A Novel Rayleigh Dynamical Model for Remote Sensing Data Interpretation

© 2020 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This article introduces the Rayleigh autoregressive moving average (RARMA) model, which is useful to interpret multiple different sets of remotely sensed data, from wind measurements to multitemporal synthetic aperture radar (SAR) sequences. The RARMA model is indeed suitable for continuous, asymmetric, and nonnegative signals observed over time. It describes the mean of Rayleigh-distributed discrete-time signals by a dynamic structure including autoregressive (AR) and moving average (MA) terms, a set of regressors, and a link function. After presenting the conditional likelihood inference for the model parameters and the detection theory, in this article, a Monte Carlo simulation is performed to evaluate the finite signal length performance of the conditional likelihood inferences. Finally, the new model is applied first to sequences of wind speed measurements, and then to a multitemporal SAR image stack for land-use classification purposes. The results in these two test cases illustrate the usefulness of this novel dynamic model for remote sensing data interpretation

Efficient probabilistic inversion of geophysical data

Estimation of uncertainties is critical for subsequent decision making in all applications of geosciences such as geological hazard analysis and risk mitigation, management and exploitation of subsurface resources, and environmental waste disposal. More efficient probabilistic inversion methods in geosciences are vital to making rapid and improved predictions of geological hazards and estimation of subsurface resources from geophysical data, and estimation of associated uncertainties. While this thesis focuses on seismic data inversion for the estimation of geological properties, the methods developed may find a wide variety of applications in all fields of research that involve spatial data analysis. New concepts, models and methods are developed to perform more efficient probabilistic inversion by making use of the latest developments in machine learning and Bayesian inverse theory to solve geophysical inverse problems. The major contribution of this thesis is the development of efficient geostatistical inversion methods for approximate inference for structured inverse problems where probabilistic dependence between unknown model parameters may be expressed as a Markov random field (MRF). These methods are many orders of magnitude faster than the corresponding sampling based methods in such types of inverse problems. Further, some of the commonly used but avoidable assumptions in conventional geostatistical inversion methods are progressively relaxed and finally removed in this research. The faster inversion methods allow more complex models to be evaluated for more accurate predictions and improved estimation of uncertainty for given compute power and time. Most existing geostatistical inversion methods are based on the localized likelihoods assumption, whereby the seismic data at a location are assumed to depend on the geology only at that location. Such an assumption is unrealistic because of imperfect seismic data acquisition and processing, and fundamental limitations of seismic imaging methods. It is also assumed in most such previous research that the data are completely free of any correlated noise or errors. Although these requirements are almost never met in reality, existing methods use these assumptions to make solutions computationally tractable. Both of these assumptions are progressively removed in this thesis while still allowing computationally tractable solutions to be found for suitably structured problems. The class of problems considered here spans a broad range of spatial data analysis and geosciences, where geology at a location is assumed to depend directly only on the geology within some pre-specified neighbourhood of that location – the so called Markovian assumption – which is the core assumption across the entire literature of geostatistics and has been proven to be valid for all practical purposes. Exact Bayesian inference is intractable in most models of practical interest because it requires normalization of the posterior distribution by integrating model parameters over a very high dimensional space. Therefore, approximate inference is used in practice. Stochastic sampling (e.g., by using Markov-chain Monte Carlo – McMC) is the most commonly used approximate inference method but is computationally expensive and detection of its convergence is often based on subjective criteria and hence is unreliable. New Bayesian inversion methods are introduced that estimate the spatial distribution of geological properties from attributes of seismic data, by showing how the usual probabilistic inverse problem can be solved using an optimization framework while still providing full probabilistic results – the so called variational inference approach. The intractable posterior distribution is replaced by a tractable approximation in the variational approach. Inference can then be performed using the approximate distribution in an optimization framework, thus circumventing the need for sampling, while still providing probabilistic results. The methods developed in this thesis infer the post-inversion (posterior) probability density of the unknown model parameters from seismic data and geological prior information. These methods are shown to be robust against weak prior information and correlated noise in the data. The methods are computationally efficient, and are expected to be applicable to 3D models of realistic size on modern computers without incurring any significant computational limitations