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 threedimensional seismic velocity structure of the Earth's interior from a finite number of data (delay times). Originally the method 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 rowaction 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 rowaction 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 southeastern Europe, the Mediterranean region and the Middle East.
When this research started little was known about the characteristics of rowaction 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.
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 rowaction 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 rowaction 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 southeastern Europe, the Mediterranean region and the Middle East.
When this research started little was known about the characteristics of rowaction 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.
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  14 Sept 1988 
Place of Publication  Utrecht 
Publisher  
Print ISBNs  9071577066 
Publication status  Published  14 Sept 1988 