Earth Resources Laboratory :: Abstracts

Seismic Borehole Tomography

Tien-when Lo

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.