THE SCATTERING OF SH-CHANNEL WAVES BY A FAULT IN A COAL SEAM*

The imaging of faults in coal seams by the in-seam seismic method has now become standard practice. In the UK over 300 surveys have been undertaken and the technique is now part of the exploration arsenal of colliery planners. From these users comes the pressure for two major improvements, namely an increase in range and target identification. This paper is directed towards the latter problem. It has long been recognized that the reflected channel waves must contain information on the fault structure that caused the reflection, and model experiments have been undertaken to investigate the reflection process. Only recently, however, have attempts been made to quantify the reflection process. Calculations using both the finite-difference and finite-element techniques have been carried out, and estimates of the reflection coefficient as a function of frequency have been obtained. The object of this paper is to extend these considerations by calculating analytically the scattering matrix of an SH-channel wave after interaction at a fault plane. The scattering matrix is calculated as a function of frequency, hade angle, and fault throw. The method employed is based on the decomposition of the incident SH-channel wave into Fourier components, the calculation of plane wave reflection and transmission coefficients within the constraints of geometrical acoustics, and finally the synthesis of the scattering matrix by application of the Helmholtz-Kirchhoff integral. The calculation throughout is restricted to normal modes.