Handling the nonuniqueness and ambiguity of geophysical inversion results is a major challenge in characterizing the subsurface. Geophysical inversion is the process of estimating the physical properties of the subsurface from the measured geophysical data, such as seismic, electromagnetic, gravity, or magnetic signals. However, there are often many different subsurface models that can fit the same data adequately well. Therefore, it is important to evaluate the uncertainty and reliability of the inverted models and integrate other sources of information, such as geologic, petrophysical, or geochemical data, to reduce uncertainty. Despite the industry's advances in recent decades, the number of subsurface outcomes that fall outside predicted ranges is disproportionate to the supposed certainty of those ranges. This leads to inefficient allocation of investment budgets, which is particularly painful due to the capital-intensive nature of the oil and gas industry.

Handling the nonuniqueness and ambiguity of geophysical inversion results is a major challenge in characterizing the subsurface. Geophysical inversion is the process of estimating the physical properties of the subsurface from the measured geophysical data, such as seismic, electromagnetic, gravity, or magnetic signals. However, there are often many different subsurface models that can fit the same data adequately well. Therefore, it is important to evaluate the uncertainty and reliability of the inverted models and integrate other sources of information, such as geologic, petrophysical, or geochemical data, to reduce uncertainty. Despite the industry's advances in recent decades, the number of subsurface outcomes that fall outside predicted ranges is disproportionate to the supposed certainty of those ranges. This leads to inefficient allocation of investment budgets, which is particularly painful due to the capital-intensive nature of the oil and gas industry.

There are many sources of subsurface uncertainty. One is uncertainty in our measurements. We can reduce this by using better equipment and designing good surveys, but we cannot eliminate it entirely. Another source is the uncertainty that comes from not having enough data to uniquely determine subsurface properties. This type of uncertainty is often referred to as the “null space” of the inverse problem. More data and different types of information can reduce the null space, but in practice we are far from eliminating it and thereby leaving behind massive nonuniqueness in our subsurface models. Yet another form of uncertainty stems from our limited understanding of, or ability to practically model, the true physics. We make approximations, which on one hand serve us well but on the other leave gaps between the truth and our model of the truth.

We have made progress on all fronts. Some efforts have led us toward reducing uncertainty within our measurements and some have helped us quantify the remaining uncertainty. In this special section, we present four papers that attempt to address various aspects of this massive challenge.

The first paper illustrates a common but often overlooked aspect of wave propagation and therefore seismic imaging. It examines the interactions between waves traveling in the subsurface and layer boundaries, specifically, rugosity of the interfaces. Lau and Gonzalez demonstrate the detrimental impact of misrepresenting complex interfaces, on waves, as they travel through the medium. This phenomenon leads to loss of resolution in the resulting seismic images, which in turn, leads to uncertainty in interpreting fine details on a seismic volume.

The next paper in the special section reviews some of the different methods that can be applied to assess uncertainty in seismic workflows. Walker et al. focus on three specific methods. The first uses gather flatness, and how well we can measure it, as an indicator of depth uncertainty. The second uses a variational inference algorithm in full-waveform inversion to measure nonuniqueness of the inverted models. The third presents a Bayesian inversion framework to estimate reservoir properties and capture the statistics that can be used for uncertainty quantification.

Machine learning is becoming widely used and implemented in almost all scientific fields. The third paper in this special section, by Sun and Williamson, uses a machine learning algorithm — specifically, an invertible neural network — to measure the uncertainty in seismic tomography, which is routinely used to estimate seismic velocities. The proposed idea could address both epistemic and aleatoric uncertainties.

The final paper of the special section, by Connolly and Dutton, presents a discussion of how seismic inversion for facies classification deals with uncertainty. The author introduces an algorithm — optimized rejection sampling — that can perform inversion more efficiently. The method addresses a key challenge present in conventional stochastic sampling methods that limits the ability of those algorithms to converge to a posterior distribution.