Yup, all looks good!
When building material models for use with wave propagation solvers such as Salvus, there are a few factors one needs to consider. Obviously we need to ensure that the spatial complexity of the model is adequetly captured by whatever spatial discretization we are choosing. What is less obvious however is that the details of the solver's spatial discretization are intimitely to both the spatial complexity of the model
and the spatial complexity of the physical process we are solving for. When considering the propagation of seismic waves we are somewhat lucky that the solutions are
band-limited and the spatial complexity of the solution can be reliably estimated before any simulations are run.
Using the simple formula
λmin=vmin⋅fmax−1, we have an estimate
λmin for the minimum wavelength in our simulation when given the minimum velocity in the model (
vmin) and the maximum frequency in the forcing function (
fmax). It is this minimum wavelength, in conjuction with the spatial complexity of the model itself, which places the most restrictions on how we should build and discretize our model. No matter which numerical method we choose to solve the wave-equation we must have
at least a certain number of "points" per minimum wavelength to ensure an accurate solution. In finite-difference (FD) simulations, these points are the discrete points of the FD grid. In spectral-element simulations (such as those performed by Salvus) these points are the GLL point locations with each spectral-element.
In Salvus, to properly balance accuracy and performance, we suggest to use anywhere from 6 - 9 points per minimum wavelength. When using standard 4th order elements (which have 5 GLL points along each edge), this equates to using 1.25 - 2 elements per wavelength. With this discussion in mind, one must first determine what frequency band they are interested in before one proceeds to the meshing stage, and this is why we now begin with the definition of our source wavelet. Below we choose a Ricker wavelet with a peak frequency of 5Hz, and plot the source-time function as well as the wavelet's frequency content.