Regarding the velocity and acceleration components

[VarunD21029]

Hello everyone !!!

I am simulating an event of Mw>7 in specfem3d using the CMT solution of USGS. My displacement time histories are very smooth without oscillating frequencies. Due to velocity time histories, amplitudes are very low. Although I have a minimum resolvable frequency of 1 Hz the, Fourier spectra of the same do not show amplitude up to 1Hz. Ant suggestions on how to handle it. I am using the gaussian source time function.

[jpampuero]

The spectrum of a gaussian source time function is also a gaussian. A gaussian spectrum decays very steeply with increasing frequency. To simulate a more realistic frequency content, you can use a different source time function.

[VarunD21029]

The spectrum of a gaussian source time function is also a gaussian. A gaussian spectrum decays very steeply with increasing frequency. To simulate a more realistic frequency content, you can use a different source time function.

Thanks for your reply. Can you also suggest which source time function I should use from the available options in the specfem3d?

[jpampuero]

I think the only source time function (STF) available in specfem3d is a gaussian. Thus, to use an arbitrary STF you should run specfem3d with "half duration = 0" (implying a Dirac STF to compute Green's functions, https://specfem3d.readthedocs.io/en/latest/05_running_the_solver/), then convolve the output seismograms by your own STF. An example of STF that has an omega-squared spectrum, typical of earthquakes, is given by equations 2 and 3 of Juhel et al (2018, https://doi.org/10.1029/2018JB016698). After convolving by your preferred STF, I recommend low-pass filtering the seismograms to remove frequencies that are above the maximum frequency resolved by the simulation (fmax ~ S_wave_speed / element_size ).

[VarunD21029]

Thanks a lot these replies are extremely valuable for me, who is starting with the software.

[jpampuero]

Actually, several STFs are available as well as arbitrary STF defined by the user. See "source_time_function" and "USE_EXTERNAL_SOURCE_FILE" in https://specfem3d.readthedocs.io/en/latest/05_running_the_solver/#running-the-solver-xspecfem3d Also, Hom Nath Gharti is implementing Brune's STF, which has a more realistic spectrum for earthquakes (omega-squared decay): https://github.com/SPECFEM/specfem3d/pull/1649