Date of Award

8-2010

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Bogdan Nita

Committee Member

Arup Mukherjee

Committee Member

Philip Yecko

Abstract

The goal of this thesis is to test the capability and efficiency of an inverse scattering algorithm for imaging seismic data. The algorithm we are investigating simultaneously images and inverts one-dimensional, one-parameter (velocity), acoustic reflection data. The algorithm does not require a velocity model or any other a priori information about the medium under investigation, the only input being a reference velocity (the speed of sound in water) and the data collected in the experiment. We assume that the data contains no source wavelet and all other events except primary reflections have been removed in preprocessing. We simulate two types of data: full frequency spectrum impulse data, using the Dirac delta function, and band-limited data, using the Sine function. The data is collected over four different models that exemplify different conditions that can be found in a one-dimensional medium with variable velocity. We show that the algorithm can precisely locate the interfaces and discover the correct velocity changes at those interfaces. We also compare this algorithm with the inverse scattering leading order imaging algorithm that Shaw presented in An inverse scattering series algorithm for depth imaging o f reflection data (See [12]). The latter uses certain imaging terms from the inverse scattering series to approximate the location of the interfaces in the unknown medium without providing any information about the change in the velocity at those interfaces. We show that the present algorithm located the interfaces more accurately in all the test cases.

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