Modelling P-SV seismic wave in homogeneous media for the Brazilian territory

Resumo

In the literature, there are few works of seismic modeling in Brazil. We know that Brazil is on the
South American plate making the country have very few seismic events, but it is not a guarantee for some faults
can collapse at any time, and earthquakes of magnitude greater than normal are possible. Earthquakes are violent
vibratory phenomena of short duration and, at times, of great intensity generated around a point source called
procedente, in which large displacements of masses are produced, generating longitudinal and transverse waves.
The longitudinal waves vibrate in the direction of the wave propagation and they are the first to be perceived. The
tranverse waves vibrate perpendicular to the propagation direction and they delay in relation to longitudinal waves.
In this context, the mathematical modeling of seismic waves allows the elaboration of theorical seismograms that
allow predicting the characteristics of earthquakes, depending on the geogical conditions. This work describes
the propagation of P (longitudinal waves) and SV (transverse waves) seismic waves modeled by equations of
motion in elastical media, since the Earth behaves as a deformable material. So, our partial differential equations
(PDE) describe the propagation of seismic waves in a vertical two-dimensional system (x and z coordinates), in
homogeneous media, given by a source, assuming Neumann boundary conditions. For simplicity, the vertical
two-dimensional domain is considered rectangular. The point source is modeled using a Gaussian-type function,
located at a point inside the domain. To solve this PDE system, the finite difference method (FDM) is used. The
boundary conditions are also discretized by FDM. The simulations will be carried out for different media, described
by different densities in the terrestrial layers, and for different vertical positions for the point source (hypocenter),
generating different seismological maps.