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We present a seismic model of the Africa Plate, constructed with the technique of full-waveform inversion. The purpose of our model is to serve as a foundation for quantitative geodynamic and geochemical interpretation, earthquake-induced ground motion predictions, and earthquake source inversion. Starting from the first-generation Collaborative Seismic Earth Model, we invert seismograms filtered to a minimum period of 35 s and compute gradients of the misfit function with respect to the model parameters using the adjoint state method. We use dynamically changing mini-batches of the complete data set to compute approximate gradients at each iteration. This approach has three significant advantages: (a) it reduces computational costs for model updates and the inversion, (b) it enables the use of larger datasets without increasing iteration costs, and (c) it makes it trivial to assimilate new data since we can extend the data set without changing the misfit function. We invert data from 397 unique earthquakes and 184,356 unique source-receiver pairs. We clearly image tectonic features such as the Afar triple junction and low-velocity zones below the Hoggar, Air, and Tibesti Mountains, pronounced more than in earlier works. Finally, we introduce a new strategy to assess model uncertainty. We deliberately perturb the final model, perform additional mini-batch iterations, and compare the result with the original final model. This test uses actual seismic data instead of artificially generated synthetic data and requires no assumptions about the linearity of the inverse problem., Journal of Geophysical Research: Solid Earth, 128 (6), ISSN:2169-9313, ISSN:0148-0227, ISSN:2169-9356

Measurements of pore pressure variations contain important information for the production of hydrocarbon reservoirs. Here, we couple surface-wave velocity changes directly to pore pressure change using sensitivity kernels. Using these kernels for realistic pore pressure changes in the Harlingen chalk gas reservoir, we modelled yearly Rayleigh-wave velocity changes. The velocity variations appear sufficiently large to be detectable on a yearly basis using passive image interferometry. This implies that, for specific formations, field-wide pore pressure monitoring is feasible with continuous seismic noise recordings at the surface.

In this paper, we consider a simplified model of turbulence for large Reynolds numbers driven by a constant power energy input on large scales. In the statistical stationary regime, the behaviour of the kinetic energy is characterised by two well defined phases: a laminar phase where the kinetic energy grows linearly for a (random) time $t_w$ followed by abrupt avalanche-like energy drops of sizes $S$ due to strong intermittent fluctuations of energy dissipation. We study the probability distribution $P[t_w]$ and $P[S]$ which both exhibit a quite well defined scaling behaviour. Although $t_w$ and $S$ are not statistically correlated, we suggest and numerically checked that their scaling properties are related based on a simple, but non trivial, scaling argument. We propose that the same approach can be used for other systems showing avalanche-like behaviour such as amorphous solids and seismic events., Comment: 12 pages, 10 figures

Imaging is a field of mathematics and physics that aims to retrieve information about the internal structure of an object that can only be accessed on its boundary. Many imaging methods are based on the following principle: a source outside of the object emits a wave. The wave propagates through the object. Wherever the physical structure of the object changes, scattered waves are induced. These scattered waves are measured by receivers outside of the object, and these scattered data are used to invert for the interior composition of the medium under investigation. The Marchenko integral was originally introduced for one-dimensional inverse scattering problems in the context of quantum mechanics. It can be related to Green's functions and so-called focusing functions - fields that produce a focus when injected into a medium from a single side. About ten years ago, the Marchenko integral was extended to two and three dimensions. This paved the way for, e.g., the elimination of imaging artefacts due to multiple scattering and Green's function retrieval for virtual source locations. However, many questions about the full potential as well as the accuracy of the Marchenko equation in two and three dimensions remain unanswered. In this thesis we present a new derivation for the multidimensional Marchenko integral. Our derivation is based on a generalised framework for wavefield focusing and circumvents the limiting assumptions of the previous extension. As we use partial differential equations rather than integral equations to define focusing functions, it allows for new physical insights. For instance, our approach indicates that it is possible to model Marchenko-type focusing functions with a conventional wave equation. Ultimately, this enables us to study Marchenko-type focusing in different 2D and 3D media and learn about the accuracy of the concept. We present a straightforward modelling approach for 1D as well as a least-squares modelling approach for 2D and 3D. The latter suggests that the Marchenko integral might be inherently approximative in multiple dimensions. We also discuss Green's function retrieval with our newly derived Marchenko integral, i.e. without wavefield decomposition. This method allows for estimating Green's functions for virtual sources inside of the medium. While it requires single-sided scattering data and an estimate of the first arrival of the desired Green's function there is no need to have an actual source or receiver inside of the medium. Our results demonstrate that we can retrieve good estimates of the full-spectrum Green's functions, involving evanescent and refracted waves, which were believed to not be retrievable with the previously derived Marchenko integral. Ultimately, we discuss imaging with these Marchenko-based Green's functions. Being able to include measurements for virtual sources inside of the medium allows for a natural linearisation of the imaging problem. Thus, we use the Marchenko integral to linearise state-of-the-art imaging approaches, similar to full waveform inversion or least-squares reverse time migration, and estimate the scattering potential. Our Marchenko-based linearisation accounts for all orders of scattering and performs slightly better than a single-scattering approximation.

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.

During a megathrust earthquake cycle, the plates accumulate strain in the interseismic stage due to locking of a portion of the megathrust that separates them. This strain is released during the earthquake and following rapid postseismic relaxation. As summarised in Chapter 1, this understanding was built through decades of seismological and geodetic observations and of advances in physics-based models. Models link properties and structures to observable quantities and are crucial to interpreting observed surface deformation in terms of the processes and materials in the inaccessible subsurface. However, different models can approximate the same observations roughly equally well. Furthermore, more sophisticated models do not necessarily reflect better the processes and properties of the subsurface; at the same time, simpler models that can explain some observations do not necessarily reflect the key processes occurring throughout one or multiple earthquake cycles. This thesis uses relatively simple three-dimensional models that still capture the key processes occurring during repeated earthquake cycles, without attempting to reproduce the structure or properties of specific subduction zones, to examine possible explanations of geodetic observations from global navigation satellite systems (GNSSs) at different stages of the cycle. Chapter 2 focuses on the interseismic, horizontal deformation of the overriding plate, which is in apparent contrast with observations of far-reaching coseismic displacement. We estimate the spatial patterns, with uncertainties, of GNSS velocities in South America, Southeast Asia, and northern Japan. Interseismic velocities with respect to the overriding plate generally decrease with distance from the trench with a steep gradient up to a “hurdle”, beyond which the gradient is distinctly lower and velocities are small. The hurdle is located 500-1000 km away from the trench for the trench-perpendicular velocity component, and either at the same distance or closer for the trench-parallel component. The trench-perpendicular hurdle generally follows major tectonic or geological boundaries and seismological contrasts. We formulate and test the hypothesis that both the interseismic hurdle and the coseismic response result from a mechanical contrast in the overriding plate. Our models show that overriding plates with a sufficient contrast respond to locked interseismic convergence similarly to observations. The compliance contrast is probably mainly responsible for the observed hurdle and in turn results from thermal, compositional and thickness contrasts. Chapter 3 is concerned with the increased landward velocities that were recorded onshore after 6 megathrust earthquakes in subduction zone regions adjacent to the ruptured portion. We investigate whether bending can be expected to reproduce this observed enhanced landward motion (ELM). We find that viscous relaxation, but not afterslip, produces ELM when a depth limit is imposed on afterslip. This ELM results primarily from in-plane elastic bending of the overriding plate due to trenchward viscous flow in the mantle wedge near the rupture. Modeled ELM is, however, incompatible with the observations, which are an order of magnitude greater and last longer. This conclusion does not significantly change when varying key model parameters. The observed ELM consequently appears to reflect faster slip deficit accumulation, implying a greater seismic hazard in lateral segments of the subduction zone. In Chapter 4, we study postseismic landward motion observed on the overriding plate in the vicinity of a major megathrust rupture. We argue that relocking of the megathrust, particularly at shallow depths, is needed for postseismic relaxation to produce landward motion on the tip of the overriding plate. We discuss how that this finding is consistent with previous simulations that implicitly relock the megathrust where afterslip is not included. We conclude that the Tohoku megathrust relocked within less than two months of the earthquake. This suggests that the shallow megathrust probably behaves as a true, unstably sliding asperity.

The physical and chemical properties of the Earth’s mantle govern the cause of natural disasters, such as earthquakes and volcanoes. Since we do not have direct access to mantle materials, their properties are often inferred from laboratory measurements and surface observations (e.g. seismic data from earthquake recordings). This thesis addresses some key problems we face while utilising these data to constrain the thermal and chemical properties of the mantle. Firstly, we propose a data-driven approach based on machine learning to explain the laboratory measurements and quantify their uncertainties in the absence of an adequate physical model. Our results show that although conventional approaches based on fitting the measurements to an assumed model may appear better constrained, they could potentially provide biased results. Secondly, we use the data-driven approach to explore which thermochemical parameters can be constrained (and to what extent) with limited seismic observables- wave speeds and density. Our results show that these observables constrain temperature and major chemical parameters (silicon, magnesium, and iron), and they indicate the presence of thermochemical heterogeneities at the lowermost mantle. The dense and slow piles at the bottom of the lower mantle seen in seismic data can be explained by an enrichment in silica and iron content- characteristic feature of enstatite chondrites. The inferred heterogeneities have profound implications for the dynamics of the mantle and outer core. The methodology developed in this thesis is extremely efficient. It can easily incorporate additional observables and thus, has wide applications in the seismology and mineral physics community.