12,812 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
A unified theory of cone metric spaces and its applications to the fixed point theory
In this paper we develop a unified theory for cone metric spaces over a solid
vector space. As an application of the new theory we present full statements of
the iterated contraction principle and the Banach contraction principle in cone
metric spaces over a solid vector space.Comment: 51 page
Non-local image deconvolution by Cauchy sequence
We present the deconvolution between two smooth function vectors as a Cauchy
sequence of weight functions. From this we develop a Taylor series expansion of
the convolution problem that leads to a non-local approximation for the
deconvolution in terms of continuous function spaces. Optimisation of this form
against a given measure of error produces a theoretically more exact algorithm.
The discretization of this formulation provides a deconvolution iteration that
deconvolves images quicker than the Richardson-Lucy algorithm.Comment: 12 pages, 3 figure
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Markov chain Monte Carlo is a key computational tool in Bayesian statistics,
but it can be challenging to monitor the convergence of an iterative stochastic
algorithm. In this paper we show that the convergence diagnostic
of Gelman and Rubin (1992) has serious flaws. Traditional will
fail to correctly diagnose convergence failures when the chain has a heavy tail
or when the variance varies across the chains. In this paper we propose an
alternative rank-based diagnostic that fixes these problems. We also introduce
a collection of quantile-based local efficiency measures, along with a
practical approach for computing Monte Carlo error estimates for quantiles. We
suggest that common trace plots should be replaced with rank plots from
multiple chains. Finally, we give recommendations for how these methods should
be used in practice.Comment: Minor revision for improved clarit
Wittgenstein on Pseudo-Irrationals, Diagonal Numbers and Decidability
In his early philosophy as well as in his middle period, Wittgenstein holds a purely
syntactic view of logic and mathematics. However, his syntactic foundation of logic
and mathematics is opposed to the axiomatic approach of modern mathematical logic.
The object of Wittgenstein’s approach is not the representation of mathematical properties within a logical axiomatic system, but their representation by a symbolism that identifies the properties in question by its syntactic features. It rests on his distinction of descriptions and operations; its aim is to reduce mathematics to operations. This paper illustrates Wittgenstein’s approach by examining his discussion of irrational numbers
Rank-normalization, folding, and localization: An improved for assessing convergence of MCMC
Markov chain Monte Carlo is a key computational tool in Bayesian statistics,
but it can be challenging to monitor the convergence of an iterative stochastic
algorithm. In this paper we show that the convergence diagnostic
of Gelman and Rubin (1992) has serious flaws. Traditional will
fail to correctly diagnose convergence failures when the chain has a heavy tail
or when the variance varies across the chains. In this paper we propose an
alternative rank-based diagnostic that fixes these problems. We also introduce
a collection of quantile-based local efficiency measures, along with a
practical approach for computing Monte Carlo error estimates for quantiles. We
suggest that common trace plots should be replaced with rank plots from
multiple chains. Finally, we give recommendations for how these methods should
be used in practice.Comment: Minor revision for improved clarit
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