Time and FrequencyΒΆ

simulation_start_time_sec

  • Optional: Yes

  • Type: Float

  • Description: The start time (in second) for the simulation. This is an optional parameter and the default value is 0.

simulation_end_time_sec

  • Type: Float

  • Description: The end time (in second) for the simulation.

simulation_delta_time_sec

  • Type: Float

  • Description: The time step length (in second) used in the simulation.

simulation_wave_max_freq_hz

  • Type: Float

  • Description: The maximum wave frequency (in Hz) for the simulation.

simulation_node_per_wavelength

  • Type: Integer

  • Description: The number of nodes per wavelength.

simulation_shear_velocity_min

  • Type: Float

  • Description: The minimum shear velocity. Shear velocities in the simulation that are smaller than this value will be replaced with it.

Since Hercules utilizes explicit FEM, the element size \(h\) is determined with shear velocity \(V_S\), nodes per wavelength \(N_p\), and maximum wave frequency \(f_{max}\). The formula can be expressed as

\[h = \frac{V_S}{N_p f_{max}}\]

And since we also defined the minimum shear velocity \(V_{S, min}\), the minimum element size \(h_{min}\) can be derived by

\[h_{min} = \frac{V_{S, min}}{N_p f_{max}}\]

Once you get the minimum element size, the time step \(\Delta t\) can derive as follows.

\[\Delta t = \frac{h_{min}}{V_{P, max}}\]

where \(V_{P, max}\) is the maximum P wave velocity in the domain.