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

Aziridine-Metathesis based Approaches to Alkaloid Synthesis

The aim of the project is to synthesise (-)-morphine utilising aziridine and metathesischemistry. The thesis is divided into three chapters.Chapter 1 provides brief reviews on the subjects of total synthesis of morphine; ringrearrangementmetathesis (RRM) and regioselective ring-opening of aziridines.Chapter 2 focuses on the research findings in the past three years. Two routes, A and B,were investigated in attempts to synthesise morphine (Scheme 1). In route A, sulfonylcyclopentene II was prepared from ring-closing metathesis of a diene precursor, whichwas synthesised from lithiated cinnamylsulfone and butadiene monoxide. Subsequently,RRM reactions of several [alpha]-SO2Ph allyl derivatives of II were investigated and someinteresting results were obtained. The synthesis of 2,3-trans vinylaziridine III wasachieved in seven steps beginning with a Grignard reaction of (4-methoxyphenyl)magnesium bromide with butadiene monoxide. Subsequently, somehighly regioselective ring-opening reactions of III with sulfur-stabilised anionicnucleophiles were achieved. However, in an attempt to synthesise compound I from IIand III, no reaction was observed. This led to the investigation of route B, in which fivemethods for the synthesis of compound IV were investigated. The practical approachdeployed a novel Al-mediated substitution of the 4-tosyl group of the tosyltetrahydropyridine counterpart of IV, prepared from V and III, with a phenylthio group.Chapter 3 provides the experimental details and characterisation data.Imperial Users onl

Comment: Bayesian Checking of the Second Level of Hierarchical Models: Cross-Validated Posterior Predictive Checks Using Discrepancy Measures

Comment: Bayesian Checking of the Second Level of Hierarchical Models [arXiv:0802.0743]Comment: Published in at http://dx.doi.org/10.1214/07-STS235B the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Turing machines based on unsharp quantum logic

In this paper, we consider Turing machines based on unsharp quantum logic. For a lattice-ordered quantum multiple-valued (MV) algebra E, we introduce E-valued non-deterministic Turing machines (ENTMs) and E-valued deterministic Turing machines (EDTMs). We discuss different E-valued recursively enumerable languages from width-first and depth-first recognition. We find that width-first recognition is equal to or less than depth-first recognition in general. The equivalence requires an underlying E value lattice to degenerate into an MV algebra. We also study variants of ENTMs. ENTMs with a classical initial state and ENTMs with a classical final state have the same power as ENTMs with quantum initial and final states. In particular, the latter can be simulated by ENTMs with classical transitions under a certain condition. Using these findings, we prove that ENTMs are not equivalent to EDTMs and that ENTMs are more powerful than EDTMs. This is a notable difference from the classical Turing machines.Comment: In Proceedings QPL 2011, arXiv:1210.029