Seismic wave modelling using the boundary element method
The main objective of this thesis is to use the boundary element method as an efficient and advantageous numerical approach to model the seismic signals received at selected receiver points due to a source located within a geophysical structure. These signals may travel through different geophysical structures. This work determines whether rock interfaces can be identified from the signals received at selected points. The method proves to be most satisfactory and more easily applicable for unbounded media than for bounded media. Each layer in the media of interest is assumed to be linearly elastic, homogeneous and isotropic. This assumption is used for both two- and three-dimensional geometries. Throughout this research linear and constant time approximations are used to represent the displacements and tractions, respectively. With the use of these temporal variations all time integrations are evaluated analytically. The two-dimensional boundary kernels and internal flux kernels have been derived. New kernels for boundary and internal points have also been obtained for three-dimensional scalar waves. In addition, the three­ dimensional elastodynamic boundary kernels have been evolved. Constant elements are normally employed to discretize the boundary. To determine the dynamical response constant elements are seen to be well suited for the geometries used here. The improper integrals are evaluated analytically in two dimensions. In three dimensions two different techniques are used to cope with the singularities. Some available computer codes for the boundary nodes are extended to determine material behaviour at internal points. For three-dimensional cases some programs are developed with the help of the two-dimensional programs. For layered materials these codes are expanded for each layer as subprogram. In spite of the fact that the existence of the interfaces makes the solution of the problem tend to instability, this analysis shows that the BEM is capable of treating layered media problems. In general, the examples presented show that the time domain direct BEM is stable for practical applications. Some supplemental layered media results are also presented to show the usefulness and range of the method in real applications. These results also demonstrate the validity of the extended and developed programs in this thesis. Where possible the current work is compared with that of others. Strong interface and other reflections are visible in all seismograms though somewhat weaker in the case of three dimensions. The potential and flux changes across a plane body have been examined in two and three dimensions.
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