Imaging and inversion with seismic data recorded with sources and receivers at the surface are powerful tools to infer knowledge about the subsurface. However, creating an image with seismic data is unfortunately not as easy as taking a picture with a smartphone. The estimated subsurface models in many situations are far from ideal due to the low quality nature of the data. One of the reasons can be weathering of the near-surface geology that generates unconsolidated material characterized by slow velocity with rapidly varying, heterogeneous and season-dependent nature. Acquiring seismic data on such near-surface leads to complex wave propagation, posing challenges to imaging and inversion. In this dissertation, we tackle the weathering effects during seismic data processing, imaging and inversion with low-rank-based methods. One approach to tackle the weathering effects on seismic data is removing them during seismic data processing. To do so for 2D data, we propose a model-independent low-rank-based near-surface estimation and correction in the midpoint-offset-frequency domain. In this domain, ideal data exhibit low rank structures, which get destroyed due to the influence of the weathering layers. Accordingly, the method makes use of the redundant nature of seismic data that allows for accurate approximation by low-rank matrices. To estimate the time shifts that compensate for the weathering effects, we cross-correlate a data set influenced by the near-surface weathering layers with its low-rank approximated version. Since we estimate time shifts (commonly referred to as statics) and no longer the directly low-rank approximated data, we avoid losses of the amplitude information. To improve the estimated statics and to alleviate the need for accurate rank selection for low-rank approximation, we implement the method in an iterative and multi-scale fashion. Since the low-rank approximation deteriorates at high frequencies, we utilize its better performance at low frequencies and exploit the common statics amongst different frequency bands. Using synthetic and field data, we demonstrate the performance of the proposed proposed, which requires no knowledge of the subsurface model, demands minimal data pre-processing, and provides accurate solutions with high computational efficiency compared to existing techniques. When seismic data acquired on complex near-surface are additionally subsampled for economical reasons, such as monitoring of sequestrated carbon dioxide and hydrogen, the problem is further exacerbated. Both the weathering layers and randomized subsampling render coherent energy incoherent. Therefore, they both contribute to destruction of the low-rank structure commonly associated with statics-free densely-sampled data. Frugal data acquisition in complex near-surface regimes makes separation of the distinct sampling and weathering effects on the rank structure difficult, which as a result lead to poor reconstruction. To overcome that, we propose to reconstruct the data with joint rank-reduction-based near-surface correction and interpolation. The method simultaneously accounts for the weathering and subsampling effects to provide accurate reconstruction. Since low-rank approximation is used for near-surface correction, we also utilize it in rank-minimization interpolation as a cost-free initial solution to the optimization problem. As both near-surface correction and interpolation operate in the midpoint-offset domain, we avoid the cost of transformations back and forth from the source-receiver to midpoint-offset transform domain. Consequently, the proposed reconstruction, which shows its potential on synthetic and field data, additionally increases the computational efficiency. While the aforementioned near-surface correction deals with 2D data, the Earth is a 3D object that requires acquisition of 5D data for proper subsurface model estimation. For 5D data, the limitations and challenges of conventional near-surface correction methods are magnified. To avoid them, we propose a 5D model-independent low-rank-based near-surface correction. To compute the singular value decomposition of 5D data volumes with 1 temporal and 4 spatial dimensions, which is necessary for low-rank approximation, we need to perform matricization of the 5D data, i.e. organization of the 5D data into matrices. At the same time, it is essential that the chosen organization domain reveals the underlying low-rank structure. Therefore, we first analyze different matricization domains that can be used to organize the 5D data. Similar to the 2D case, we show that --- in the potential domain --- the near-surface weathering layers render coherent energy incoherent, which results in slowly decaying singular values compared to the statics-free data that are of low-rank nature. The proposed method, which we show on synthetic and field data, enjoys the same benefits of the proposed method for 2D data, in addition to being able to capture the 3D nature of the Earth. Due to the complex nature of the near-surface and due to its impact on the subsurface model, the near-surface model gets treated separately from the subsurface model. However, the optimal goal is not to remove the near-surface effects with data processing, but to accurately estimate near- and sub-surface models simultaneously. To do so, we use the inherent scale separation of joint migration inversion that estimates a low-wavenumber velocity and high-wavenumber reflectivity. Since rapid variations in surface elevation and near-surface model result in high wavenumber effects, they end up affecting the reflectivity model. At the same time, the estimated reflectivity influences velocity estimation. Consequently, JMI provides erroneous subsurface models in the presence of complex weathering layers. To mitigate that, we use multi-scale low-rank updates in the reflectivity domain. The proposed method reduces the near-surface effects at the initial iterations, but it allows more details of the near-surface model to enter the solution at later iterations. In the end, we estimate accurate near- and sub-surface models simultaneously without the need to bypass the weathering layers.@en

A model is designed for solving gravitational profiles of self-gravitating and rotating planets via the use of Poisson's equation for total gravity, i.e., the sum of the gravitational and rotational potential. Poisson's equation is a partial differential equation that is solved with the usage of Green's functions. This is a major advantage because Earth's surface is an equipotential, which leads to a Dirichlett boundary condition. We apply this methodology to a spherical Earth, where the Green's function is closed. It is demonstrated that, when this Green’s functions based methodology is applied to a homogeneous density, a linear spherical density and the PREM density profiles (where all density profiles are spherically symmetric), then discontinuities occur in the accelerationof gravitation across the surface of the Earth, in the range of 0.01 %- 0.13 %. Such an effect is a symptom of incompatibility with the laws of physics for geostaticalequilibrium, and it is certainly significant as compared to the numerical accuracy of the solution. Moreover, the discrepancy is dependent on geographical latitude, as was to be expected, because it somehow reflects the centrifugal effect. The conclusion is made that this method is indeed capable of detecting, and even quantifying, the incompatibility of spherically symmetric mass distributions with the fundamental laws of physics for self-gravitating and rotating planets. This opens a way -and this is one of the main results- to computing corrections to spherically symmetric mass distributions, such as the PREM model. Based on this method, a further way forward to this end is suggested.

When humans started started exploiting the abundant underground natural resources the Earth has to offer such as hydrocarbons, minerals and heat, we started to experience earthquakes that are related to this exploitation, so called induced earthquakes. Under certain conditions those can damage local infrastructure. However, most events are weak and only sensed by seismic sensors. Microseismic monitoring plays a vital role to optimize and insure the safety of these underground activities and new technologies such as carbon capture and storage. One key task besides the detection of microseimsic events is to determine the source location of these events using data recorded at the surface. In this thesis we investigate a method to localize weak microseismic events, using a deterministic approach, assuming a dense network of sensors. In simple words this method takes the seismic signals recorded at the Earth’s surface and sends them back into the Earth, where the signals start to focus at the point they originated from. This focusing method uses one-way wavefield extrapolation with an estimate of the background velocity model. The advantage of this method is that the weak signals recorded by the different sensors at the surface are amplified as they approach the location of the event that emitted the signal due to constructive interference. However, this is not enough to reliably recover the source location because typically earthquakes do not radiate seismic waves evenly; complex radiation patterns are typically observed depending on the mechanical properties of the rupture. To obtain a strong focused signal at the optimal source location we therefore perform a grid search over possible source mechanisms and increase the strength of the signal by deconvolution. Without taking the source mechanism into account we are not able to obtain accurate source locations, especially at low signal-to-noise ratios. However, by taking the source mechanism into account we are able to retrieve accurate source locations while also retrieving information about the source mechanism. Good results were obtained for 2D synthetic data for both a simple subsurface model as well as the realistic Annerveen salt model even when realistic noise was added... @en

The seismic method has many applications. It is important in the critical sector of energy. Besides being used in imaging oil and gas reservoirs, it is also utilized in other sectors of energy such as geothermal energy exploration and development. It also plays a role in extracting other resources such as minerals or in the process of monitoring CO2 sequestration to reduce the carbon footprint of humankind. While seismic waves can occur naturally, their study gives insight in analysing the occurrence of and mitigating risks related to earthquakes. As far as active-source seismic is concerned: seismic images make it possible to see what is in the subsurface with minimal expensive and invasive operations such as drilling unnecessary holes in the subsurface — similar to what medical professionals use ultrasound or X-ray images for. Several methods have been proposed to analyze seismic data. A popular method nowadays is full waveform inversion (FWI), for instance, which attempts to fit all the recorded waveformwith amodel. This process solves, in fact, a very complicated highly non-linear inverse problem. Another process that uses such inversion process, but which tries to separate classes of parameters to reduce non-linearity, is joint migration inversion (JMI), in which scattering properties of the subsurface are separated from the propagation properties of seismicwaves. Currently those two methods, FWI and JMI, are generally model-dependent — that is they have been formulated to fit specific physics model such as isotropic acoustic media, transversally isotropic media with or without absorption. Hence, they would tend to have biases towards those particular models. Another paradigmis the so-called data-driven paradigm, or data-adaptive paradigm, and since it is formulated in terms of operators, one could also refer to it as operatorbased. Since it contains less biases towards a particular physics model or require no detailed knowledge of model parameters, beforehand, some also refer to it as modelindependent, as it does not need to force the data to fit a specific model, rather the process adapts to the model contained within the data. A process such as surface-related multiple elimination follows this paradigm. Another process, which is also shown in this dissertation, separates the surface multiples scattering-order-by-scattering-order without the need to assume a specific physics model. The process is referred to as scattering order decomposition. So, this dissertation looks into the problem of extending the inversion process to the model-independent or the operator-based paradigm. This dissertation looks first into the theoretical underpinning of this problem, where integral representations are used to study it. These representations are divided into four categories: first model-based representations are derived and presented as directional and non-directional. So, it places in context those theories. Next, the operator-based representations are also divided into directional and non-directional. Finally, four representations are derived, in this dissertation, which have the potential for applications in modeling, inversion and various seismic data analysis processes. Modeling is needed before any inversion since the inverse problem is ill-posed or illconditioned and hence no unique solutions exist but rather preconditioned or regularized solutions to these problems are normally used. Moreover, the inverse problem uses modeling iteratively and also back-projects the data residuals with the forward modeling mechanism. Therefore, the next chapters study operator generation and the subsequent modeling of wavefields with these derived operators...@en

Seismic data acquisition is a trade-off between cost and data quality subject to operational constraints. Due to budget limitations, 3D seismic acquisition usually does not have a dense spatial sampling in all dimensions. This causes artefacts in the processed images, velocity models, or other physical properties. However, we rely on, for example, the accurate images in determining the location of oil and gas-bearing geological structures, and the accurate elastic properties to characterise the reservoir. In this thesis, we propose new methods to improve existing technologies that can optimise marine seismic acquisition. In Part I, we aim at obtaining dense data in less time by improving the so-called blended seismic acquisition techniques. In Part II, we aim at obtaining an improved target illumination with a limited number of sources and receivers by developing an acquisition optimisation framework. @en