Imaging seismic reflections
Op 't Root, Timotheus Johannes Petrus Maria (2011) Imaging seismic reflections. thesis.
|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 one-way wave equation with attention to the amplitude of the
waves. In our study of reverse-time 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 one-way wave equation is a 1st-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 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 one-way wave
equation is an application of pseudo-differential operators.
Reverse-time 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 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 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.
|Link to this item:||http://purl.utwente.nl/publications/76619|
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