Abstract

The Direct Solution Method (DSM) is used to solve the 1-dimensional scalar elastic equation of motion numerically. We calculate synthetic seismograms for a homogeneous medium. A comparison between the numerical (DSM) and analytical solutions is made to verify the accuracy of the former. The analytical solution is obtained from the strong form of the 1-D equation of motion. The relative error of the numerical solutions is negligible (0.07%), and matches the theoretical relative error expected for the DSM. Theoretical waveforms are computed. An analysis of phase arrivals and polarities provides a good illustration of the physics of waves propagating up and down in a 1-D homogeneous medium.

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