Velocities of compressional and shear waves in limestones

Carbonate rocks are important hydrocarbon reservoir rocks with complex textures and petrophysical properties (porosity and permeability) mainly resulting from various diagenetic processes (compaction, dissolution, precipitation, cementation, etc.). These complexities make prediction of reservoir characteristics (e.g. porosity and permeability) from their seismic properties very difficult. To explore the relationship between the seismic, petrophysical and geological properties, ultrasonic compressional- and shear-wave velocity measurements were made under a simulated in situ condition of pressure (50 MPa hydrostatic effective pressure) at frequencies of approximately 0.85 MHz and 0.7 MHz, respectively, using a pulse-echo method. The measurements were made both in vacuum-dry and fully saturated conditions in oolitic limestones of the Great Oolite Formation of southern England. Some of the rocks were fully saturated with oil. The acoustic measurements were supplemented by porosity and permeability measurements, petrological and pore geometry studies of resin-impregnated polished thin sections, X-ray diffraction analyses and scanning electron microscope studies to investigate submicroscopic textures and micropores. It is shown that the compressional- and shear-wave velocities (V-p and V-s, respectively) decrease with increasing porosity and that V-p decreases approximately twice as fast as V-s. The systematic differences in pore structures (e.g. the aspect ratio) of the limestones produce large residuals in the velocity versus porosity relationship. It is demonstrated that the velocity versus porosity relationship can be improved by removing the pore-structure-dependent variations from the residuals. The introduction of water into the pore space decreases the shear moduli of the rocks by about 2 GPa, suggesting that there exists a fluid/matrix interaction at grain contacts, which reduces the rigidity. The predicted Biot-Gassmann velocity values are greater than the measured velocity values due to the rock-fluid interaction. This is not accounted for in the Biot-Gassmann velocity models and velocity dispersion due to a local flow mechanism. The velocities predicted by the Raymer and time-average relationships overestimated the measured velocities even more than the Biot model.

Convectively coupled equatorial waves in high resolution Hadley centre climate models

Current global atmospheric models fail to simulate well organised tropical phenomena in which convection interacts with dynamics and physics. A new methodology to identify convectively coupled equatorial waves, developed by NCAS-Climate, has been applied to output from the two latest models of the Met Office/Hadley Centre which have fundamental differences in dynamical formulation. Variability, horizontal and vertical structures, and propagation characteristics of tropical convection and equatorial waves, along with their coupled behaviour in the models are examined and evaluated against a previous comprehensive study of observations. It is shown that, in general, the models perform well for equatorial waves coupled with off-equatorial convection. However they perform poorly for waves coupled with equatorial convection. The vertical structure of the simulated wave is not conducive to energy conversion/growth and does not support the correct physical-dynamical coupling that occurs in the real world. The following figure shows an example of the Kelvin wave coupled with equatorial convection. It shows that the models fail to simulate a key feature of convectively coupled Kelvin wave in observations, namely near surface anomalous equatorial zonal winds together with intensified equatorial convection and westerly winds in phase with the convection. The models are also not able to capture the observed vertical tilt structure and the vertical propagation of the Kelvin wave into the lower stratosphere as well as the secondary peak in the mid-troposphere, particularly in HadAM3. These results can be used to provide a test-bed for experimentation to improve the coupling of physics and dynamics in climate and weather models.

Approximations to the scattering of water waves by steep topography

A new method is developed for approximating the scattering of linear surface gravity waves on water of varying quiescent depth in two dimensions. A conformal mapping of the fluid domain onto a uniform rectangular strip transforms steep and discontinuous bed profiles into relatively slowly varying, smooth functions in the transformed free-surface condition. By analogy with the mild-slope approach used extensively in unmapped domains, an approximate solution of the transformed problem is sought in the form of a modulated propagating wave which is determined by solving a second-order ordinary differential equation. This can be achieved numerically, but an analytic solution in the form of a rapidly convergent infinite series is also derived and provides simple explicit formulae for the scattered wave amplitudes. Small-amplitude and slow variations in the bedform that are excluded from the mapping procedure are incorporated in the approximation by a straightforward extension of the theory. The error incurred in using the method is established by means of a rigorous numerical investigation and it is found that remarkably accurate estimates of the scattered wave amplitudes are given for a wide range of bedforms and frequencies.