Figure E.1 presents data on shallow seismic refraction surveys. Field testing data indicates that point A = 0.04 second and point d′ = 100 feet. At the junction of the V2 and V3 straight line segments, the travel time is 0.07 seconds at a distance of 300 feet. Determine the thickness of the upper stratum (i.e., H1). Can a Caterpillar D11R rip the upper and lower stratum?

 

• Figure E.1 presents data on shallow seismic refraction surveys. Field testing data indicates that point A = 0.04 second and point d′ = 100 feet. At the junction of the V2 and V3 straight line segments, the travel time is 0.07 seconds at a distance of 300 feet. Determine the thickness of the upper stratum (i.e., H1). Can a Caterpillar D11R rip the upper and lower stratum?

  Figure E.1

  

  Solution:

  V2 = (300 ft)/(0.07 − 0.04) = 10,000 ft/sec (3,000 m/s)

  Determining the travel time at the junction of the V1 and V2 straight line segments:

  Travel time = 0.04 + (100)/10,000 ft/sec = 0.05 sec

  V1 = 100 ft/0.05 sec = 2,000 ft/sec (600 m/s)

  sin α = V1/V2 = 2,000/10,000 = 0.2, or α = 11.5°

  H1 = [(T1V1)/(2 cos α)] = [(0.04)(2,000)]/(2 cos 11.5°) = 41 feet (12 m)

  Checking using the following equation, where d′ = 100 feet (30.5 m)

  H1 = ½ d′ [(V2 − V1)/(V2 + V1)]½ = ½ (100) [(10,000 − 2,000)/ (10,000 + 2,000)]½ = 41 feet (12 m)

  Since the upper stratum has a low seismic wave velocity of 2,000 ft/sec (600 m/sec), it will be easy for a Caterpillar D11R to remove this material. For the lower stratum, the seismic wave velocity is 10,000 ft/sec (3,000 m/sec) and it could be ripped if it is shale, but granite would probably be non-rippable .