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Locating an earthquake in an absolute sense can come with considerable uncertainty, but locating earthquakes relative to one another is far more accurate and can provide exciting insights into subsurface processes.

Yellowstone Caldera Chronicles is a weekly column written by scientists and collaborators of the Yellowstone Volcano Observatory. This week's contribution is from David Shelly, seismologist with the U.S. Geological Survey.

Absolute versus relative earthquake locations associated with 2019 Ridgecrest, California, foreshock and aftershock sequence
Absolute versus relative earthquake locations associated with 2019 Ridgecrest, California, foreshock and aftershock sequence.  Animated GIF image compares the routine catalog earthquake locations with those from an enhanced catalog employing precise relative locations.  Depths are color-coded as shown.  Triangles indicate seismic stations.  Note the numerous faults illuminated in the enhanced catalog not visible in the routine catalog. Adapted from Shelly (2020).

The methods of routinely detecting and locating earthquakes are simple and robust.  With the aid of computer algorithms, seismologists identify the onset times of P (and sometimes S) waves at seismic stations across a network.  Then, using a model of the seismic wave speeds in different parts of the crust, a best-fitting source location is determined.  Because of uncertainties in the seismic velocity model and in the P- and S-wave onset times, however, the estimated location is never exact.

This “independent” earthquake location works well for general use.  But in some cases, particularly when seismicity is concentrated in space and time during an earthquake swarm or aftershock sequence, we can dramatically improve the results by locating a large group of nearby earthquakes simultaneously and relative to each other.  

To get a sense of relative versus independent earthquake location, consider trying to meet a friend in a crowd near Old Faithful geyser.  If you tell your friend that you will meet them 1000 steps away in a certain direction from where you are both standing, you are providing them with a location referenced directly to the starting point. However, your friend may have a hard time finding you because their step length may not precisely match yours, and their direction may be slightly off.  This is analogous to providing an independent earthquake location, where the location estimate may differ from the true location because we don’t know the precise speed at which seismic waves travel in each part of the crust.

image related to volcanoes. See description
Evolution of the 2017 Maple Creek earthquake swarm. Plots show earthquake locations colored by time. a) Map view. b) West-east cross-section. c) Three-dimensional view, looking from the east-southeast, along the axis for much of the swarm activity.

In contrast, if you have some familiarity with the Old Faithful area, you might be able to describe a place to meet your friend based on its relative location with known landmarks closer to your destination.  For example, you could decide to meet “just outside the north entrance to the visitor center” or “halfway between the visitor center and the benches toward Old Faithful.”  This is analogous to relative earthquake location, where earthquakes are located relative to other earthquakes that are nearby.  This approach eliminates most of the effects of unmodeled seismic velocity structure (think slight differences in step length), so that small differences in the timing of P- and S-wave arrivals for two earthquakes across the seismic network can be very precisely attributed to differences in the earthquake locations.  And, when many earthquakes are located simultaneously, we can compute the optimal “web” of relative locations among many different earthquakes, which stabilizes the locations and helps reduce the influence of errors in determining the P- or S-wave arrival times. 

In ideal cases, this procedure can reduce absolute location uncertainties of one kilometer (0.6 mile) or more to relative uncertainties approaching 10 meters (about 33 feet).  That is, even if the absolute location of the entire group of earthquakes is not exactly known, we can precisely resolve the relative positions and determine the structure within the locations of the group.

Precisely located seismicity can produce exciting scientific insights.  For example, precise locations sometimes reveal systematic migration of an earthquake swarm with time.  They can also show whether the earthquakes are occurring on a single fault, an array of faults, or are activating a broad volume of crust.  These features can help scientists determine the physical process(es) underlying the seismic activity, such as triggering by stress transfer, water pressure, or magma movement.  This provides valuable information about dynamic processes deep in the subsurface, which is critical to understanding the seismic and volcanic implications for areas like Yellowstone.

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