This study investigates the depositional environment, source area, sandstone composition, diagenetic properties, reservoir quality and palaeogeography of the Middle–Upper Cretaceous strata at the Unity and Heglig Fields in the SE Muglad Rift Basin, Sudan. In this study, the subsurface Cretaceous sediments were investigated essentially by seven sedimentological techniques. These included subsurface facies analysis, which was based on 1500 cutting samples and seven conventional cores description as well as on wire line logs and three seismic section analyses, petrographic analyses that included heavy mineral analysis, thin sections and scanning electron microscopic investigations, clay mineral as well as geochemical analyses. The facies description and the analysis of conventional cores from the Bentiu, Aradeiba, and Zarga Formations in the Unity and Heglig Field revealed the presence of nine major lithofacies types, all of them are siliciclastic sediments. They can be interpreted as deposits of fluvial, deltaic and lacustrine environments. Moreover, based on wire line logs, cores and cutting sample descriptions and analyses and also on seismic section analyses, the Middle–Upper Cretaceous strata in Unity and Heglig Fields can be classified into three different units of first-order sequences, i.e. fluvial-dominated unit, lacustrine-dominated unit and deltaic-dominated unit. These depositional units most probably testify to environmental change in response to main tectonic pulses during the Turonian – Late Senonian second rifting phase. The seismic analysis revealed that the maximum thickness of the Cretaceous sediments in the study area reaches about 6000 m in the NW part of the Heglig Field. Moreover, the seismic interpretation has revealed three seismic facies reflection patterns: parallel and subparallel reflection patterns (uniform rates of deposition), divergent reflection pattern (differential subsidence rates) and hummocky clinoform pattern (clinoform lobes of delta). The thin section investigations of the core samples revealed that feldspar accounts for 13.5 – 22 %, that of the quartz and the lithic fragments are ranging between 75.7 – 85.2 % and 0.0 7.3 % respectively. Consequently, the sandstones of the study area are classified as subarkoses. Moreover, the modal analysis of the sandstones revealed, that they stem generally from a continental provenance, transitional between the stable interior of a craton and a basement uplift, which is a basement area of relatively high relief along rifts. This allows the detrital components to be recycled and transported for rather long distances and to be deposited in extensional and pull-apart basins. The reservoir quality of the Bentiu and Aradeiba Formations in general is better than that of the Zarga Formation. The porosity of the Bentiu and Aradeiba Formations ranges between 16.7 – 30.0 % and 18.6 – 25.3 %, respectively, whereas the porosity of the Zarga Formation ranges between 16.3 – 23.7 %. Moreover, the thin section investigations and the scanning electron microscope (SEM) analysis for the sandstones of the study area revealed that their reservoir quality was affected positively and negatively by several diagenetic processes. These processes include: mechanical compaction factors (grain slippage and crushing of the ductile grains), quartz overgrowths, precipitation of siderite and calcite, feldspar and clay mineral authigenesis, dissolution of carbonate and of the labile detrital grains and clay infiltration. Furthermore, the reservoir quality of the study intervals was not only affected by the above mentioned diagenetic processes, but also in a large-scale by the type of depositional environment. The study of the heavy minerals revealed that the amounts of the heavy minerals kyanite and garnet supersede those of zircon, tourmaline and rutile. This indicates a metamorphic source rock of originally granitic and/or granodioritic composition for the sediments of the study area. Three heavy mineral assemblage zones with obvious lateral and vertical continuity were identified: a zircon-rutile zone (ZR), a sillimanite-epidote-hornblende zone (SEH) and a kyanite-staurolite-andalusite-garnet zone (KStAnG). On the basis of the ZTR (zircon-tourmaline-rutile) index as well as on the SEH (sillimanite-epidote-hornblende) index, four major maturation levels were constructed: immature, moderately mature, mature and overmature. The clay mineral analysis allowed the subdivision of the Middle–Upper Cretaceous strata into three to two clay mineral zones, which reflect mainly different environmental and diagenetic conditions. The lower clay mineral zone consists of kaolinite, illite/smectite mixed layer, illite, smectite and chlorite. Whereas, the middle zone consists of kaolinite, smectite, illite/smectite mixed layer, illite and chlorite. The upper zone comprises kaolinite, illite, illite/smectite mixed layer, chlorite and smectite. The lower and the upper clay mineral zones contain higher values of kaolinite in comparison to the middle clay mineral zone, whereas the middle zone contains a higher value of smectite in comparison to the lower and the upper clay mineral zones. The higher amount of the kaolinite in the lower and in the upper zones suggest most probably the intensity of chemical weathering and leaching processes under warm humid climate. The marked presence of smectite in the middle zone suggest that the warm humid climate was interrupted by dry seasons. Moreover, the lower clay mineral zone, which shows an increase of illite, chlorite, mixed layer illite/smectite and a higher illite crystallinity, indicates mixed and transitional influences from environmental/tectonic to burial diagenetic controls. Geochemical investigations revealed preferential enrichment and depletion of certain chemical elements in the lacustrine/fluvial/deltaic environments. For instance, the less mobile elements Ti, Ga, Cr and Zr remained in higher amounts in the proximal facies (i.e. in the fluvial channel bar deposits and in the deltaic mouth bar deposits). In contrast, the more mobile elements Mg, Ca, K and Rb occur in higher concentrations in the distal facies (i.e. in the lacustrine deposits, deltaic distal bar deposits and floodplain sediment).

This study investigates the depositional environment, source area, sandstone composition, diagenetic properties, reservoir quality and palaeogeography of the Middle–Upper Cretaceous strata at the Unity and Heglig Fields in the SE Muglad Rift Basin, Sudan. In this study, the subsurface Cretaceous sediments were investigated essentially by seven sedimentological techniques. These included subsurface facies analysis, which was based on 1500 cutting samples and seven conventional cores description as well as on wire line logs and three seismic section analyses, petrographic analyses that included heavy mineral analysis, thin sections and scanning electron microscopic investigations, clay mineral as well as geochemical analyses. The facies description and the analysis of conventional cores from the Bentiu, Aradeiba, and Zarga Formations in the Unity and Heglig Field revealed the presence of nine major lithofacies types, all of them are siliciclastic sediments. They can be interpreted as deposits of fluvial, deltaic and lacustrine environments. Moreover, based on wire line logs, cores and cutting sample descriptions and analyses and also on seismic section analyses, the Middle–Upper Cretaceous strata in Unity and Heglig Fields can be classified into three different units of first-order sequences, i.e. fluvial-dominated unit, lacustrine-dominated unit and deltaic-dominated unit. These depositional units most probably testify to environmental change in response to main tectonic pulses during the Turonian – Late Senonian second rifting phase. The seismic analysis revealed that the maximum thickness of the Cretaceous sediments in the study area reaches about 6000 m in the NW part of the Heglig Field. Moreover, the seismic interpretation has revealed three seismic facies reflection patterns: parallel and subparallel reflection patterns (uniform rates of deposition), divergent reflection pattern (differential subsidence rates) and hummocky clinoform pattern (clinoform lobes of delta). The thin section investigations of the core samples revealed that feldspar accounts for 13.5 – 22 %, that of the quartz and the lithic fragments are ranging between 75.7 – 85.2 % and 0.0 7.3 % respectively. Consequently, the sandstones of the study area are classified as subarkoses. Moreover, the modal analysis of the sandstones revealed, that they stem generally from a continental provenance, transitional between the stable interior of a craton and a basement uplift, which is a basement area of relatively high relief along rifts. This allows the detrital components to be recycled and transported for rather long distances and to be deposited in extensional and pull-apart basins. The reservoir quality of the Bentiu and Aradeiba Formations in general is better than that of the Zarga Formation. The porosity of the Bentiu and Aradeiba Formations ranges between 16.7 – 30.0 % and 18.6 – 25.3 %, respectively, whereas the porosity of the Zarga Formation ranges between 16.3 – 23.7 %. Moreover, the thin section investigations and the scanning electron microscope (SEM) analysis for the sandstones of the study area revealed that their reservoir quality was affected positively and negatively by several diagenetic processes. These processes include: mechanical compaction factors (grain slippage and crushing of the ductile grains), quartz overgrowths, precipitation of siderite and calcite, feldspar and clay mineral authigenesis, dissolution of carbonate and of the labile detrital grains and clay infiltration. Furthermore, the reservoir quality of the study intervals was not only affected by the above mentioned diagenetic processes, but also in a large-scale by the type of depositional environment. The study of the heavy minerals revealed that the amounts of the heavy minerals kyanite and garnet supersede those of zircon, tourmaline and rutile. This indicates a metamorphic source rock of originally granitic and/or granodioritic composition for the sediments of the study area. Three heavy mineral assemblage zones with obvious lateral and vertical continuity were identified: a zircon-rutile zone (ZR), a sillimanite-epidote-hornblende zone (SEH) and a kyanite-staurolite-andalusite-garnet zone (KStAnG). On the basis of the ZTR (zircon-tourmaline-rutile) index as well as on the SEH (sillimanite-epidote-hornblende) index, four major maturation levels were constructed: immature, moderately mature, mature and overmature. The clay mineral analysis allowed the subdivision of the Middle–Upper Cretaceous strata into three to two clay mineral zones, which reflect mainly different environmental and diagenetic conditions. The lower clay mineral zone consists of kaolinite, illite/smectite mixed layer, illite, smectite and chlorite. Whereas, the middle zone consists of kaolinite, smectite, illite/smectite mixed layer, illite and chlorite. The upper zone comprises kaolinite, illite, illite/smectite mixed layer, chlorite and smectite. The lower and the upper clay mineral zones contain higher values of kaolinite in comparison to the middle clay mineral zone, whereas the middle zone contains a higher value of smectite in comparison to the lower and the upper clay mineral zones. The higher amount of the kaolinite in the lower and in the upper zones suggest most probably the intensity of chemical weathering and leaching processes under warm humid climate. The marked presence of smectite in the middle zone suggest that the warm humid climate was interrupted by dry seasons. Moreover, the lower clay mineral zone, which shows an increase of illite, chlorite, mixed layer illite/smectite and a higher illite crystallinity, indicates mixed and transitional influences from environmental/tectonic to burial diagenetic controls. Geochemical investigations revealed preferential enrichment and depletion of certain chemical elements in the lacustrine/fluvial/deltaic environments. For instance, the less mobile elements Ti, Ga, Cr and Zr remained in higher amounts in the proximal facies (i.e. in the fluvial channel bar deposits and in the deltaic mouth bar deposits). In contrast, the more mobile elements Mg, Ca, K and Rb occur in higher concentrations in the distal facies (i.e. in the lacustrine deposits, deltaic distal bar deposits and floodplain sediment).

This thesis provides a feasibility study on the determination of formation anisotropy parameters from logging-while-drilling (LWD) borehole acoustic measurements. For this reason, the wave propagation in fluid-filled boreholes surrounded by transverse isotropic (TI) formations is investigated in great detail using the finite-difference method. While the focus is put on quadrupole waves, the sensitivities of monopole and flexural waves are evaluated as well. All three wave types are considered with/without the presence of an LWD tool. Moreover, anisotropy-induced mode contaminants are discussed for various TI configurations. In addition, the well-known plane wave Alford rotation has been generalized to cylindrical borehole waves of any order, except for the monopole. This formulation has been extended to allow for non-orthogonal multipole firings, and associated inversion methods have been developed to compute formation shear principal velocities and accompanying polarization directions, utilizing various LWD (cross-) quadrupole measurements.:1 Introduction 1.1 Borehole acoustic configurations 1.2 Wave propagation in a fluid-filled borehole in the absence of a logging tool 1.3 Wave propagation in a fluid-filled borehole in the presence of a logging tool 1.4 Anisotropy 2 Theory 2.1 Stiffness and compliance tensor 2.1.1 Triclinic symmetry 2.1.2 Monoclinic symmetry 2.1.3 Orthotropic symmetry 2.1.4 Transverse isotropic (TI) symmetry 2.1.5 Isotropy 2.2 Reference frames 2.3 Seismic wave equations for a linear elastic, anisotropic medium 2.3.1 Basic equations 2.3.2 Integral transforms 2.3.3 Christoffel equation 2.3.4 Phase slowness surfaces 2.3.5 Group velocity 2.4 Solution in cylindrical coordinates for the borehole geometry 2.4.1 Special case: vertical transverse isotropy (VTI) 2.4.2 General case: triclinic symmetry 3 Finite-difference modeling of wave propagation in anisotropic media 3.1 Finite-difference method 3.2 Spatial finite-difference grids 3.2.1 Standard staggered grid 3.2.2 Lebedev grid 3.3 Heterogeneous media 3.4 Finite-difference properties and grid dispersion 3.5 Initial conditions 3.6 Boundary conditions 3.7 Parallelization 3.8 Finite-difference parameters 4 Wave propagation in fluid-filled boreholes surrounded by TI media 4.1 Vertical transverse isotropy (VTI) 4.1.1 Monopole excitation 4.1.2 Dipole excitation 4.1.3 Quadrupole excitation 4.1.4 Summary 4.2 Horizontal transverse isotropy (HTI) 4.2.1 Monopole excitation 4.2.2 Theory of cross-multipole shear wave splitting 4.2.3 Dipole excitation 4.2.4 Quadrupole excitation 4.2.5 Hexapole waves 4.2.6 Summary 4.3 Tilted transverse isotropy (TTI) 4.3.1 Monopole excitation 4.3.2 Dipole excitation 4.3.3 Quadrupole excitation 4.3.4 Summary 4.4 Anisotropy-induced mode contaminants 4.4.1 Vertical transverse isotropy (VTI) 4.4.2 Horizontal transverse isotropy (HTI) 4.4.3 Tilted transverse isotropy (TTI) 4.4.4 Summary 5 Inversion methods 5.1 Vertical transverse isotropy (VTI) 5.2 Horizontal transverse isotropy (HTI) 5.2.1 Inverse generalized Alford rotation 5.2.2 Inversion method based on dipole excitations 5.2.3 Inversion method based on quadrupole excitations 5.3 Tilted transverse isotropy (TTI) 5.4 Challenges in real measurements 5.4.1 Signal-to-noise ratio (SNR) 5.4.2 Tool eccentricity 6 Conclusions References List of Abbreviations and Symbols List of Figures List of Tables A Integral transforms A.1 Laplace transform A.2 Spatial Fourier transform A.3 Azimuthal Fourier transform A.4 Meijer transform B Stiffness and compliance tensor B.1 Rotation between reference frames B.2 Cylindrical coordinates C Christoffel equation C.1 Cartesian coordinates C.2 Cylindrical coordinates D Processing of borehole acoustic waveform array data D.1 Time-domain methods D.2 Frequency-domain methods D.2.1 Weighted spectral semblance method D.2.2 Modified matrix pencil method