SME
Geophysics · Problem type
Reflection time and normal moveout
Use this for “A reflector lies 600 m down in rock carrying waves at 2,000 m/s. When does its echo reach a geophone 800 m from the shot, and what is the moveout?”
Diagram
t₀
=
2h
v
=
600
ms.
t
=
√
x
2
+ 4h²
v
=
721.1
ms,
so
the
moveout
is
121.1
ms.
Farther receivers hear the echo later: the times lie on a hyperbola.
This is an example. Type your own values to start a new problem.
h
Depth to reflector
example
v
Wave speed
example · m/s
x
Offset
example
t₀
Zero-offset time
calculated
t
Time at the offset
calculated
Δt
Moveout
calculated
Formulas
t₀
=
2
×
h
v
0.6
=
2
×
600
2,000
t
=
√
x
2
+ 4 ×
h
2
v
0.7211
=
√
800
2
+ 4 ×
600
2
2,000
Δt
=
t
−
t₀
0.1211 = 0.7211 − 0.6
Formulas are worked in s. The step-by-step shows the conversions.
Assumptions
•
One flat reflector under a layer of even speed; the shot and the geophone are on the surface.
•
The ray reflects halfway between them, so its path is √(x² + 4h²) long.
•
The zero-offset time t₀ is straight down and back up; the moveout is the extra time at the offset.
Step-by-step
WE KNOW
h = 600 m, v = 2,000 m/s, x = 800 m
FIND
zero-offset time (t₀), time at the offset (t), moveout (Δt)
Step 1 · Find zero-offset time (t₀)
Use t₀ = 2 × h ÷ v
Straight down and back up: twice the depth over the speed.
t₀
=
2
×
600
2,000
t₀
=
1,200
2,000
t₀
=
0.6
s
Step 2 · Find time at the offset (t)
Use t = √(x² + 4 × h²) ÷ v
The path down to the reflector and back up to the geophone, over the speed.
t
=
√
800
2
+ 4 ×
600
2
2,000
t
=
√
640,000 + 4 × 360,000
2,000
t
=
√
640,000 + 1,440,000
2,000
t
=
√
2,080,000
2,000
t
=
1,442
2,000
t
=
0.7211
s
Step 3 · Find moveout (Δt)
Use Δt = t − t₀
The extra time at the offset over the zero-offset time.
Δt = 0.7211 − 0.6
Δt = 0.1211 s
Step 4 · Convert the answers
Change each answer back to the unit you chose.
t₀ = 0.6 s = 600 ms (1 s = 1000 ms)
t = 0.7211 s = 721.1103 ms (1 s = 1000 ms)
Δt = 0.1211 s = 121.1103 ms (1 s = 1000 ms)
Check
Put the numbers back in. Both sides should match.
0.6
=
2
×
600
2,000
✓
0.7211
=
√
800
2
+ 4 ×
600
2
2,000
✓
0.1211 = 0.7211 − 0.6 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.