User_Guide_MCE

USER GUIDE for Completeness Magnitude Estimation
After the User adds the Service into his/hers personal workspace, the following screen appears (Figure 1):

Figure 1.
The user is now requested to fill the fields shown in figure 1.

• Use Seismic catalog: The user may click on "change input" button in order to use a seismic catalog data among the ones that are already uploaded in his/hers personal workspace.
• Select Magnitude Scale: The user may chose among different magnitude scales (e.g M_L, M_W), in the Episodes where these scales are available.
• Time Unit: The user can here select a time unit among 'Day', 'Month' and 'Year'. This step is necessary in order to normalize the a-value of the Gutenberg-Richter law, according to the selected unit.
• Number of synthetic datasets: The user inserts the number of synthetic datasets in the empty box which should be an integer between 10 and 10,000 (default value is 500). Each synthetic datasets comprises events of the same number and same distribution as the original dataset catalog (see 'Reference Guide' for details).

After defining the aforementioned parameters, the user shall click on the "Run" button and the calculations are performed. The Status changes from "CREATED" to "SENT_TO_SERVER" and the output is created. The results appear on the screen after clicking on the mccalc_output button (lower left corner in figure 2). These results are:

Figure 2.

1. Analysis results: A table including information on the obtained results, as a function of minimum magnitude, available after clicking on the "Show" button (Figure 2). The columns of the table correspond to:

• Magnitude: minimum magnitude, M
• n: number of events with magnitude =M
• N: number of events with magnitude ≥M
• b-value: b-value of the Gutenberg-Richter law
• berr: b-value standard error
• a-value: a-value of the Gutenberg-Richter law
• a-value normalized: a-value normalized per unit time as was selected by the user
• Rs[%]: Residual between observed data and power law
• Rf[%]: Average residual between synthetic catalogs and power law

1. A table with Completeness Magnitude, M_C, as it was estimated by four different approaches, 90% and 95% Goodness of Fit Tests, Maximum Curvature and Modified Goodness of Fit Test (Figure 2).
2. A plot of the number of events (interval, n, and cumulative, N) as a function of minimum magnitude, shown on logarithmic Y-axis. (Figure 2, 3). The user can click on a certain point of the plot to draw the power law fitting curve corresponding to this minimum magnitude (red dashed line, Figure 3). The interval, cumulative and the theoretical number of events for each magnitude bin is shown in the screen as well, by moving the cursor on the circles, squares, or along the fitting curve, respectively (Figure 3). The plotting points can be shown/ hidden after clicking on the parameters shown in the legend of the figure.

Figure 3.

Figure 4.

1. Residual Plot: This option provides to the user the opportunity to evaluate the Goodness-of-Fit results as a function of magnitude by examining the residuals between real and modeled data. The modeled data corresponds to power law of the frequency magnitude distribution (black dots) and to the synthetic datasets following this power law (red squares). The horizontal dashed lines indicate the residual values of 10% (upper line) and 5% (lower line), which correspond to the commonly used in literature recommended levels (Figure 4).
2. Plot of b-values with errorbars: This final option shows the b-value fluctuation as a function of magnitude (Figure 5). The errorbars which indicate ± one standard deviation are shown as well. In such way the user may consider the accuracy of calculations and the stability of the b-value as the magnitude changes. The dashed horizontal line denotes b=1.0, which is a value that often characterizes seismic activity in several scales.

Figure 5.
Note that zooming option is enabled for all of the aforementioned plots (see information tips at the low part of Figures 3, 4 and 5)