Data- and machine-learning-driven retrieval and imaging of seismic-reflection data in complex media

The first study in this thesis is designed to cover both approaches of Marchenko redatuming and Marchenko-based primary estimation in a range of subsampling scenarios, providing insights that can inform acquisition sampling choices as well as processing parameterization and quality control, e.g., to set up appropriate data filters and scaling to accommodate the effects of dipole fields, or to help ensuring that the data interpolation achieves the desired levels of reconstruction quality that minimize subsampling artifacts in Marchenko-derived fields and images. With the aim of handling short-period multiples in laterally-varying media with complex, realistic layering, a updated augmented Marchenko approach is proposed in this thesis providing reliable approximations to the problem. This is achieved through combining an adapted 1.5D approach and additional post-processing with the recently proposed Marchenko-type demultiple formula. The new approach and its limitations are demonstrated with a range of numerical models that capture varying degrees of lateral heterogeneity in the overburden. The benchmark of migrated images after removing short-period multiples suggests promising applications to field data. As a next step in the reflection-data processing chain, the migrated images are nonetheless blurred with uneven amplitudes and low resolution, despite a successful multiples removal procedure. As an important post-processing step, seismic image deblurring aims to enhance both the resolution and amplitude balance. Conventional methods developed for such an inverse problem are usually cumbersome and slowly converging, and require case-dependent user interference, e.g. in the form preconditioning, and the fine-tuning of free parameters for regularization. This thesis proposes instead to address the problem with a physics-based Machine Learning technique --- the (invertible) Recurrent Inference Machine, by explicitly employing the point spread function as the forward operator and thus prior information. With a simple almost-flat synthetic training model and very cheap computational costs, this new approach outperforms the benchmark of the invertible UNet - a commonly-used convolutional neural network architecture - in a series of tests, designed with both complex synthetic models and the field data application. Different from the other methods, the neural networks in this study are trained to map the migrated image into an impedance perturbation model, rather than the reflectivity model, making it closer to the next-level application of the impedance inversion for reservoir characterisation and time-lapse monitoring. In the last part of the thesis, a general and unified framework is proposed, which flexibly incorporates all kinds of interface conditions for any type of wave equations. With the new approach, the implementation of a wave equation solver can be benchmarked by comparing different angles of plane wave simulations to transmission/reflection coefficients from plane-wave analysis with exact boundary conditions. This is illustrated with the case of poroelastic wave equation, which has a wide application in rock physics and reservoir monitoring.