When reflection images are studied, often only the zero-offset reflectivity is considered, however, taking into account the angle-dependent reflectivity can add additional information about the Earth's subsurface. This additional information can be used to extract the properties of the subsurface using the amplitude variation with offset (AVO) analysis techniques. However, the presence of a complex overburden can significantly deteriorate the AVO response, especially for deep targets. To overcome this problem, the overburden effects can be removed by redatuming the reflection response at a depth level below the overburden. The Marchenko method has the potential to correctly retrieve the angle-dependent reflectivity in acoustic media without distortions due to multiple scattering caused by the overburden. The method estimates the downgoing and upgoing Green's functions of a virtual source located in the subsurface from surface reflection data and an estimate of the direct arrival from the location of the virtual source. The estimated Green's functions represent accurate upgoing and downgoing wavefields as they contain all orders of internal multiple reflections of the subsurface. These internal multiple reflections contribute to retrieving the reflectivity accurately in the redatumed reflection response. By deconvolving the retrieved upgoing Green’s function with the downgoing Green’s function, a new reflection response is obtained, with virtual sources and virtual receivers in the subsurface. The resultant reflection response is free of spurious events related to internal multiples in the overburden and contains the correct amplitudes. The angle-dependent reflectivity of the redatumed response can be obtained by summing the reflection coefficients along lines of constant ray parameter or angle. Potentially, the retrieved angle-dependent reflection coefficients obtained by this method can be used as input in a subsequent inversion process to obtain the velocity and density of the subsurface.

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.