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e = elevation from horizontal to sensor a = azimuth from ground point to sensor

e = elevation from horizontal to sensor a = azimuth from ground point to sensor L = line of sight motion of ground point to sensor. Up. L. North. Horizontal. a. e. East. Up. s = strike d = dip r = rake D = displacement. North. s. Horizontal. r. d. East. D. Fault.

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e = elevation from horizontal to sensor a = azimuth from ground point to sensor

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  1. e = elevation from horizontal to sensor a = azimuth from ground point to sensor L = line of sight motion of ground point to sensor Up L North Horizontal a e East Up s = strike d = dip r = rake D = displacement North s Horizontal r d East D Fault Strike is defined such that the fault always dips to the right when moving along strike Rake 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

  2. Find angle (q) between line-of-sight (L) direction and rake (r): Determine relative E (LE), N (LN), and U (LU) components for line of sight direction: LE = cos(90-a)cos(e) LN = sin(90-a)cos(e) LU = sin(e) Determine relative strike-slip (rs) and dip-slip (rd) components of displacement: rs = cos(r) rd = sin(r) Determine relative E(rE), N(rN), and U(rU) components for rake direction: 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)]

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