Radiation Pattern of Seismic Sources Via Disc-Source Analysis

Seismic exploration industry is largely based on the concept of the explosive point source, whose radiation pattern is spherically isotropic in acoustic homogeneous media.. In elastic media. the radiation pattern of a point source is not uniform over the phase surface and depends on the load direction and on the type of the generated waves. The situation drastically changes when one considers the drill-bit radiation source. The use of drill-bit as a source of energy was advocated a few decades ago, but it 'rang hollow until recently. Nowadays it emerges as one of the most attractive technologies: the method does not require any borehole recording, and therefore no risk to the borehole is involved. What is striking, however, is that the drill-bit source is poorly understood, probably due to the high complexity of its mathematical treatment. This makes difficult an accurate interpretation of continuously reeorded data. In the current study we develop a theory for disk-type sources with a combined load that generates elastodynamic waves, that tackles the drillbit source radiation pattern problem. We derived an explicit expression for the drill-bit source and solved the inhomogeneous wave equations for the Lame's potentials using Fourier-Hankel transform. We show that the radiation pattern of the drill-bit source significantly differs from the point source radiation pattern. This is in agreement with the observed data generated in the drill-bit experiments, demonstrating the viability of disk-type sources,