In Activity #5, it was noted that many people are surprised at how many earthquakes occur every day in southern California. That surprise, it was said, stems from the fact that all but a few of those are too small for the shaking they generate to be felt, and that only on rare occasions do earthquakes large enough to cause widespread damage occur. In other words, small earthquakes are much more common than moderate earthquakes, which are much more common than large earthquakes.
Looking at the seismicity maps in Activity #7 should have reinforced that idea. But we have yet to investigate whether a direct relation exists between magnitude, the measure of earthquake "size", and the rate of earthquake occurrence. The activity below will give you the chance to do just that, re-creating the work of two notable seismologists from decades past.
The Gutenberg - Richter Relation
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Can you deduce the same rule of the magnitude-dependent distribution
of seismicity as described by two of the pioneers of modern
seismology? |
When plotting earthquake counts against magnitude on a logaritmic scale, you should have found a value for b, the slope of the line that best fit those points, that was roughly equal to one. This is true for most parts of the world -- regional b values are generally found to be within the range of 0.7 to 1.0 around the globe.
Though the b value within a given region can be thought of as a characteristic property of that region, values for b can vary noticeably on a smaller scale. The most common influence on the b value of a localized area is an aftershock sequence, the sudden jump in the local seismicity rate following a large earthquake.
The 10-year count of earthquakes in southern California you plotted in Activity #8 contained a great many aftershocks (from large earthquakes in 1987, 1992, and 1994). Did this affect its validity? One way to approach this question is to look at a relatively aftershock-free set of data, and plot its Gutenberg-Richter distribution (depending on the past year's activity, you may have already done this!). Another approach is to look at Gutenberg-Richter plots of aftershock sequences and find typical b values for them.
