Abstract
The goal of reflection seismic imaging is making images of the Earth subsurface using surface measurements of reflected seismic waves. Besides the position and orientation of subsurface reflecting interfaces it is a challenge to recover the size or amplitude of the discontinuities. We investigate two methods or techniques of reflection seismic imaging in order to improve the amplitude. First we study the \textsl{oneway wave equation} with attention to the amplitude of the waves. In our study of \textsl{reversetime migration} the amplitude refers to the amplitude of the image. Though the approach in the thesis is formal, our results have practical implications for seismic imaging algorithms, which improve or correct the amplitudes.
The oneway wave equation is a $1^{\rm st}$order equation that describes wave propagation in a predetermined direction. We derive the equation and identify the steps that determine the wave amplitude. We introduce a \textsl{symmetric square root operator} and a wave field normalization operator and show that they provide the correct amplitude. The idea to use a symmetric square root is generally applicable. Our amplitude claims are numerically verified. The oneway wave equation is an application of \textsl{pseudodifferential operators}.
\textsl{Reversetime migration} (RTM) is an imaging method that uses simulations of the source and receiver wave fields through a slowly varying estimate of the subsurface medium. The receiver wave is an in reverse time continued field that matches the measurements. An \textsl{imaging condition} transforms the fields into an image of the small scale medium contrast.
We investigate the linearized inverse problem and use the RTM procedure to reconstruct the perturbation of the medium. We model the scattering event by the scattering operator, which maps the medium perturbation to the scattered wave. We propose an approximate inverse of the scattering operator, derive a novel imaging condition and show that it yields a reconstruction of the perturbation with correct amplitude. The study extensively uses the theory of \textsl{Fourier integral operators} (FIO). Besides that we globally characterize the scattering operator as a FIO, we also obtain a local expression to calculate the amplitude explicitly. The claims are confirmed and illustrated by numerical simulations.
Original language  Undefined 

Awarding Institution 

Supervisors/Advisors 

Thesis sponsors  
Award date  6 Apr 2011 
Place of Publication  Zutphen 
Publisher  
Print ISBNs  9789036531504 
DOIs  
Publication status  Published  6 Apr 2011 
Keywords
 MSC00A69
 Reversetime migration
 Oneway wave modeling
 EWI19953
 Seismic inversion
 IR76619
 METIS277600
 NWOVIDI 639.032.509
Cite this
op 't Root, T. J. P. M., & Op 't Root, T. J. P. M. (2011). Imaging Seismic Reflections. Zutphen: University of Twente. https://doi.org/10.3990/1.9789036531504