Explainable Artificial Intelligence driven mask design for self-supervised seismic denoising

The presence of coherent noise in seismic data leads to errors and uncertainties, and as such it is paramount to suppress noise as early and efficiently as possible. Self-supervised denoising circumvents the common requirement of deep learning procedures of having noisy-clean training pairs. However, self-supervised coherent noise suppression methods require extensive knowledge of the noise statistics. We propose the use of explainable artificial intelligence approaches to see inside the black box that is the denoising network and use the gained knowledge to replace the need for any prior knowledge of the noise itself. This is achieved in practice by leveraging bias-free networks and the direct linear link between input and output provided by the associated Jacobian matrix; we show that a simple averaging of the Jacobian contributions over a number of randomly selected input pixels, provides an indication of the most effective mask to suppress noise present in the data. The proposed method therefore becomes a fully automated denoising procedure requiring no clean training labels or prior knowledge. Realistic synthetic examples with noise signals of varying complexities, ranging from simple time-correlated noise to complex pseudo rig noise propagating at the velocity of the ocean, are used to validate the proposed approach. Its automated nature is highlighted further by an application to two field datasets. Without any substantial pre-processing or any knowledge of the acquisition environment, the automatically identified blind-masks are shown to perform well in suppressing both trace-wise noise in common shot gathers from the Volve marine dataset and colored noise in post stack seismic images from a land seismic survey

Seeing through the CO2 plume: joint inversion-segmentation of the Sleipner 4D Seismic Dataset

4D seismic inversion is the leading method to quantitatively monitor fluid flow dynamics in the subsurface, with applications ranging from enhanced oil recovery to subsurface CO2 storage. The process of inverting seismic data for reservoir properties is, however, a notoriously ill-posed inverse problem due to the band-limited and noisy nature of seismic data. This comes with additional challenges for 4D applications, given inaccuracies in the repeatability of the time-lapse acquisition surveys. Consequently, adding prior information to the inversion process in the form of properly crafted regularization terms is essential to obtain geologically meaningful subsurface models. Motivated by recent advances in the field of convex optimization, we propose a joint inversion-segmentation algorithm for 4D seismic inversion, which integrates Total-Variation and segmentation priors as a way to counteract the missing frequencies and noise present in 4D seismic data. The proposed inversion framework is applied to a pair of surveys from the open Sleipner 4D Seismic Dataset. Our method presents three main advantages over state-of-the-art least-squares inversion methods: 1. it produces high-resolution baseline and monitor acoustic models, 2. by leveraging similarities between multiple data, it mitigates the non-repeatable noise and better highlights the real time-lapse changes, and 3. it provides a volumetric classification of the acoustic impedance 4D difference model (time-lapse changes) based on user-defined classes. Such advantages may enable more robust stratigraphic and quantitative 4D seismic interpretation and provide more accurate inputs for dynamic reservoir simulations. Alongside our novel inversion method, in this work, we introduce a streamlined data pre-processing sequence for the 4D Sleipner post-stack seismic dataset, which includes time-shift estimation and well-to-seismic tie.Comment: This paper proposes a novel algorithm to jointly regularize a 4D seismic inversion problem and segment the 4D difference volume into percentages of acoustic impedance changes. We validate our algorithm with the 4D Sleipner seismic dataset. Furthermore, this paper comprehensively explains the data preparation workflow for 4D seismic inversio

Reciprocity-based imaging using multiply scattered waves

In exploration seismology, seismic waves are emitted into the structurally complex Earth. Its response, consisting of a mixture of arrivals including primary reflections, conversions, multiples, and transmissions, is used to infer the internal structure and properties. Waves that interact multiple times with the inhomogeneities in the medium probe areas of the subsurface that are sometimes inaccessible to singly scattered waves. However, these contributions are notoriously difficult to use for imaging because multiple scattering turns out to be a highly nonlinear process. Conventionally, imaging algorithms assume singly scattered energy dominates data. Hence these require that energy that scatters more than once is attenuated. The principal focus of this thesis is to incorporate the effect of complex nonlinear scattering in the construction of subsurface elastic images. Reciprocity theory is used to establish an exact relation between the full recorded data and the local (zero-offset, zero-time) scattering response in the subsurface which constitutes our image. Fully nonlinear, elastic imaging conditions are shown to lead to better illumination, higher resolution and improved amplitudes in pure-mode imaging. Strikingly it is also observed that when multiple scattering is correctly handled, no converted-wave energy is mapped to any image point. I explain this result by noting that conversions require finite time and space to manifest. The construction of wavefield propagators (Green’s functions) that are used to extrapolate recorded data from the surface to points in the Earth’s interior is a crucial component of any imaging technique. Classical approaches are based on strong assumptions about the propagation direction of recorded data, and their polarization; preliminary steps of wavefield decomposition (directional and modal) are required to extract upward propagating waves at the recording surface and separate different wave modes. These algorithms also generally fail to explain the trajectories of multiply scattered and converted waves, representing a major problem when constructing nonlinear images as we do not know where such energy interacted with the scatterers to be imaged. A secondary aim of this thesis is to improve on the practice of wavefield extrapolation or redatuming by taking advantage of the different nature of multi-component data compared with single-mode acoustic data. Two-way representation theorems are used to define novel formulations in elastic media which allow both up- and downward propagating fields to be back-propagated correctly without ambiguity in the direction, and such that no cross-talk between wave modes is generated. As an application of directional extrapolation, the acoustic counterpart of the new approach is tested on an ocean-bottom cable field dataset acquired over the Volve field, North Sea. Interestingly, the process of redatuming sources to locations beneath a complex overburden by means of multi-dimensional deconvolution also requires preliminary wavefield separation to be successful: I propose to use the two-way convolution-type representation as a way to combine full pressure and particle velocity recordings. Accurate redatumed wavefields can then be obtained directly from multi-component data without separation. Another major challenge in seismic imaging is to construct detailed velocity models through which recorded data will be extrapolated. Nowadays the information contained in the extension of subsurface images along either the time or space axis is commonly exploited by velocity model building techniques acting in the image domain. Recent research has shown that when both extensions are taken into account, it is possible to estimate the data that would have been recorded if a small, local seismic survey was conducted around any image point in the subsurface. I elaborate on the use of nonlinear elastic imaging conditions to construct such so-called extended image gathers: missing events, incorrect amplitudes, and spurious energy generated from the use of only primary arrivals are shown to be mitigated when multiple scattering is included in the migration process. Finally, having access to virtual recordings in the subsurface is also very useful for target-oriented imaging applications. In the context of one-way representation, I apply the novel methodology of Marchenko redatuming to the Volve field dataset as a way to unravel propagation effects in the overburden structure. Constructed wavefields are then used to synthesize local, subsurface reflection responses that are only sensitive to local heterogeneities, and detailed images of target areas of the subsurface are ultimately produced. Overall the findings of this thesis demonstrate that, while incorporating multiply scattered waves as well as multi-component data in imaging may be not a trivial task, such information is vital for achieving high-resolution and true-amplitude seismic imaging

Seis2Rock: A Data-Driven Approach to Direct Petrophysical Inversion of Pre-Stack Seismic Data

The inversion of petrophysical parameters from seismic data represents a fundamental step in the process of characterizing the subsurface. We propose a novel, data-driven approach named Seis2Rock that utilizes optimal basis functions learned from well log information to directly link band-limited petrophysical reflectivities to pre-stack seismic data. Seis2Rock is composed of two stages: training and inference. During training, a set of optimal basis functions are identified by performing singular value decomposition on one or more synthetic AVO gathers created from measured or rock-physics synthesized elastic well-logs. In inference, seismic pre-stack data are first projected into a set of band-limited petrophysical properties using the previously computed basis functions; this is followed by regularized post-stack seismic inversion of the individual properties. In this work, we apply the Seis2Rock methodology to a synthetic dataset based on the Smeaheia reservoir model and the open Volve field dataset. Numerical results reveal the ability of the proposed method in recovering accurate porosity, shale content, and water saturation models. Finally, the proposed methodology is applied in the context of reservoir monitoring to invert time-lapse, pre-stack seismic data for water saturation changes

Laterally constrained low-rank seismic data completion via cyclic-shear transform

A crucial step in seismic data processing consists in reconstructing the wavefields at spatial locations where faulty or absent sources and/or receivers result in missing data. Several developments in seismic acquisition and interpolation strive to restore signals fragmented by sampling limitations; still, seismic data frequently remain poorly sampled in the source, receiver, or both coordinates. An intrinsic limitation of real-life dense acquisition systems, which are often exceedingly expensive, is that they remain unable to circumvent various physical and environmental obstacles, ultimately hindering a proper recording scheme. In many situations, when the preferred reconstruction method fails to render the actual continuous signals, subsequent imaging studies are negatively affected by sampling artefacts. A recent alternative builds on low-rank completion techniques to deliver superior restoration results on seismic data, paving the way for data kernel compression that can potentially unlock multiple modern processing methods so far prohibited in 3D field scenarios. In this work, we propose a novel transform domain revealing the low-rank character of seismic data that prevents the inherent matrix enlargement introduced when the data are sorted in the midpoint-offset domain and develop a robust extension of the current matrix completion framework to account for lateral physical constraints that ensure a degree of proximity similarity among neighbouring points. Our strategy successfully interpolates missing sources and receivers simultaneously in synthetic and field data