Acoustic Wavefield Simulation in TTI Media with High-order Stagger-grid Finite-difference Scheme

2.5D finite-difference (FD) time domain seismic modelling is a common method to study elastic wave propagation in and around axially symmetric boreholes. Boreholes are often characterized by strong parameter contrasts on a small scale compared to the dominant wavelength. In order to study the influence of the FD-grid spacing on the accuracy of the method, we compare FD-waveforms and dispersion curves of borehole guided waves with analytical results for a simplified Logging-While-Drilling borehole model. Small scale structures of the borehole have to be resolved by a sufficient number of grid points to ensure reliable results. Thus the model is massively oversampled on a scale in the order of one wavelength compared to what is necessary to avoid grid dispersion. This results in an enormous computational effort when using FD-grids with a constant grid spacing. We show that the application of FD-grids with variable grid cell size allows to reduce the required memory and computation time considerably without any loss of accuracy. The variable grid can be refined where necessary, e.g. in the vicinity of the borehole. Furthermore it allows to adjust the FD-grid to exact positions of source, receivers and layer interfaces.