Uncertainty Wedge Analysis: Quantifying the Impact of Sparse Sound Speed Profiling Regimes on Sounding Uncertainty

Recent advances in real-time monitoring of uncertainty due to refraction have demonstrated the power of estimating and visualizing uncertainty over the entire potential sounding space. This representation format, referred to as an uncertainty wedge, can be used to help solve difficult survey planning problems regarding the spatio-temporal variability of the watercolumn. Though initially developed to work in-line with underway watercolumn sampling hardware (e.g. moving vessel profilers), uncertainty wedge analysis techniques are extensible to investigate problems associated with low-density watercolumn sampling in which only a few sound speed casts are gathered per day. As uncertainty wedge analysis techniques require no sounding data, the overhead of post-processing soundings is circumvented in the situation when one needs to quickly ascertain the impact of a particular sampling regime. In keeping with the spirit of the underlying real-time monitoring tools, a just in time analysis of sound speed casts can help the field operator assess the effects of watercolumn variability during acquisition and objectively seek a watercolumn sampling regime which would balance the opposing goals of maximizing survey efficiency and maintaining reasonable sounding accuracy. In this work, we investigate the particular problem of estimating the uncertainty that would be associated with a particular low-density sound speed sampling regime. A pre-analysis technique is proposed in which a high-density set of sound speed profiles provides a baseline against which various low-density sampling regimes can be tested, the end goal being to ascertain the penalty in sounding confidence that would be associated with a particular low-density sampling regime. In other words, by knowing too much about the watercolumn, one can objectively quantify the impact of not knowing enough. In addition to the goal-seeking field application outlined earlier, this allows for more confi- dent attribution of uncertainty to soundings, a marked improvement over current approaches to refraction uncertainty estimation

Bayesian Framework for Simultaneous Registration and Estimation of Noisy, Sparse and Fragmented Functional Data

Mathematical and Physical Sciences: 3rd Place (The Ohio State University Edward F. Hayes Graduate Research Forum)In many applications, smooth processes generate data that is recorded under a variety of observation regimes, such as dense sampling and sparse or fragmented observations that are often contaminated with error. The statistical goal of registering and estimating the individual underlying functions from discrete observations has thus far been mainly approached sequentially without formal uncertainty propagation, or in an application-specific manner by pooling information across subjects. We propose a unified Bayesian framework for simultaneous registration and estimation, which is flexible enough to accommodate inference on individual functions under general observation regimes. Our ability to do this relies on the specification of strongly informative prior models over the amplitude component of function variability. We provide two strategies for this critical choice: a data-driven approach that defines an empirical basis for the amplitude subspace based on available training data, and a shape-restricted approach when the relative location and number of local extrema is well-understood. The proposed methods build on the elastic functional data analysis framework to separately model amplitude and phase variability inherent in functional data. We emphasize the importance of uncertainty quantification and visualization of these two components as they provide complementary information about the estimated functions. We validate the proposed framework using simulation studies, and real applications to estimation of fractional anisotropy profiles based on diffusion tensor imaging measurements, growth velocity functions and bone mineral density curves.No embarg

Bayesian inference of nanoparticle-broadened x-ray line profiles

A single and self-contained method for determining the crystallite-size distribution and shape from experimental x-ray line profile data is presented. We have shown that the crystallite-size distribution can be determined without assuming a functional form for the size distribution, determining instead the size distribution with the least assumptions by applying the Bayesian/MaxEnt method. The Bayesian/MaxEnt method is tested using both simulated and experimental CeO$_{2}$ data. The results demonstrate that the proposed method can determine size distributions, while making the least number of assumptions. The comparison of the Bayesian/MaxEnt results from experimental CeO$_2$ with TEM results is favorableComment: 43 pages, 13 Figures, 5 Table

Estimation of Sounding Uncertainty from Measurements of Water Mass Variability

Analysis techniques are introduced that allow for estimation of potential sounding uncertainty due to water mass variability from reconnaissance campaigns in which oceanographic parameters are measured at a high temporal and spatial resolution. The analysis techniques do not require sounding data, thus analyses can be tailored to match any survey system; this allows for pre-analysis campaigns to optimize survey instrumentation and sound speed profiling rates such that a desired survey specification can be maintained. Additionally, the output of the analysis methods can potentially provide a higher fidelity estimation of sounding uncertainty due to water mass variability than uncertainty models in common use

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 Sparse Bayesian Estimation Framework for Conditioning Prior Geologic Models to Nonlinear Flow Measurements

We present a Bayesian framework for reconstruction of subsurface hydraulic properties from nonlinear dynamic flow data by imposing sparsity on the distribution of the solution coefficients in a compression transform domain