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Local, regional and teleseismic earthquakes recorded at seismic stations in northern Kenya have been analysed to determine the seismicity in this region and the crustal and upper mantle structure beneath an array on the north-eastern flank of the Kenya dome. A total of 389 microearthquakes, occurring during the period 17th Jan. to 26th Aug., 1981, have been located using a simple half space velocity model. The seismic activity is mainly confined to the Kenya rift and a zone approximately 150km to the east of the main rift. The northward extent of the activity suggests that the active section of the rift continues beneath Lake Turkana. Apparent velocities of local and regional earthquakes recorded at the Ngurunit array have been interpreted in terms of crustal velocity structure. A two layered crustal velocity model has been derived. The velocity of the upper crustal layer is considered to increase linearly with depth, according to the function V = 5.8 + 0.0245z. The velocity of the lower crustal layer is 6.5 0.2 km/s and the intermediate crustal boundary is placed at 24km. The variation of apparent velocity with azimuth of Moho arrivals suggests an eastwardly dipping Moho of 7 beneath the array. The depth of the Moho directly beneath the array is derived to be 46km and the velocity of sub-Moho material is 8.3 0.2 km/s. Delay times and slowness measurements of teleseismic P wave arrivals indicate the presence of anomalously low P wave velocity material in the upper mantle. Three-dimensional ray tracing modeling suggests a thickening of the anomalous body to the north and east of the array, such that the top surface of the body reaches to within 60-80km of the ground surface. The thickening may be associated with rift structures beneath Lake Turkana and Quaternary volcanic activity observed on the eastern flank of the Kenya dome.

A seismic refraction profile was undertaken to investigate the source of an aeromagnetic anomaly located above the Widmerpool Gulf, East Midlands. Ten shots were fired into 51 stations at c. 1.5km spacing in a 70km profile during 41 days recording. The refraction data were processed using standard techniques to improve the data quality. A new filtering technique, known as Correlated Adaptive Noise Cancellation was tested on synthetic data and successfully applied to controlled source and quarry blast data. Study of strong motion data reveals that the previous method of site calibration is invalid. A new calibration technique, known as the Scaled Amplitude method is presented to provide safer charge size estimation. Raytrace modelling of the refraction data and two dimensional gravity interpretation confirms the presence of the Widmerpool Gulf but no support is found for the postulated intrusion. Two dimensional magnetic interpretation revealed that the aeromagnetic anomaly could be modelled with a Carboniferous igneous source. A Lower Palaeozoic refractor with a velocity of 6.0 km/s is identified at a maximum depth of c. 2.85km beneath the Widmerpool Gulf. Carboniferous and post-Carboniferous sediments within the gulf have velocities between 2.6-5.5 km/s with a strong vertical gradient. At the gulf margins, a refractor with a constant velocity of 5.2 km/s is identified as Dinantian limestone. A low velocity layer of proposed unaltered Lower Palaeozoics is identified beneath the limestone at the eastern edge of the Derbyshire Dome. The existence and areal extent of this layer are also determined from seismic reflection data. Image analysis of potential field data, presents a model identifying 3 structural provinces, the Midlands Microcraton, the Welsh and English Caledonides and a central region of complex linears. This model is used to explain the distribution of basement rocks determined from seismic and gravity profiles.

Marine seismic exploration is a method employed by the hydrocarbon industry to find geological structures in the sub-surface with the potential to contain trapped hydrocarbons. A source of seismic energy is towed behind a ship. The energy produced by the source propagates as a sound wave through the sea into the sub-surface. Within the sub-surface the energy is reflected, refracted and diffracted. The ship also tows an array of hydrophones behind the seismic source, and these are used to measure the wavefield. If the source signal is known, then the received signal at each hydrophone can be deconvolved for the source signal to obtain the impulse response of the earth between the source and the hydrophone. These impulse responses can highlight some of the structures in the subsurface. Maps of the subsurface built up from these impulse responses are then interpreted to estimate the locations of trapped hydrocarbons. The most commonly used seismic source is the seismic air gun, which is a canister containing highly compressed air. The air is released into the sea, forming an oscillating bubble. There are two methods used by industry to determine the signal produced by an air gun or air gun array: (1) modelling, and (2) extrapolation from near-field measurements. Traditionally, industry uses the first method. With broader bandwidth data that are being recovered in data processing by removing the sea-surface reflection at the source and receiver (source and receiver ghosts), it has been found that modelling is inferior to extrapolation from near field measurements, although industry has been slow to adopt the second method. Despite this change, modelling remains a valuable tool in the design of air gun arrays, where designs can be optimised by adjusting parameters of the array and using modelling to determine the wavefield of each variation of the array. The aim of this work is to develop methods which can improve on current air gun bubble modelling. In this thesis I develop a novel artificial boundary condition for use in finite volume simulations of oscillating bubbles. The purpose of the work is an improvement to the modelling of seismic air gun bubbles. However, the techniques presented in this thesis are not limited to air gun bubbles, but are applicable to any oscillating bubbles, or indeed any fluid dynamics problem which is spherical in nature, close to spherically symmetric, and produces flow speeds of low (< 0:1) Mach number some distance from the region of interest. The boundary condition is based on an existing approximation to the motion around a spherical bubble, which is derived from the asymptotic solution to the motion in the far field. It is applied as follows: (1) use the solution on the domain boundary to calculate the approximate solution external to the domain; (2) use the approximate external solution to calculate spatial derivatives of properties on the domain boundary, due to the external solution, and (3) use the spatial derivatives to describe characteristic waves incoming to the domain. I develop a finite volume scheme in which I apply this boundary condition. I present the results of one- and two-dimensional of simulations using this scheme, and demonstrate the efficacy of this boundary condition. The boundary condition performs well, allowing finite volume simulations of bubbles to be carried out for long run-times (5 105 time steps with a CFL number of 0:8) on highly truncated domains, in which the boundary condition may be applied within 0:1% of the maximum bubble radius. Conservation errors due to the boundary condition are found to be of the order of 0:1% after 105 time steps. One- and two-dimensional results show a third-order convergence rate of errors due to the boundary condition as the domain is enlarged. The one- and two-dimensional simulations of air gun bubbles I present are, to my knowledge, the first finite volume simulations of air gun bubbles carried out, and the first air gun bubble simulations in which the contents of the bubble are not considered to be homogeneous. Two-dimensional results show non-spherical aspects of air gun bubbles, which may be incorporated into models used by industry. The model captures surface instabilities, bubble translation and deformation due to gravity, and the formation of jets due to asymmetries on collapse. The results indicate that bubble surfaces are unstable throughout collapse. These phenomena are shown to increase the damping of bubble oscillations. The results of the two-dimensional air gun modelling highlight the potential value of my artificial boundary condition, and also the aspects of my computational scheme which require improvement. I extend the numerical scheme to include viscous effects, which I show to have limited impact on the signals emitted by air gun bubbles, although the influence of a boundary layer around the bubble is significant, causing an 18% reduction in rise rates. I extend the scheme to include the effects of the sea surface, and present results which show the impact of the reflection from the sea surface (the ghost wave) on the bubble. This extension shows the reflection of the ghost wave off the bubble, which provides a novel explanation of some of the higher frequencies present in measurements. This extension further increases the practical value of my contribution, and further demonstrates the ability of the boundary condition to handle asymmetrical flow features.

The Derbyshire Dome is thought to have been a stable uplifted area since at least Lower Carboniferous times. This project is principally concerned with four 30km seismic refraction lines which crossed the limestone outcrop of Derbyshire and N. Staffordshire in order to investigate the Dome's upper crustal structure, using quarry blasts as seismic sources. A time-term analysis of refracted arrival data defined basement structure more complicated than implied by the surface geology. The interpretation of these data was complicated by high (5.6-5.8km/s) velocity refractions from dolomitic horizons within the limestone sequence; the mean overburden velocity was determined to be about 5.2 km/s. The Dome could be divided into two pre-Carboniferous geological units separated approximately by the line of the NNW trending Bonsall Fault. To the north a broadly domal refractor of velocity 5.5-5.55km/s was mapped, and thought to correlate with both the shallow pre-Carboniferous volcanics encountered by the Woo Dale borehole and"the Ordovician shales encountered by the Eyam borehole below 1.8km of limestone. This refractor accordingly deepens beneath the Carboniferous sedimentary basins flanking the Dome. To the south of the Bonsall Fault zone, the Carboniferous was found to be underlain by a refractor of velocity 5.63-5.7km/s, thought to be of Precambrian material similar to the rocks of Charnwood Forest, Leicestershire, some 40km south. By analysing later arrivals, this refractor has been mapped to the north of the Bonsall Fault at a depth of 2.5-3.5km. The shallower Lower Palaeozoic refractor is thought to be no more than 500m thick, and underlain by lower velocity, possibly Cambrian, material. This interpretation is consistent with the Bouguer anomaly map of the region, and sheds light on the structural control of Carboniferous sedimentation. The basement fault dividing the two pre-Carboniferous units is thought to have been active during the Dinantian as the northern unit tilted eastwards.

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