e = elevation from horizontal to sensora = azimuth from ground point to sensorL = line of sight motion of ground point to sensor

e

Up

East

North

a

Horizontal

L

s = striked = dipr = rakeD = displacement

Strike is defined such that the fault always dips to the right when moving along strikeRake is defined by motion of hanging wall (upper block) relative to the footwall (lower block)Rake: 180°=right-lateral, -90°=normal, 0°=left-lateral, 90°=thrust

Up

East

Norths Horizontal

d

FaultD

r

Find angle (q) between line-of-sight (L) direction and rake (r):

LE = cos(90-a)cos(e)LN = sin(90-a)cos(e)LU = sin(e)

Determine relative E (LE), N (LN), and U (LU) components for line of sight direction:

Determine relative E (rE), N (rN), and U (rU) components for rake direction:

Determine relative strike-slip (rs) and dip-slip (rd) components of displacement:

rs = cos(r)rd = sin(r)

rE = rscos(90-s)+rdcos(d)cos(180-s) = cos(r)cos(90-s)+sin(r)cos(d)cos(180-s)rN = rssin(90-s)+ rdcos(d)sin(180-s) = cos(r)sin(90-s)+ sin(r)cos(d)sin(180-s)rU = rdsin(d) = sin(r)sin(d)

q = cos-1 (LErE+LNrN+LUrU)

Find displacement projection:

D = L/cos( )q

D = L/[cos(90-a)cos(e)[cos(r)cos(90-s)+sin(r)cos(d)cos(180-s)]+sin(90-a)cos(e)[cos(r)sin(90-s)+sin(r)cos(d)sin(180-s)]+sin(e)sin(r)sin(d)]