Geometry and equations illustrating how to calculate surface offset given scarp length (L), scarp angle (θs), footwall (θf), and hanging wall (θh) far-field slope angles, where θf ≠ θh.

Given:

If θf ≠ θh, break the calculation into two parts, as follows:

Calculate the upper portion of the vertical offset due to footwall far field slope

x'f = ½ × L × sin θs =
zf = ( (½ × L)2 - x'f2 )½ =
xf = zf × tan θf =
yf = x'f - xf =

Calculate the lower portion of the vertical offset due to hanging wall far field slope

x'h = ½ × L × sin θs =
zh = ( (½ × L)2 - x'h2 )½ =
xh = zh × tan θh =
yh = x'h - xh =

Surface Offset

S = yf + yh =