Transient Constant Area Surface and Downhole Wave Models - Measurement While Drilling Signal Analysis, Optimization and Design - page 103

Figure 4.1c . Wide signal - low data rate.

4.1.4 Run 2. Narrow pulse width - high data rate.

C CASE 2. NARROW PULSE WIDTH
C Clearly see interference between upgoing and reflected pulses
A = 20.0
R = 100.0
G = A*(TANH(R*(T-0.100))-TANH(R*(T-0.101)))/2.
C

Due to the properties of the hyperbolic tangent function used above to
model a real-world pulse, emphasizing that it is not the Heaviside step function,
the “0.101 - 0.100” time difference of 0.001 sec is not directly related to pulse
width (a step function would yield unrealistic infinite derivatives at the front and
back ends of the pulse). For pulse width, refer directly to the black upgoing
wave. The pulse width, from Figure 4.1d, is small and indicates high data rate.

x Roundtrip delay = 0.02 sec
x Sampling time = 0.001 sec = 1 ms

Figure 4.1d . Narrow pulse width - high data rate (with widened green trace).