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Using Velocities from a Triangle of GPS Sites to Investigate Crustal Strain UNAVCO GPS Crustal Strain Curriculum Team September 9, 2012

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Using Velocities from a Triangle of GPS Sites to

Investigate Crustal Strain

UNAVCO GPS Crustal Strain Curriculum Team

September 9, 2012

September 9, 2012

September 9, 2012 Locate three non-colinear GPS sites

September 9, 2012 E-W and N-S components of sites’ velocities

September 9, 2012 E-W + N-S components = total site velocity

September 9, 2012 Total site velocities

September 9, 2012 Define the triangle between the GPS sites

September 9, 2012 Define the centroid of the triangle

September 9, 2012

Transform coordinate system to a new origin at the centroid of the triangle

September 9, 2012

Inscribe a circle in the center of the undeformed triangle

September 9, 2012

The average of the three total site velocities is the translation vector

September 9, 2012

The triangle deforms as it moves. The vector from the centroid of the undeformed triangle to the centroid of the deformed triangle is

the same as the translation vector.

September 9, 2012

Subtracting the translation vector from the site velocities brings the two triangle centroids together.

September 9, 2012

Subtracting the translation vector from the site velocities brings the two triangle centroids together.

September 9, 2012

The total site velocities minus the translation vector yields the site vectors associated with the change in shape of the triangle.

September 9, 2012

The red line is the major axis of the strain ellipse, and the blue line is the minor axis

September 9, 2012

The ellipse axes remain perpendicular to each other when the strain is reversed.

September 9, 2012

September 9, 2012

The rotational component of strain is indicated by the angular change in the orientation of the red lines.

September 9, 2012

September 9, 2012

September 9, 2012