Ensemble Kalman filtering and conditional normalizing flows for seismic monitoring via data assimilation
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Bruer, Grant
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Abstract
This research focuses on the application of the ensemble Kalman filter
(EnKF) for monitoring subsurface injected carbon dioxide (CO2) using seismic
measurements and physical models. Monitoring CO2 plumes in underground
storage reservoirs is critical to avoid failure scenarios, e.g., by early
detection of overpressuring that could lead to leaks or seismic activity, and
also enables real-time optimization of CO2 injection using computer
simulations.
Seismic measurements provide a non-intrusive method for determining the
spatial distribution of the CO2 based on changes in the subsurface density
and wave velocity. Alternatively, fluid flow models can predict the CO2
spread by simulating the system based on estimates of the subsurface flow
parameters, such as permeability. These two sources of
information---observation and transition physics---can be combined using
Bayesian data assimilation (DA). This statistical framework mathematically
describes how to combine information from multiple sources over time to
estimate hidden states---in this case, the evolving CO2 plume.
The EnKF is a scalable ensemble-based algorithm for sequential Bayesian DA. It
is exact for linear transition and observation operators in the limit of
infinite ensemble size and has demonstrated practical value for nonlinear
systems with modest ensemble sizes, as established in weather forecasting.
The research described herein improves upon existing DA works in the
seismic-CO2 domain by applying the EnKF to a synthetic high-dimensional CO2
reservoir that incorporates two-phase flow dynamics and realistic time-lapse
full waveform seismic data. We show more accurate estimates of the CO2
saturation field with the EnKF compared to using either the seismic data or
the fluid physics alone. Moreover, we examine the few hyperparameters of the
standard EnKF, giving guidance on their selection for seismic CO2 reservoir
monitoring.
Furthermore, we explore conditional normalizing flow filters (CNFFs) as a
nonlinear extension of the EnKF. We examine the typical affine coupling layer
used in CNFFs and compare it to the EnKF for a small Gaussian system. Through
this theoretical comparison, we propose a different, easier parametrization
of the affine coupling layer, which we call the "decorrelation" coupling
layer. On small systems, we empirically show that this layer produces
networks that are much more robust to noise compared to the standard affine
coupling layers, while an comparison on the large geophysical system shows
similar expressiveness between the two CNFF methods.
The empirical comparison for the large system shows a major shortcoming of the
EnKF---spurious correlations drastically reduce the posterior variance. We
attribute the lack of this issue in the two CNFF methods to their
convolutional structures. Convolutions give the CNFFs builtin covariance
localization, whereas the EnKF requires extra implementation work to apply
force covariance localization. These comparisons demonstrate that there is
benefit to hybridizing CNFF methods with ideas from classical filters and
vice versa.
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Date
2025-12
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Resource Type
Text
Resource Subtype
Dissertation (PhD)