This thesis explores machine learning in geoscience with a special focus on deep learning in 4D seismics. Recently, machine learning and neural networks in particular have made essential impacts in many scientific disciplines, with geoscience exploring these new approaches as well. This study contributes to this body of emerging work in deep neural networks and computer vision systems for the modelling and analysis of geoscientific data. The main contribution being a physics-based neural architecture for pressure-saturation inversion and a novel algorithm for 3D timeshift extraction in 4D seismic.

The growing interest in machine learning sometimes overlooks the fact that the underlying idea of machine learning was introduced in 1950. 11.2 reviews the history of machine learning with a special focus on geoscience. Geoscience and in particular geophysics has followed the innovation in artificial intelligence and especially neural networks closely. Early applications of neural networks include seismic processing and seismic inversion. Moreover, gps were early introduced in geostatistics as kriging, which have gained interest in a wider machine learning context as gp. Recently, dl becoming popular and particularly breakthroughs in computer vision have sparked interest in applying machine learning computer vision to asi in the hopes for increased accuracy, reproducibility and automation.

In recent years, 4D seismic itself has made an impact in geophysical reservoir analysis and other geophysical areas. The method enables imaging of changes in the subsurface. This is essential in hydrocarbon production, enabling extended production, reducing the direct environmental footprint and ensuring resource safety. Moreover, it enables CO₂ sequestration monitoring for reservoir and seal integrity and has applications in nuclear test treaty compliance, waste storage, and deep geothermal monitoring. 4D seismic matching has exposed deficits in 3D seismic processing, therefore furthered our understanding of amplitude-preserving and surface-consistent processing steps. Additionally, furthering our understanding of in-situ validation of geomechanical concepts and update of heterogeneous subsurface models.

The structure of this study is composed of topical groupings of five peer-reviewed and two submitted publications into chapters. Each chapter will provide an individual introduction to the topic and outline relevant theoretical and methodological aspects, where the publication falls short. This is particularly relevant for the shorter workshop and conference papers.

11 provides a theoretical introduction into 4D seismic principles, followed by a thorough overview of the development of machine learning with a special focus on geoscience. This chapter focuses particularly on the development of machine learning applications in geoscience through history. The main contribution in this chapter is a peer-reviewed book chapter published in Advances in Geophysics (Jesper Sören Dramsch 2020c).

12 contains a workshop paper (Jesper Sören Dramsch, Amour, and Lüthje 2018), which explores the application of unsupervised learning to the segmentation of chalk grains in bsem images. The chapter expands on the method and provides a theoretical treatment of the methods applied in the short paper. The method is also compared to classical image processing techniques. Then an overview of additional computational granulometry based on the segmentation maps is presented to apply the work and close out the chapter.

13 discusses a conference paper contribution to asi using dl (Jesper Sören Dramsch and Lüthje 2018a). The paper uses transfer learning of neural networks pre-trained on natural image data sets to fine-tune the network to perform asi on seismic data. The chapter expands on the data and training of the neural network. The chapter then expands on the applications that resulted from the paper, using the composition of nns into more adequate architectures for a task that is called semantic segmentation, which more closely resembles asi.

14 covers a journal paper on the application of complex-valued convolutional neural networks to seismic data (Jesper Sören Dramsch, Lüthje, and Christensen 2019). These networks perform a complex convolution in the nn layers. The paper tests the hypothesis that providing phase information explicitly can improve the capacity of the convolutional neural network, which is tested on an ae architecture, which lossily compresses the data at different rates and measures the reconstruction error. The phase information is derived directly from the seismic data via a Hilbert transform, hence a dnn could, in theory, extract this information automatically. For this chapter, networks at varying compression were trained for both real-valued and complex-valued networks to perform an adequate comparison.

15 consists of two workshop papers which introduce a dnn architecture for 4D quantitative pressure-saturation inversion (Jesper Sören Dramsch, Corte, et al. 2019d, 2019a). The dnn regression model implements a layer that computes basic physical knowledge within the network architecture to stabilize the network. The physical knowledge encoded in the layer is the avo gradient between the input seismic data. This data is passed into a vae architecture. In this work, we show that this network can be trained on simulation data and transferred to field data by applying Gaussian noise to the noise-free simulation input data to condition the network to accept noisy inputs from field data.

16 is comprised of a re-submitted journal paper and introduces a robust method for 3D time shift extraction in 4D data (Jesper Sören Dramsch, Christensen, et al. 2019). Time shifts in 4D data are commonly extracted in 1D due to computational cost and often poor performance of 3D methods. This method uses a self-supervised deep learning system to extract the timeshift mapping of two seismic volumes without supplying a-priori timeshift data. Moreover, the method limits the neural network to the extraction of the stationary timeshift but leaves the matching to a non-learning 3D interpolation to increase the transparency of the method. Additionally, the method supplies uncertainty values for the warp velocity. Constraining the possible 3D time shifts is vital to ensure sensible results for the time shifts, as well as, the aligned monitor seismic. This is ensured by implementing a geologically intuitive constraint on the 3D timeshifts, which prohibits crossing or looping of reflectors after mapping the seismic volumes. This learning-based method can be trained in advance, providing fast 3D results on previously unseen data, which is essential in 4D seismic analysis.

Finally, 17 is the conclusion of this thesis recapitulating the contributions and findings of the papers and scientific work. The contributions span multiple geoscientific disciplines with a focus in geophysics and particularly 4D seismic unified by machine learning.