Abstract:
This thesis shall consider the analytical construction and numerical computation of synthetic seismograms for models of the Earth's structure that have seismic activity present.
The procedure of working in the frequency domain with the terms that describe the nature of the source of the seismic activity, the nature of the medium that the seismic waves propagate through, the interaction of the seismic radiation with the surface of the medium, and the properties of the seismograph that measures the resulting surface motion is developed. Then the process of constructing what hereinafter shall be known as the displacement product in the frequency domain and inverting it to obtain the seismograph displacement as a function of time is developed. Furthermore, the numerical computation of the Fourier transform, the inverse Fourier transform, and the associated Hilbert transform is discussed.
With the general theory of producing and computing synthetic seismograms having been established it is applied to two specific examples. The first example is the seismogram resulting from the reflection of seismic radiation at the Earth's surface due to a fault slip buried beneath it. The discussion shall consider the modelling of the fault slip as a double couple and the approximation of the seismic radiation distribution by a plane wave distribution and examine qualitatively the effects of it. The second example is the seismogram resulting from the reflection of seismic radiaion at the Earth's surface, after it has already been reflected off a subducting zone beneath the surface, having originated from the detonation of an explosive charge on the surface. The explosive charge is modelled a point source potential and the subducting zone by an arbitrarily orientated dipping layer package. Using the reflectivity method, the stationary phase technique, and coordinate system transformations the seismogram is obtained. Finally, a procedure for calculating the arrival times of the seismic waves reflecting off each layer in the layer package is obtained and a possible application of this is suggested.
