Elastic wave propagation in model sediments – II

Summary. A fluid-saturated cubic packing of like elastic spheres is taken to be in equilibrium under the effect of gravity and the effects of a superimposed low-frequency elastic wave are considered. In the first place, expressions for the wave velocity, dispersion and attenuation are derived for the dry packing. This dynamic theory leads to the result that, for very low frequencies, the wave velocity is proportional to the third root of the depth and not the sixth root as is obtained by using the effective elastostatic modulus of the packing. For the fluid-saturated packing, two waves, termed respectively the 'solid wave' and the 'fluid wave', are found to propagate. The 'solid wave' has the characteristics of a wave propagating within a dry packing whose parameters differ in a specified way from those of the original packing, whereas the 'fluid wave' has those of a wave within a homogeneous fluid with similarly modified parameters.     

The Calculation of the Electromagnetic Fields of a Sheet Current Source with Arbitrary Spatial Intensity Distribution over a Layered Half Space—I.: The General Method and Results

Electromagnetic induction by a non-uniform source over a layered half-space is studied. A method is described for solving such problems when the current intensity distribution is such that no analytic integration to obtain the field quantities is possible. A number of models are considered using a general computer program. Apparent resistivity curves are calculated and compared with previous results. Phase curves and field component profiles are calculated.     

P-wave seismograms from continuously varying transition zones—II. Elastic media

Summary. A class of elastic transition zones are modelled by considering a homogeneous half space overlying an inhomogeneous half space with a bounded and monotonically increasing profile for the rigidity modulus and constant Poisson's ratio and density. Reflected P waves due to a compressional point source in the upper half space are studied in the frequency and time domains by means of numerical contour integration in the complex k plane and the Fast Fourier Transform (FFT). Results from the exact fourth-order elasticity theory are compared with those from the approximate decoupled equations for P and SV waves. Agreement is observed between the two theories at high frequencies beyond the caustic range.     

Elastic wave propagation in model sediments —I

Summary. A fluid-saturated packing of like elastic spheres is used as a model of an oceanic sediment and a method is presented for calculating the effective velocities of elastic waves in such a medium. In particular the method is applied to low-frequency waves travelling vertically down a cubic packing, saturated with an inviscid fluid and initially at rest under a uniform compressive force. It is found that two waves propagate and moreover, that their velocities are not related through the usual equations of classical elasticity to the effective elastic moduli for static deformation of the packing. For a dry packing, there is found to exist a 'cut-off' frequency above which the wave decays with depth. An extension of the method to slightly viscous fluids is also given.