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

How Vertex reinforced jump process arises naturally

We prove that the only nearest neighbor jump process with local dependence on the occupation times satisfying the partial exchangeability property is the vertex reinforced jump process, under some technical conditions. This result gives a counterpart to the characterization of edge reinforced random walk given by Rolles.Comment: 14 pages, 3 figures, version

A Mathematical Model of a Neuron with Synapses based on Physiology

The neuron, when considered as a signal processing device, itsinputs are the frequency of pulses received at the synapses, and its output is the frequency of action potentials generated- in essence, a neuron is a pulse frequency signal processing device. In comparison, electrical devices use either digital or analog signals for communication or processing, and the mathematics behind these subjects is well understood. However, in regards to pulse frequency processing devices, there has not yet been a clear and persuasive mathematical model to describe the functions of neurons. It goes without saying that such a model is very important, not only for understanding neuron and neural system behavior, but also for undeveloped potential applications in industry. This paper proposes a method for obtaining the mathematical relationship between the input and output signals of a neuron based on physiological facts. The proposed method focuses on the currents across the postsynaptic membrane of each synapse, and the key is to recognize that the net charge across the whole membrane of a neuron over each action potential cycle must equal to zero. By analyzing the relationship between the input of a synapse and the currents across the postsynaptic membranes, a dynamic pulse frequency model of the neuron can be obtained. Here, we show that the transfer function of a neuron depends on the function of thepostsynaptic current of each synapse in resting state, which can be found by detecting the postsynaptic current when a pulse is received at the synapse. The transfer function of a typical neuron generally includes addition and subtraction of feedthrough terms and/or first order lag functions. To focus on the most basic characteristics of a neuron, accommodation, adaptation, learning, etc. are not discussed in this paper

Robot autonomous navigation

Autonomous vehicle navigation is a very popular research area in the vision and control field. Based on Prof. Dickmanns' philosophy, we implement a navigation algorithm on thc small robot. The robot can rely on its eyes (the camera mounted on thc top of the robot) and control its wheels to walk through the sub-basement hallways of Caltech Moore Lab building. The speed we achieve is robot's mechanical maximum speed 0.5 m/s