Waves in Discontinuous Coal Seams with Absorption: Finite Difference Simulations

The finite-difference method is a well-established tool for the forward modelling and migration of seismic wavefields in complicated geological media. One problem, however, has been that one could not include the effects of intrinsic attenuation because of numerical limitations. It has been suggested that a Padé approximation to the viscoelastic moduli turns the equations into a numerically tractable form. To achieve this approximation we suggest an approach which is based partly on physical considerations and partly on numerical curve fitting, and is superior to earlier approaches both in accuracy and computational efficiency. Our finite-difference programs for acoustic and elastic wavefields only require about twice as much computer time and storage as for a calculation without absorption. We have carried out numerical simulations of channel waves in discontinuous coal seams and have investigated the reflection and transmission responses of different types of discontinuities for models with and without intrinsic attenuation. The results show that for the most likely range of attenuation (Qcoal~50−100) serious damping of the higher frequencies occurs, especially of the fundamental mode Airy phase. The differences in the reflectivities and transmissivities of different discontinuities are reduced considerably. This makes it much more difficult to detect faults and to discriminate between different fault types and throws than is expected from previous modelling of seam waves without attenuation.