Lower Bounds (mb) on the Completeness Threshold
of the 1995 Bulletin by Seismic Region
This map shows estimated lower bounds on completeness threshholds in Flinn-Engdahl regions with at least 100 shallow focus (h<=70 km) earthquakes for which the ISC computed mb. The threshold for completeness may be higher in some cases, but it seems unlikely that reasonable seismologist would examine magntitude/frequency relationships and conclude that the threshold was lower than stated here.
This table contains a link to a PostScript-format frequency/magnitude plot for each region and depth range with at least 1 ISC-computed body wave magnitude during 1995. In each figure, green symbols show the interval frequency and red symbols show the cumulative frequency.
| Region | 01 | 02 | 03 | 04 | 05 | 06 | 07 | 08 | 09 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Shallow | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X |
| Intermediate | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | |||
| Deep | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | |||||||||
| - | |||||||||||||||||||||||||
| Region | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 |
| Shallow | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | X | |
| Intermediate | X | X | X | X | X | X | X | X | X | X | X | X | X | ||||||||||||
| Deep | X | X | X | X | X |
In most cases, the peak of the interval frequency plot is a plausible lower bound of the completeness threshold. The lower bound on completeness is never less than the peak, but it is greater in some cases.
There are several reasons why these estimates might be in error.
- Insufficient data
- If there are not enough magnitudes measured in a region, no unambiguous trend can be established, and the true completeness threshold may be greater or less than the the magnitude of peak frequency, leading to an estimate that may be very high or very low. To limit this, only regions with at least 100 mb values are included. See, for example, shallow focus earthquakes in region 7.
- Slow rolloff
- If a sufficient fraction of earthquakes just below the threshold are detected, then the mag/freq may continue to rise even below the completeness threshold, leading to an underestimate. See, for example, shallow focus earthquakes in region 16.
- b > 1
- If the b-value significantly exceeds 1, then the mag/freq may continue to rise even below the completeness threshold, leading to an underestimate. See, for example, shallow focus earthquakes in region 18.
- Two populations
- If there are two sets of earthquakes with different thresholds, the frequency density at the lower threshold may exceed the density at the higher threshold, leading to an underestimate. See, for example, shallow focus earthquakes in region 15.
