Synthetic magnitude generation

Sometimes it is needed to create synthetic earhtquake magnitudes. Here, we describe briefly the way generate magnitudes drawn from an exponential distribution with a given discretization and completeness.

>>> from seismostats.utils import simulate_magnitudes_binned
>>> from seismostats.plots import plot_mags_in_time
>>> n = 100         # number of events to simulate
>>> b_value = 1.5   # b-value of the synthetic catalog
>>> delta_m = 0.05  # magnitude binning of the synthetic catalog
>>> mc = np.ones(n) # completeness of the synthetic catalog
>>> mc[n//2:] = 1
>>> mags = simulate_magnitudes_binned(n, b_value, mc, delta_m)
>>> ax = plot_mags_in_time(mags, np.arange(len(mags)))

Some notes on the implementation:

1. The magnitudes are first drawn from an exponential distribution (with the b-value provided), and then discretized with delta_m. If no delta_m is given, the magnitudes are continuous (down to the float precision)

2. It is possible to vary the completeness and b-value for each earthquake. In the example below, we did so for the parameter mc. If this is not desired, just mc can be given as a simple float.

3. It is also possible to generate magnitudes from a truncated exponential distribution. For this, privide the parameter mag_max.

Figure 1: Synthetic magnitudes with a b-value of 1.5 and changing completeness.