# NCEDC News/Blog

## Geoid Depth FAQ

October 7, 2015

What is Geoid depth?

The depth of an earthquake location can be reported relative to the mathematical
geoid surface within the earth, which is very close to sea level. In simplified terms, the geoid is an
imaginary surface within the earth which is close to sea level over the oceans and approximates what the
ocean height would be over continents if the ocean could extend inland (see http://en.wikipedia.org/wiki/Geoid for a more complete explanation of the geoid).

What are the advantages of geoid depth?

We have many seismic networks around the country that independently locate
earthquakes within their networks. If all networks report geoid depths, then there
are no systematic shifts between earthquake depths located by different networks due
to differences in datum. Earthquake geoid depths also eliminate systematic bias caused
by the topography of mountain ranges.

How can an earthquake have a negative geoid depth?

Earthquakes are always within the solid earth. If a computed earthquake hypocenter
is above sea level, it will have a negative geoid depth, and still be below the earthquake's
surface. For example, if the earth's surface near the earthquake is 2 kilometers (1.24
miles or about 6,300 ft) above sea level, and the earthquake focus is 1 kilometer below the
surface, it has a geoid depth of -1 kilometer. If it is 4 kilometers below the surface, it
has a geoid depth of 2 kilometers. Areas where the earthquakes are very shallow and the
ground's surface is well above sea level, such as the Geysers geothermal area in northern
California, can thus have events with negative geoid depths.

What depths did we calculate before we started reporting geoid depths?

To simplify the calculation of locating earthquakes, both before and with computers, we
assumed the earth has a smooth surface and no topography. The earth model has a seismic velocity
structure below its top surface where rays propagate from the earthquake source and travel times
are calculated to the seismic stations that record it. If all stations are at the earthquake's surface
with no topography, calculations are simplified. Depths calculated within this simplified smooth-surface
earth model are called model depths. Model depths are essentially depths below the earth surface near the
earthquake, and model depths were reported before we changed to reporting geoid depths. Model depths are
still recoverable from some versions of the earthquake catalog.

How do we get geoid depths now?

Model depths are still calculated for every earthquake. That is because the calculation of travel
times in an earth model with a smooth surface is much more practical, even with complications like
velocity layers with linear velocity gradients. We get the geoid depth by correcting the model depths that
we calculate (which are always positive) by subtracting the elevation of the nearby ground surface. Thus
for an earthquake with a model depth of 3 kilometers (below the surface) and a nearby surface that is one
kilometer above sea level, the geoid depth is 3-1 = 2 kilometers.

We use the average elevation of the closest 5 stations to estimate the elevation of the nearby ground
surface. The geoid datum used to measure the station elevations thus becomes the reference datum of the
earthquake depths, currently WGS84. Geoid models continue to evolve, but the differences between sea level
and between various geoid datums are typically a few meters, which is much smaller than the accuracy of
locating earthquakes. Some seismic networks using simpler crustal velocity models consisting of constant-velocity
layers use a calculation procedure that gives geoid depths directly. This approach has the disadvantages of
giving up models with velocity gradients and would have introduced artifacts into the catalog. The earth
velocity models used normally for routine and fast earthquake locations are one-dimenstional (vary only
with depth), and are an approximation to a three dimensional earth.