P. Hornby

On the Reality of Antisymmetric Stresses in Fast Granular Flows

Starting from the virtual power expression for fast flow of dense assemblies of rough, slightly inelastic spheres, we derive expressions for the average stress tensor, momentum and angular momentum balances and corresponding variational boundary conditions. We show that the stress tensor can be decomposed into two parts with distinct physical significance. The first part can be interpreted as an area averaged stress tensor, which is nonsymmetric in general. The second part is obtained as the divergence of a third order tensor which can be interpreted as the difference between the area and the volume averages of the stress tensor. Accordingly, the stress tensor is symmetric for quasistatic flow.

Energy and averages in the mechanics of granular materials

Abstract We derive a general thermo-mechanical theory for particulate materials consisting of granules of arbitrary whose material points possess three translational and three independent rotational degrees of freedom. Additional field variables are the translational and rotational granular temperatures, the kinetic energies shape and size. The kinematics of granulate is described within the framework of a polar continuum theory of the velocity and spin fluctuations respectively and the usual thermodynamic temperature. We distinguish between averages over particle categories (averages in mass/velocity and moment of inertia/spin space, respectively) and particle phases where the average extends over distinct subsets of particle categories (multi phase flows). The relationship between the thermal energy in the granular system and phonon energy in a molecular system is briefly discussed in the main body of the paper and discussed in detail in the Appendix A .

Improved edge detection in potential field maps and graphical estimation of depth-to-the-top

Summary We present an algorithm that improves the detection of minor anomalies and patterns in potential field maps. Its use in conjunction with standard edge detection algorithms provides a tool for visual estimation of depth-to-the-source in gravity and magnetic maps.

Geophysical feature removal by multiscale edge suppression

We present a procedure to remove or isolate specific features from 1D profiles or images. The procedure works by manipulating the multiscale edges and reconstructing the image. A modification of the Mallat and Zhong (1992) reconstruction algorithm is proposed. The applications are in the fields of gravity and magnetic images for geophysical prospecting.

Earthworms; "multiscale" edges in the EGM96 global gravity field

Summary We perform edge detection on the EGM96 global geodetic gravity field. The technique is in accord with our wavelet based multiscale edge analysis, which is valid for a flatearth approximation. For the spherical earth, it is not clear that the technique yields a formal wavelet transform. However, spherical results appear as interpretable as the flat-earth results at short scales. In Australia, we find general agreement with the flat-earth results, and note a correlation between results from seismic tomography and our present work.

Application of wavelet theory to the analysis of gravity data.

Summary. The fundamental equations of potential field theory have an interesting interpretation when regarded as a particular case of a multiscale wavelet transform. This allows the implementation of algorithms for image processing and inversion in a parameterisation that is geologically natural and meaningful.