The relation between the magnitude and duration of earthquake

Question

I am asking this question in reference to the recent earthquake that struck Nepal last month. I read that the magnitude 7.8 richter scale earhtquake would have caused more damage had it lasted for longer time. In case of Nepal it lasted for nearly 30 seconds. I also read that that magnitude scale was not able to release all the energy that has been stored in the form of strain in the plate.

So what I wanted to ask is that if that earthquake had lasted for more time, would it have released more energy? Similarly does an earthquake of magnitude, say 6, would release energy just as equal to 7.8 if it lasted for more time?

Answer 1

It is helpful to start with the USGS definition of magnitude, which can be seen as:

based on measurement of the maximum motion recorded by a seismograph.

According to the Seismology Research Centre page Earthquake Size and the USGS FAQ page What was the duration of the earthquake? Why don't you report the duration of each earthquake? How does the duration affect the magnitude?, the duration and magnitude are generally related, specifically given that an earthquake is the movement (motion) of an area of a fault, rather than a single point -

So the larger the area of the fault that ruptures, the longer the duration of the earthquake. And larger magnitude earthquakes have larger fault areas.

In the case of the recent Nepalese earthquake, if the fault movement area was larger, then this potentially could have resulted in a larger magnitude, longer duration earthquake.

However, a major reason for the uncertainty (why the USGS page refers to the relationship as a 'general' relationship) is due to the geology of the affected area, from the USGS:

The duration of shaking at a point on the ground depends on how long the earthquake took to occur and how the waves move through the ground to that point. If there are a lot of reflections and resonances near the point (for instance in a sedimentary valley) the shaking will last longer. In an area without resonances (for instance on a hard block of rock) it will last a shorter time.

Answer 2

The energy of an earthquake can be calculated from the moment magnitude scale value alone. Two earthquakes of different duration, but the same moment magnitude, have the same energy.

The destructive effect of an earthquake is described by the intensity, and a scale such as the Mercalli Intensity scale.

I believe there were reports that the ground motion during the Nepal earthquake (Susan Hough of USGS on BBC) had a longer period and shorter duration than initially estimated. This would mean a lower ground acceleration and duration of shaking for the magnitude. Greater destruction might have resulted if the earthquake (with the same magnitude) had had a longer duration or higher ground acceleration.

The local ground motion (period, acceleration and duration) during an earthquake vary with location due to factors such as underlying geology, fault mechanism, and orientation to fault. This is one reason that following an earthquake seismologists construct a map of earthquake intensity. As the USGS scientist said in her interview, working out the details is a research project.