Seismic wave modelling using finite difference methods
The main aim of the thesis is to determine the most satisfactory numerical approach to model numerically seismic wave propagation, and also to ascertain if rock interfaces could be inferred from signals received at a geophone. We mainly employ two different models together, namely the "Parsimonious staggered grid" and the "Box" model. So far as we are aware nobody else has studied these two models in conjunction and this is a particularly novel aspect of this work. Also this approach enhances flexibility and accuracy of the numerical solution. We consider the propagation of seismic waves in both 2-D and 3-D coordinate systems and include the use of boreholes for the source of signals, and also for geophones. One goal of this work was to begin to fill in this gap by including simple borehole configurations within elastic media our new approach modelling, which we have completed successfully. We investigate the appropriateness of the different boundary conditions used to manufacture a finite computational domain. The Reynolds ABCs are found to be marginally better than Clayton-Engquist ABCs and are stable in all cases for our approach. We also adopt a scaling technique with variable grid geometry so as to extend the scope of the domain under consideration. The approach can prove most useful in single borehole modelling if used with care. We also consider particularly the interface boundary conditions for 2-D coordinate systems and some of the models used by other researchers. Where possible we compare our work with that of others. These conditions proved stable for both 2-D acoustic and elastic wave propagation and enhanced interface reflections. Strong interface reflections were visible in all Cartesian seismograms though somewhat weaker in the case of cylindrical coordinates.
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