3,372 research outputs found
Seismic Ray Impedance Inversion
This thesis investigates a prestack seismic inversion scheme implemented in the ray
parameter domain. Conventionally, most prestack seismic inversion methods are
performed in the incidence angle domain. However, inversion using the concept of
ray impedance, as it honours ray path variation following the elastic parameter
variation according to Snell’s law, shows the capacity to discriminate different
lithologies if compared to conventional elastic impedance inversion.
The procedure starts with data transformation into the ray-parameter domain and then
implements the ray impedance inversion along constant ray-parameter profiles. With
different constant-ray-parameter profiles, mixed-phase wavelets are initially estimated
based on the high-order statistics of the data and further refined after a proper well-to-seismic
tie. With the estimated wavelets ready, a Cauchy inversion method is used to
invert for seismic reflectivity sequences, aiming at recovering seismic reflectivity
sequences for blocky impedance inversion. The impedance inversion from reflectivity
sequences adopts a standard generalised linear inversion scheme, whose results are
utilised to identify rock properties and facilitate quantitative interpretation. It has also
been demonstrated that we can further invert elastic parameters from ray impedance
values, without eliminating an extra density term or introducing a Gardner’s relation
to absorb this term.
Ray impedance inversion is extended to P-S converted waves by introducing the
definition of converted-wave ray impedance. This quantity shows some advantages in
connecting prestack converted wave data with well logs, if compared with the shearwave
elastic impedance derived from the Aki and Richards approximation to the
Zoeppritz equations. An analysis of P-P and P-S wave data under the framework of
ray impedance is conducted through a real multicomponent dataset, which can reduce
the uncertainty in lithology identification.Inversion is the key method in generating those examples throughout the entire thesis
as we believe it can render robust solutions to geophysical problems. Apart from the
reflectivity sequence, ray impedance and elastic parameter inversion mentioned above,
inversion methods are also adopted in transforming the prestack data from the offset
domain to the ray-parameter domain, mixed-phase wavelet estimation, as well as the
registration of P-P and P-S waves for the joint analysis.
The ray impedance inversion methods are successfully applied to different types of
datasets. In each individual step to achieving the ray impedance inversion, advantages,
disadvantages as well as limitations of the algorithms adopted are detailed. As a
conclusion, the ray impedance related analyses demonstrated in this thesis are highly
competent compared with the classical elastic impedance methods and the author
would like to recommend it for a wider application
Detection and extraction of signals from the epoch of reionization using higher-order one-point statistics
Detecting redshifted 21-cm emission from neutral hydrogen in the early Universe promises to give direct constraints on the epoch of reionization (EoR). It will, though, be very challenging to extract the cosmological signal (CS) from foregrounds and noise which are orders of magnitude larger. Fortunately, the signal has some characteristics which differentiate it from the foregrounds and noise, and we suggest that using the correct statistics may tease out signatures of reionization. We generate mock data cubes simulating the output of the Low Frequency Array (LOFAR) EoR experiment. These cubes combine realistic models for Galactic and extragalactic foregrounds and the noise with three different simulations of the CS. We fit out the foregrounds, which are smooth in the frequency direction, to produce residual images in each frequency band. We denoise these images and study the skewness of the one-point distribution in the images as a function of frequency. We find that, under sufficiently optimistic assumptions, we can recover the main features of the redshift evolution of the skewness in the 21-cm signal. We argue that some of these features ¿ such as a dip at the onset of reionization, followed by a rise towards its later stages ¿ may be generic, and give us a promising route to a statistical detection of reionization
Jump-sparse and sparse recovery using Potts functionals
We recover jump-sparse and sparse signals from blurred incomplete data
corrupted by (possibly non-Gaussian) noise using inverse Potts energy
functionals. We obtain analytical results (existence of minimizers, complexity)
on inverse Potts functionals and provide relations to sparsity problems. We
then propose a new optimization method for these functionals which is based on
dynamic programming and the alternating direction method of multipliers (ADMM).
A series of experiments shows that the proposed method yields very satisfactory
jump-sparse and sparse reconstructions, respectively. We highlight the
capability of the method by comparing it with classical and recent approaches
such as TV minimization (jump-sparse signals), orthogonal matching pursuit,
iterative hard thresholding, and iteratively reweighted minimization
(sparse signals)
Application of the Least Squares Solutions in Image Deblurring
A new method for the reconstruction of blurred digital images damaged by separable motion blur is established. The main attribute of the method is based on multiple applications of the least squares solutions of certain matrix equations which define the separable motion blur in conjunction with known image deconvolution techniques. The key feature of the proposed algorithms is reflected in the fact that they can be used only in symbiosis with other image restoration algorithms
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