I found an interesting phenomenon while modelling an explosion source (m_xx=m_zz=1, m_xz=0) with Specfem2D with a Dirac source-time function.
With a filter of 0.3-3Hz amplitudes appear in the seismogram after the P-wave. Their time difference would suggest, that they are related to S-waves, which I didn’t expect for an explosion source. With a lower filtering and by using a different source-time function (e.g. Ricker) those amplitudes disappear for the same model.
I was wondering whether this is a common behavior of modelling with Specfem2D, that in higher frequencies especially S-waves pattern appear due to the Dirac source time function?
Do you have a suggestion, how to choose the filter in general in order to supress non-physical patterns related to the Dirac source-time function?
Below I provided a figure with a representation of the model I used, (homogeneous, v_p=3000m/s, v_p/v_s=1.76) and the resulting seismogram for a simulation with different source models (explosion vs. horizontal fracture) and source-time functions (Dirac vs. Ricker).
This behavior is often seen, with any method, when the grid size is too coarse to resolve the relevant wavelengths of the problem. In practice, you should make sure the ratio of element size to minimum wavelength (here \lambda= v_p/(3 Hz )=1000 m ) is <1.
The dominant frequency of your Ricker seems ~1 Hz, thus it has little power at 3 Hz, it’s dominated by wavelengths \approx 3000 m and thus better resolved.
thank you very much for your fast answer!
Is it possible, that it is still related to a different problem?
I chose a gridsize dx of 280m and therefore the ratio of dx/lambda <1. I think with nearly 4 elements (around 15 GLL points) per wavelength the grid shouldn’t be too coarse, right?
Sorry, \lambda_{min} depends on v_s, not v_p as I wrote before. It is 580 m, not 1000 m.
Still, you have about 2 elements per \lambda_{min} which seems fine. I was not aware this issue could appear at such values of \lambda_{min}/\Delta x.
Note also that a Dirac source exacerbates the issue. Far-field velocity is proportional to seismic moment acceleration. Thus, if your moment rate function is a Dirac, the velocity spectrum increases proportionally to frequency. Thus it is dominated by the highest frequencies, the least well resolved. That is challenging for any numerical method. Real sources (e.g. earthquakes) have a steep spectral decay at high frequencies. If you convolve your simulated seismograms with a realistic source time function, the artificial S wave will be substantially damped.
