundred
velocity model parameters. Elegant inversion algorithms like the Singular Value
Decomposition method were used which also allowed formal computation of the errors and
of the spatial resolution in the tomographic mapping. However, square matrices of the size
of the number of unknowns needed to be inverted and, at that time, the relatively small
computer memories available imposed a severe restriction on the inversions.
This changed in the middle of the 1980's when Clayton and Comer (1984) were the
first to apply an iterative row-action method in large scale lower mantle tomography. Rowaction
methods do not perform a full matrix inversion inside the computer's memory.
Instead, one matrix row at a time is processed. Since the matrix describing the tomographic
problem can be stored on disk, the great advantage is that many more model parameters,
0(105
), can be used which allows a detailed parameterization of relatively large volumes of
the Earth. In the young history of seismic delay time tomography many geophysicists have been
impressed by the beauty of the method, but have been much less convinced of the
reliability of the results. First, the quality of the delay time data has never been thoroughly
studied. Secondly, the emphasis has been on imaging the Earth's interior rather than on
studying the reliability of the tomographic mapping, which is indeed difficult to assess.
The subject of this thesis is large scale upper mantle delay time tomography where we
use two different row-action methods to solve the inversion problem. The algorithms are
the conjugate gradient method called LSQR of Paige and Saunders (1982) and a member of
the family of Simultaneous Iterative Reconstruction Techniques (SIRT). The research is
discussed in the framework of an application to the upper mantle beneath central and
south-eastern Europe, the Mediterranean region and the Middle East.
When this research started little was known about the characteristics of row-action
methods in delay time tomography. Nolet (1985) showed in a synthetic experiment that the
LSQR method provided a much faster convergence rate to the least squares solution than
SIRT, but the behaviour of these algorithms in a real tomographic problem needed to be
scrutinized more fully. Another interesting problem to investigate was whether the
enonnous amount of ISC (International Seismological Centre) P delay time data for seismic
waves which bottom in the upper mantle were useful for tomographic inversion. In the
upper mantle the ray geometry is more complex than in the lower mantle. This poses
additional problems in delay time tomography of the upper mantle. Moreover, most of the
'upper mantle data' are derived from low magnitude events which in many cases can only
be located with poor accuracy. Consequently, delay times belonging to low magnitude
earthquakes presumably contain large errors. Hitherto in most tomographic studies only
delay time data from well detennined large magnitude events were used and only
observations from stations at distances larger than 300 were admitted. In this research the
situation is just complementary
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