Marchenko Imaging is a new technology in geophysics which enables to retrieve Green's functions at any point in the subsurface having only reflection data. This method is based on the extension of the 1D Gelfand-Levitan-Marchenko equation to a 3D medium. One of the assumptions of the Marchenko method is that the medium is lossless. If the lossy reflection response is used in the Marchenko scheme, some artefacts in the Green's functions as well as in the seismic image are present. One way to circumvent this assumption is to find a compensation parameter for the lossy reflection series so that the lossless Marchenko scheme can be applied. The main tasks of this thesis are to: [1] use the Marchenko equation to estimate the attenuation in the subsurface, [2] find a compensation parameter for the lossy reflection series so that the lossless Marchenko scheme can be applied, and [3] to create an upscaling method for wave propagation. The Artefact Removal Method was created which makes it possible to calculate an effective temporal Q-factor of the medium between a virtual source in the subsurface and receivers at the surface. This method is based on the minimization of the artefacts produced by the lossless Marchenko scheme. The minimization was performed in three ways: [1] in the space-time domain, [2] in the frequency domain and [3] to the scales of the wavelet transform applied to the artefacts. This method can also be used to find the layers with high attenuation. The upscaling method which can be used to construct macro-scale homogenized viscoelastic properties of the medium from the micro-scale properties of a heterogeneous medium was developed. This is done through linking the macro- and micro- scale Lippmann-Schwinger equations which describe the wave field and the strain field scattering in an inhomogeneous medium, respectively. In this thesis, the macro-scale homogenized viscoelastic properties were calculated by using the T-matrix Approach and the Generalized Dvorkin-Mavko Attenuation Model. All theoretical results are supported by synthetic 1D modeling. The theoretical part of the thesis and the general work flow can be used for a very complex medium.

The seismic method is an important indirect method to investigate the subsurface of the earth. By analyzing how the earth affects the propagation of mechanical waves, the structure of the earth and its seismic properties can be inferred. The seismic vibrator is the most commonly used land source in active-source exploration and monitoring to generate these waves and is the subject of this thesis. The goal of a seismic vibrator is to produce seismic waves with a known signal signature. Commonly sinusoidal signals whose frequency varies over time, called sweeps, are used for this purpose. These signals are typically quite lengthy to compensate for the fact that the instantaneous amplitudes of the vibrator are relatively weak compared to the ones from impulsive sources and the target depths faced. Via the processing step of correlation, the lengthy source signature is collapsed and virtual records are generated as if the vibrator would have released all energy at once. The quality of these virtual records depends on the ability of the vibrator engines to generate the force signature wanted and the ability of the vibrator mechanics and the vibrator-ground interaction to successfully transform the driving force to a seismic wave. In this thesis we investigate the feasibility of driving a vibrator with linear synchronous motors, the influence of drive level on the signals a vibrator generates, the effect of the vibrator-ground coupling, and the possibilities to design more robust source signals.@en

The theory of seismic interferometry predicts that the cross-correlation (and possibly summation) between seismic recordings at two separate receivers allows the retrieval of an estimate of the inter-receiver response, or Green's function, from a virtual source at one of the receiver positions. Ideally, the recordings must consist of the responses from a homogeneous distribution of seismic sources that effectively surround the receivers. This principle has successfully been exploited to retrieve from recorded passive data more easily usable and interpretable responses. In fact, the retrieval of virtual-source responses has led to a wide range of applications, including for controlled-source seismic surveys. The latter is the case for data-driven methods for redatuming reflection data to a receiver level below the source-acquisition surface, or methods to suppress surface waves in land seismic data. In this thesis, I studied the application of seismic interferometry to surface reflection data, that is, reflection data acquired with both sources and receivers at or near the earth's surface. This is a typical configuration for seismic exploration, either in land or marine surveys. The retrieval of additional virtual sources at receiver locations in that configuration would result in having effectively more shot points. Depending on whether the virtual-source responses contain relevant information, the combined source and virtual-source coverage could allow more complete illumination of the subsurface and so better imaging of its structures. This could be particularly the case for surveys with areas or directions poorly sampled by sources, including large gaps, but with receivers present. The main research questions are what are the conditions for retrieving useful virtual-source reflection responses and with what accuracy. As I first show from mathematical derivations, the retrieval of virtual-source reflection responses from the application of seismic interferometry to exploration-type reflection data does not comply with several theoretical requirements. A major requirement is that the two considered receivers would need to be enclosed by a boundary of sources. This condition is obviously not fullfilled by the single-sided illumination as in exploration surveys. Consequently, as I show using modelled reflection data, the virtual-source reflection responses are retrieved with several distortions, including the presence of undesired non-physical reflection events. Yet, in spite of the non-ideal single-sided configuration, cross-correlating the reflection records at receiver pairs and summing over source profiles allows retrieving virtual-source responses with relevant reflection signals. These virtual reflection signals are referred to as pseudo-physical reflections, as they share the same kinematics as physical reflections but contain distortions due to the {cross-correlation} process. By studying further the numerical examples, I determine the influence of several acquisition-related parameters and subsurface characteristics on the accuracy of the virtual-source reflection responses. Then, based on a theoretical approach using the convolution-type reciprocity theorems, instead of the cross-correlation type, I show how part of the distortions in the virtual-source responses retrieved by cross-correlation could be reduced by performing a multidimensional-deconvolution operation. The potential benefits of multidimensional deconvolution are verified with a numerical example, showing that the obtained virtual-source reflection responses match better the reference physical responses. In addition, I highlight the essential role of the surface-related multiples in the retrieval process of pseudo-physical reflections. In turn, the retrieved pseudo-physical reflections provide usable feedback about the surface multiples. In particular, I present a method based on the stationary-phase analysis of the retrieved pseudo-physical reflection arrivals for detecting surface-related multiple reflections in the acquired data. The results from tests on numerically modelled data show that this interferometric method allows identifying prominent surface multiples in a wide range of source-receiver offsets. Also, I determine that this correlation-based method performs still well even in the case of missing near-offset reflection data. This interesting property suggests that for robust prediction of multiples, the method could be further developed and complement convolution-based schemes which often suffer from missing near-offset data. Still, the main objective in retrieving virtual-source responses is to obtain additional desirable shot points for improving processing or imaging. In general, interpolation techniques are applied to the seismic data to compensate for the irregularities of the acquisition geometry. However, most of the direct interpolation techniques do not allow retrieval of the missing data if the gap is larger than the Nyquist criterion. I show, using numerically modelled datasets, that in these challenging cases, decisive information for imaging may be obtained from the retrieval of virtual sources as long as surface-multiple energy is present in the shot records. In particular, I show that virtual images (obtained from retrieved virtual data) can reveal initially invisible structures in the images obtained from the uncomplete reflection data. Finally, I apply seismic reflection interferometry on a 3D land seismic dataset to test further the practical feasibility of retrieving relevant virtual-source reflection responses. The survey was acquired at a mining site in a hard rock environment with recorded reflections characterized by a relatively poor signal-to-noise ratio. The first results presented in this thesis show evidences of retrieved pseudo-physical reflections. By testing different source contributions, these investigations also show that the retrieval of these desirable events may largely depend on the location and extent of the considered source patch with respect to the virtual source and receiver geometry.@en

The Marchenko method offers a new perspective on eliminating internal multiples. Instead of predicting internal multiples based on events, the Marchenko method formulates an inverse problem that is solved for an inverse transmission response. This approach is particularly advantageous when internal multiples generate complicated interference patterns, such that individual events cannot be identified. Moreover, the retrieved inverse transmissions can be used for a wide range of applications. For instance, we present a numerical example of the single-sided homogeneous Green's function representation in elastic media. These applications require a generalization of the Marchenko method beyond the acoustic case. Formally these extensions are nearly straightforward, as can be seen in the chapter on plane-wave Marchenko redatuming in elastic media. Despite the formal ease of these generalizations, solving the aforementioned inverse problem becomes significantly more difficult in the elastodynamic case. We analyze fundamental challenges of the elastodynamic Marchenko method. Elastic media support coupled wave-modes with different propagation velocities. These velocity differences lead to fundamental limitations, which are due to differences between the temporal ordering of reflection events and the ordering of reflectors in depth. Other multiple-elimination methods such as the inverse scattering series encounter similar limitations, due to violating a so-called monotonicity assumption. Nevertheless, we show that the Marchenko method imposes a slightly weaker form of the monotonicity assumption because it does not rely on event-based multiple prediction. Another challenge arises from the initial estimate that is required by the Marchenko method. In the acoustic case, this initial estimate can be as simple as a direct transmission from the recording surface to the redatuming level. In the presence of several wave-modes, an acoustic direct transmission generalizes to a so-called forward-scattered transmission, which is not a single event but a wavefield with a finite temporal duration. Former formulations of the elastodynamic Marchenko method require this forward-scattered transmission as an initial estimate. However, in practice, this initial estimate is often unknown. We present an alternative formulation of the elastodynamic Marchenko method that simplifies the initial estimate to a trivial one. This approach replaces the inverse transmission, which is often referred to as a focusing function, by a so-called backpropagated focusing function. This strategy allows us to remove internal multiples, however, unwanted forward-scattered waves persist in the data. This insight suggests that forward-scattered waves cannot be predicted by the Marchenko method: either they are provided as prior knowledge, or they remain unaddressed. The remaining forward-scattered waves may be eliminated by exploiting minimum-phase behavior as additional constraint. This approach is inspired by recent developments of the acoustic Marchenko method that use a minimum-phase constraint to handle short-period multiples. Generalizing this strategy to the elastodynamic case is challenging because wavefields are no longer described by scalars but by matrices. Hence, we start by analyzing the meaning of minimum-phase in a multi-dimensional sense. This investigation illustrates that the aforementioned backpropagation turns the focusing function into a minimum-phase object. This insight suggests that, from a mathematical view point, the backpropagated focusing function can be seen as a more fundamental version of the focusing function. Moreover, we present attempts of using this property as additional constraint to remove unwanted forward-scattered waves. Given the remaining theoretical challenges of the elastodynamic Marchenko method, we analyze the performance of an acoustic approximation. We evaluate the effect of applying the acoustic Marchenko method to elastodynamic reflection data. For this analysis, we look for geological settings where an acoustic approximation could be impactful. The Middle East is a promising candidate because, due to its nearly horizontally-layered geology, elastic scattering effects are weaker for short-offsets, which are the main contributors to structural images. Therefore, we construct a synthetic Middle East model based on regional well-log data as well as knowledge about the regional geology. In contrast to field data examples, the synthetic study allows us to include or exclude elastic effects. Hence, we can inspect the artifacts caused by an acoustic approximation. The results indicate that the acoustic Marchenko method can be sufficient for multiple-free structural imaging in geological settings akin to the Middle East.@en

Monitoring the properties of a CO2 storage reservoir is important for two main reasons: firstly, to verify that the injected CO2 is safely contained in the reservoir rock as planned, and secondly, to provide data which can be used to update the existing reservoir models and support eventual mitigation measures in case of deviation from the CO2 storage plan. Reliable quantitative monitoring of reservoir rocks and pore-filling fluids remains a challenging task in geophysical prospecting. Typically, geophysical electrical and seismic surveys are used to predict reservoir properties. Electrical properties of rocks are strongly controlled by the chemistry of the fluids that fill the pore space. Thus, electrical surveys can provide accurate estimates of pore-filling fluid composition and porosity of reservoir rock. Seismic methods are particularly sensitive to elastic heterogeneities in the subsurface. Elastic properties of reservoir rocks can be extracted from recorded seismic data. Potentially, the simultaneous use of electrical and seismic geophysical surveys can reduce the uncertainty in the quantitative characterization of reservoir rocks. In this thesis, theoretical and experimental research is conducted to show the feasibility of such an integrated approach for a CO2 storage reservoir.@en

Monitoring time-lapse changes inside the subsurface is of great significance to many geotechnical applications, such as storage of gasses in underground geological formations. Minute differences in the seismic wavefield between an initial baseline and a subsequent monitor survey have to be detected in order to observe fluid flow inside subsurface reservoirs. This problem becomes even more challenging when the reservoir is situated underneath a series of complex, highly reflective layers. Such an overburden will generate strong multiple reflections that will interfere with the reflections of the target zone. Ideally, a methodology is designed in order to remove these internal multiples to allow a clear view of the reservoir response for time-lapse analysis. The Marchenko method can redatumthe seismic wavefield to arbitrary depth levels or points in the subsurface, while accounting for all orders of internal multiple reflections. This method, therefore, has great potential to solve some of the time-lapse issues, as it is able to closely examine specific zones of interest in the subsurface without distortions from surrounding layers. Time-lapse studies are often hampered by irregular or imperfect sampling, whereas the Marchenko method relies on densely sampled, co-located sources and receivers. It is, therefore, important that the Marchenko method is able to handle more complex acquisition geometries. This can either be achieved by interpolating the reflection data as a pre-processing step or by correcting for errors inside the Marchenko scheme. Here, point-spread functions are introduced that describe the imperfections in the reflection data. These imperfections distort the focusing and Green’s functions retrieved from the Marchenko method. Next, each iteration of theMarchenko scheme is extended to deblur the imperfect focusing and Green’s functions by multidimensional deconvolution with these point-spread functions. Additionally, a slight modification is required to ensure stability of the new scheme. This new iterative Marchenko scheme is computationally more expensive, but removes all sampling artifacts. Finally, the migrated images of the target zone show significant improvements, when using either the new scheme or interpolation as pre-processing step...@en

In this thesis, I study coupled poroelastic waves and electromagnetic fields in layered media. The focus is two-fold: 1. Increase the theoretical and physical understanding of the seismo-electromagnetic phenomenon by analytically-based numerical modeling. 2. Investigate the potential of seismo-electromagnetic interferometry. After presenting the governing equations that form the basis of the theoretical framework, I capture this system into a matrix-vector representation of the wave equation. I first use literature eigenvector sets, which I normalize with respect to power-flux. I then derive new, alternative power-flux normalized eigenvector sets that I prove to be numerically more stable and accurate. The eigenvector sets form the basis of the analytically-based numerical modeling code `ESSEMOD' that I developed to model seismo-electromagnetic wave/field propagation/diffusion in layered-Earth media. The alternative eigenvector set models scenarios with no seismo-electromagnetic coupling correctly, where the literature eigenvector sets fail. In addition, the alternative set properly deals with scenarios where both small amplitude signals and large amplitude signals occur in the record, whereas the literature eigenvector sets result in noise levels masking the small events. The same holds for scenarios with a small seismo-electromagnetic coupling coefficient. I design an effective global reflection scheme that properly describes the primary and multiple reflections in the models. I implement the correct boundary conditions to account for scenarios with a free-surface, and also for scenarios containing fluid/porous medium/fluid transitions. To transform all the seismo-electromagnetic source-receiver combinations in a numerically effective way back from the horizontal wavenumber-frequency domain to the space-frequency domain, I derive and implement explicit Fourier-Bessel transformations. I then validate the developed modeling code in numerous ways. First of all, I compare the results of seismo-EM layer-code modeling in a homogeneous medium with explicit homogeneous space Green's function expressions. This comparison provides a clear validation that the layer-code models the dynamic responses in homogeneous scenarios correctly. Next, I check numerical consistency by carrying out reciprocity checks. I study homogeneous space models, models containing a free-surface and models with interfaces. As a next step, I validate the modeling results of seismo-EM layer-code modeling for typical seismo-electromagnetic laboratory configurations, i.e. models containing fluid/porous medium/fluid transitions. I first compare the purely electromagnetic part of the seismo-EM layer-code with an independently developed purely electromagnetic layered-Earth code. The results match perfectly in both phase and amplitude for full transmission and pure reflection experiments, as well as for a combination of both. I then carry out a seismo-electromagnetic reciprocity test for a fluid halfspace overlying a porous medium halfspace, proving that the coupled poroelastic and electromagnetic fields are modeled consistently and yield the expected results. As a final validation step, I compare ESSEMOD with an independently developed seismo-electromagnetic layered-Earth modeling code. The results display an almost perfect match in both phase and relative amplitudes, and a constant amplitude correction factor of 4 needs to be applied to let the absolute amplitudes match. I then carry out a small feasibility test to study the potential of the seismo-electromagnetic effect for exploration purposes. I investigate different source-receiver combinations for the same model, and focus on the signal strength recorded at different distances from the target depth level. I conclude that for the source-receiver combinations studied, the electric field due to a volume injection monopole source, as well as the magnetic field due to a seismic bulk force source, yield the strongest converted signals. The receiver-distance from the target of interest plays an important role in the signal measurability. The closer the receivers to the target, the higher the signal strengths. However, when the receivers are located too close to the target, the coseismic reflected fields can mask the interface response fields that we are mainly interested in. Next, I study if nature itself can help us to overcome the very low signal-to-noise ratio of seismo-electromagnetic converted fields, by investigating the effects of thin-bed geological structures on the seismo-electromagnetic signal. To investigate the effects of bed-thinning on the seismo-electromagnetic interference patterns, I numerically simulate seismo-electromagnetic wave propagation through horizontally layered media with different amounts and thicknesses of thin-beds. I demonstrate seismo-electromagnetic sensitivity to changes in medium parameters on a spatial scale much smaller than the seismic resolution. By simulating moving oil/water contacts during production, where the oil layer is gradually being thinned, seismo-electromagnetic signals are proven very sensitive to oil/water contacts. I now explore the application of interferometric techniques to the seismo-electromagnetic system, which might eventually lead to an improved signal-to-noise ratio of the weak converted fields. I derive the theory for interferometric retrieval of 2D SH-TE seismo-electromagnetic Green's functions. Using both a circular source configuration and a line source configuration, I show that it is possible to correctly retrieve the dynamic seismo-electromagnetic 2D SH-TE response in a homogeneous medium, using seismic boundary sources only. Using seismo-EM layer-code data, I then show that it is also possible to correctly retrieve the direct shear wave-related causal coseismic field in a homogeneous medium, in both phase and amplitude. To obtain a perfect match in absolute amplitudes, I apply a single linear scaling factor. I finally carry out interferometric experiments in a model containing a single interface at 800 m depth, proving that it is possible to correctly retrieve all 2D SH-TE causal seismic-related direct and reflected coseismic fields, as well as interface response fields, by cross-correlation interferometry, using seismic boundary sources only. These results are promising for the application of 3D seismo-electromagnetic interferometry using seismo-EM layer-code modeling, and later on, in the field. Next, I present an alternative way to effectively decompose fields into their up- and downgoing components and different field types, using recordings at multiple depth levels. I present the theory of this MDL decomposition scheme, followed by successful decomposition of synthetic elastodynamic data sets. I additionally study the implications of laterally-varying media on the horizontal wavenumber-frequency domain MDL decomposition scheme. I demonstrate successful decomposition, using an acoustic approximation and applying a combined multi-component / MDL decomposition approach, of a field data set recorded in Annerveen, in the North of the Netherlands. I address how to effectively use the MDL decomposition scheme in a unified fashion, applied to all wave phenomena including seismo-electromagnetic phenomena. I then make a step towards seismo-electromagnetic inversion, presenting an effective way to carry out a seismo-electromagnetic sensitivity analysis using resolution functions. I start by explaining the theory of resolution functions using a seismo-electromagnetic example. I define the seismo-electromagnetic resolution function for inversion for a bulk density perturbation. I demonstrate the effectiveness of this method by first carrying out a purely electromagnetic sensitivity analysis for a point perturbation in conductivity, located in an isotropic homogeneous half-space. These results are compared with literature results based on analytical homogeneous space Green's function expressions. The result using the seismo-EM layer-code is nearly identical to the literature result. The position of the scatterer is correctly resolved. At the end of this section, I present the results of the fully-coupled seismo-electromagnetic senstivity analysis for a bulk density contrast for a specific source-receiver combination, using single-frequency multi-component line data. I show that the coupled seismo-electromagnetic system is sensitive to a perturbation in bulk density and that the position of the perturbation can be correctly recovered. I finalize this thesis by discussing potential seismo-electromagnetic applications, as well as by providing a brief outlook for future research.@en