Characteristic wavefield in an experimental rock sample inferred from a 3D FDM simulation

Abstract:

We investigate the origin of wave packets in elastic waves propagate through a rock sample based on a 3D finite difference method (FDM) simulation. Though direct waves of the transmitted waves have been applied to estimate the internal structure of a rock sample, later part of the waveforms did not utilized because their origin were unclear. Understanding the reflection and conversion effect in a rock sample would help to retrieve more information from whole waveform as with the analysis in natural fields.

We numerically simulated the elastic wave propagation in a medium model which covers a cylindrical shape of a rock sample. The model was discretized into 1024 x 1024 x 2048 grid points with an interval of 54 micrometer in horizontal direction and 60 micrometer in vertical direction. The density, P wave velocity, and S wave velocity of the each grid point are assumed to be proportional to the X-ray absorption coefficient derived from the micro focus X-ray CT images of a Westery granite sample. We applied a single point force on the boundary of the model sample which mimics realistic transducer movement.

The wave propagation movie obtained from the numerical simulation shows very complicated wavefield in a rock sample. Because a rock sample is small and closed, once waves are radiated, they were trapped in the sample by repeating reflection and conversion. Many reflected waves which followed by the converted waves were generated at the sample side surface as well as the upper and lower end. The phase with the largest amplitude propagate along the curved boundary was detected as Rayleigh wave from the particle motions on the sample side surface. Additionally, the surface waves were observed not only in the horizontal section but also in the vertical section.

Our simulation indicated that the later phases of the transmitted waves are highly affected by the sample boundary. In order to extract accurate interior information from the transmitted waves, elimination technique of the boundary effect should be considered.