Project Methodology
To address the problem of terrane accretion, I designed a sandbox experiment with a rigid backstop representing the overriding plate and a pile of sand representing the accreting terrane. The backstop was pushed through the sand and a critical wedge of sand accumulated in front of it, simulating an accretionary prism at the toe of an overriding plate. Prior to the start of the experiment, the sand base was leveled off to a uniform depth of 0.5 cm for scaling purposes.

The backstop was pushed through the sand at a constant rate and photographs were taken from a stationary position above it every 5 cm of displacement. The diagram below illustrates the model set-up and procedure.
A pile of sand was created approximately 1 meter from the starting position of the backstop to represent an arc terrane. This pile was 1.5 cm higher than the surrounding topography at its highest point, was approximately 40 cm long and covered the entire width of the sandbox. The backstop and wedge were pushed into the terrane until the terrane was accreted and became part of the moving sand wedge. At this stage, the original wedge ceased deforming and the deformation front concentrated at the toe of the accreted terrane. Erosion was not allowed in this model.

After the experiment was completed, the images were digitized in order to complete a geodetic analysis of strain distribution. To calculate the components of strain, marker particles were digitized on a grid and relative positions were noted between successive frames (Epochs). Displacement vectors were calculated for the marker particles for several epochs covering the entire time of accretion. These data were then used to calculate average velocity fields in two dimensions using the mapping program Surfer8. Velocity fields were gridded by triangulating the displacement magnitudes in the x and y directions.

Subsequent to the calculation of the velocity field for each epoch, several strain components were calculated and contoured to note the difference in strain localization during accretion. The components and formulas used to calculate them (Koons and Henderson 1995) are listed below and discussed in more detail in the results section.

Pure Shear Strain

g1 = dDx/dx - dDy/dy

Simple Shear Strain

g2 = dDx/dy + dDy/dx

Total Shear Strain

G = (g12 + g22)0.5

Contraction

s = 0.5(dDx/dx + dDy/dy)

Rotation

w = 0.5(dDx/dy - dDy/dx)

Where:

Dx = dislpacement magnitude in the x direction

Dy = displacement magnitude in the y direction
The cartesian coordinate system used for the strain analysis is illustrated in the figure below.