If an Earthquake Has a Total Horizontal Displacement of S $M = \frac { S } { 2 } \left( 1 - \frac { 2 } { \pi } \tan ^ { - 1 } \frac { d } { D } \right)$

Multiple Choice

If an earthquake has a total horizontal displacement of S meters along its fault line, then the horizontal movement M of a point on the surface of Earth d kilometers from the fault line can be estimated using the formula $M = \frac { S } { 2 } \left( 1 - \frac { 2 } { \pi } \tan ^ { - 1 } \frac { d } { D } \right)$ where D is the depth (in kilometers) below the surface of the focal point of the earthquake. For the San Francisco earthquake of 1906, S was 4 meters and D was 3.08 kilometers. Approximate M for d = 6 kilometers. Round the answer to the nearest hundredth.

A) $$M = 0.45$$ m
B) $$M = 0.6$$ m
C) $M = 0.65$ m
D) $M = 0.5$ m
E) $M = 1$ m