The first eight chapters of this thesis describe a study of the magnetic effects of drilling on bore cores of sedimentary rocks. Extensive rock and palaeo- magnetic methods were used to investigate such effects in three collections of bore cores from the North Sea and Sellafield, U.K., and Prudhoe Bay, Alaska. It is evident that a drilling imposed remanent magnetisation (DIRM) resides in the North Sea and Prudhoe Bay bore cores which is characterised by symmetries in its intensity and direction relative to the core axis. Such DIRM correlated well with the theoretically modelled magnetic field at one end of a steel drill barrel. The DIRM intensity distribution also appeared to be correlated with variation in the radial remanence susceptibility (i.e. the capacity of remanence acquisition) in the North Sea and Prudhoe Bay cores and magnetic susceptibility in the North Sea cores. Simulation experiments of shock impact conducted on bore core materials suggests that shock/vibration of the drill barrel is the major process that is responsible for the radial variation in core magnetic properties. Titanomagnetite (including magnetite) and pyrrhotite are the major carriers of DIRM but there is no DIRM identified in bore cores in which hematite is the only ferromagnetic mineral. Chapter 9 describes a novel attempt in using fractal geometry to statistically depict the geomagnetic field reversal sequence. A fractal distribution is shown to occur for longer geomagnetic polarity intervals (> 0.28 Ma) in terms of a power law relationship between interval length and cumulative number for the last 158 Ma. A simulation study indicates that the deviation from the power law at shorter intervals (< 0.28 Ma) is caused by missing of short intervals due to the limit of resolving power. This is strongly supported by a fractal model (i.e. a Cantor set) introduced for relating the shortest polarity interval, the transition time and the fractal dimension. Normal and reversed polarity intervals have similar fractal dimensions, suggesting that there is no, statistically, fundamental difference between the two magnetic polarity states.