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Seismic Borehole Tomographyby Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on October, 1987 in partial fulfillment of the requirements for the degree of Doctor of Philosophy ABSTRACT
Seismic ray tomography and seismic diffraction tomography are tested by ultrasonic
laboratory experiments simulating cross-borehole, vertical seismic profiling (VSP),
and surface reflection configurations. Experimental results indicate that: 1)
Both seismic ray tomography and seismic diffraction tomography are hampered by
the limited view angle problem, although seismic diffraction tomography is less
sensitive to this problem. 2) When the scattered field can be measured, seismic
diffraction tomography is in general superior to seismic ray tomography, not only
because it is less sensitive to the limited angle view problem, but also because
seismic diffraction tomography can image small objects with size comparable to
the wavelength of the illuminating waves. 3) The advantage of the ray tomography
is that reconstruction can be done using the first arrivals only, the most easily
measured quantity, and there is less restriction on the properties of the object
to be imaged. 4) For seismic diffraction tomography, the Rytov approximation is
valid over a wider frequency range that the Born approximation in the cross-borehole
configuration. The emphasis of this thesis is on seismic diffraction tomography,
which has received attention for geophysical applications only recently. To make
seismic diffraction tomography a subsurface imaging technique that provides high
resolution reconstructions comparable to ultrasonic medical tomography and ultrasonic
medical tomography – the limited view angle problem- has to be solved. This
thesis develops two methods to solve the limited view angle problem. The first
method is to apply the minimum cross entropy estimation to seismic diffraction
tomography. The minimum cross entropy method helps the limited view problem by
making the most objective estimate of data that can mot be measured by the finite
aperture seismic source – receiver array. As explained in this thesis, when
the minimum cross entropy estimation is applied to seismic diffraction tomography,
it has the effect of extending the source array and the receiver array and therefore
it is equivalent to a finite aperture compensation. By numerical and ultrasonic
laboratory tests of this method, we find that the minimum cross entropy diffraction
tomography can reduce the artifacts in the reconstruction and improve the horizontal
resolution of the cross-borehole tomography. This method is especially useful
for objects consisting of isolated impulses in a homogeneous background medium. The
second method we develop for solving the limited view angle problem is the iterative
multi-frequency diffraction tomography. This method is a combination of the multi-frequency
reconstruction algorithm and the iterative least squares spectrum extrapolation
algorithm. The multi-frequency method provides more measured data, the spectrum
extrapolation algorithm estimates the data that can not be measured by the source-
receiver array of seismic borehole tomography. Results from numerical and ultrasonic
laboratory experiments indicate that for a finite extent object function in a
homogeneous background medium, the iterative multi-frequency diffraction tomography
can help the limited view angle problem by improving the horizontal resolution
and the signal/noise ratio. Return to Theses Return to ERL Home Updated: June, 1999
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