Mina Spremic

We describe different approaches that were used to test and investigate potential improvements in various aspects of the posterior Markov chain. This includes different ways of combining Up and Down chains, and inclusion of all available transitions within a window. Additionally, an alternative algorithm for computing the posterior Markov chain was tested, relying on forward-backward algorithm, using a higher order chain to obtain the posterior Lfcs. Proposed approaches were tested on both PCube paper example and Volund dataset, and results from the latter are presented. First approaches yielded some changes, but not significant improvements implying that current approach is a robust and reasonable choice. On the other hand, the proposed alternative algorithm produced different results. However, it is not straightforward to conclude, whether the results are to be preferred over the ones produced by the existing approach.

Local approaches have gained interest because they can provide fast approximate solutions for inverse problems. Following the idea of split-and-conquer, one aims to effectively condition variables to data using only small parts of the big model. We study and compare local approaches for conditioning in the context of seismic amplitude data and tomography, with two datasets relevant to improved oil and gas recovery in the North Sea and groundwater characterization in Denmark. In our comparison we study a local variant of an extended rejection sampler, termed localized extended rejection sampler (LERS), and a local ensemble transform Kalman filter (LETKF). Using various output statistics, we investigate the performance of the methods at marginal (e.g. mean and variance) level and joint properties (e.g. volume uncertainty and connectivity) of the subsurface variables of interest. Computed posterior statistics are compared with a reference Markov chain Monte Carlo solution. The results highlight benefits of the methods, such as fast reliable performance on the marginal properties, while joint properties in the more difficult cases show potential challenges of applying these local methodologies. Based on the results in our two cases, we discuss the applicability of the methods. We conclude that the localization methods are efficient and useful for estimating marginal properties and associated uncertainty, and can be an inexpensive tool for evaluating the need for further data processing. Local assimilation as outlined here is not suitable for generating posterior realizations of the spatial process variables.

Full waveform inversion (FWI) has enjoyed increased attention in the past decade, becoming the state of the art for estimating parameters influencing wave propagation in a medium. However, only a few recent emerging efforts have attempted to tackle the challenge of uncertainty quantification in FWI. In this study, we suggest joining FWI with the Bayesian approach, where we provide a post-processing step with an advantageous starting point defined by the global minimum stemming from a deterministic FWI algorithm. Then, using the local ensemble transform Kalman filter (LETKF), we obtain the uncertainty as a follow-up step to the FWI procedure. Within a probabilistic Bayesian inversion framework, the LETKF uses local seismic data to update sets of variables in the subsurface domain. Seismic data for each shot and receiver in the time-domain is in this way matched with subsurface layers, and assimilated in a sequential manner. The methodology is showcased on a realistic model of the Gullfaks field in the North Sea, where we study effects of various seismic acquisition design set-ups, algorithm and model parameter settings. We investigate how these acquisition designs and parameters influence the uncertainty reduction and bias of the inversion results. We highlight the importance of studying statistical performance metrics to ensure a balance between bias and underestimation of uncertainty.