In order to correct for any axial displacement, we used an automated tracking system that first determines the axial displacement map for each ultrasound frame pair.
For measurement of residual displacement, we used conventional radiographs, since they are readily available and are most commonly used by most orthopedic surgeons in outpatient clinical settings.
Because the hurricane-affected region experienced population displacement, we used special population estimates from the US Census Bureau for rate estimations for 2006 (6 ).
In computation of fluid structure interactions involving large displacements, we use a mesh update method composed of mesh moving and remeshing-as-needed.
Note that, using the approximation of relatively small displacements, we use Cartesian coordinates to follow previous treatments, e.g. Friston et al. (2010a).
To enhance the resolution of the optically recorded displacement data, we used an instrumental variables technique [24] to predict the optically measured endpoint displacements from the displacements estimated from the robot sensors.
We use displacement time-series at 341 GEONET stations near the source region of the 2011 Tohoku megathrust earthquake, as represented by solid triangles.
The measurement that distinguishes the two possibilities is a two-outcome POVM (mathcal{E}={[e_],[e_).10 We use the displacement operator (8) to shift to the local model around (alpha_{0}), such that the possible coherent states of the auxiliary mode are now (vert 1 rangle) and (vert {-1} rangle ).
To look for the signals of the Earth's free oscillation, we use the displacement time-series data during 18 hour after the mainshock in three directions: North-South component, East-West component, and vertical component.
To restore the displacement along the analyzed structures, we use two different methods on the basis of the deformation style: the fault parallel flow algorithm for faulted horizons and the trishear algorithm for fault-propagation folds.
