### What is Critical Damping?

#### Resonance

Seismic signals are detected in land seismic surveys with geophones. The essentials of a geophone are a magnet; a coil; and a spring. The magnet is attached to the geophone case, so that when the ground moves up and down with the seismic signal, the coil, attached to the case by a spring, tends to remain in the same place. The movement of the magnetic field through the coil induces an electric voltage in the coil, and this voltage is the signal recorded for processing and interpretation. If the coil were totally unconnected to the case, it would record this signal accurately. But the spring connection means that when the case moves a force is applied to the coil proportional to the displacement of the case relative to the coil. If movement changes direction (from up to down) slowly, the coil can follow the movement of the case. If changes in direction are very rapid, the coil has hardly started to move before it is pulled in the opposite direction, so it hardly moves at all. In between, there is a frequency of direction change where the reversal of direction joins with the energy stored in the spring to pull the coil back to the rest position and past it, with the cycle repeated in the other direction. At this frequency, the geophone coil movement is very large. So is the signal. This is the resonant frequency.

#### Damping

If no energy is taken from the system, a weight on a spring (which is what a geophone really is), once excited, will oscillate at the resonant frequency indefinitely. This is obviously not what is needed for recording a seismic signal, where we want to distinguish one reflection from the next.

If energy is taken out of the oscillating system, the amplitude of oscillation decreases. This is called "damping". "Critical damping" occurs when the system just fails to oscillate.
The figure to the left shows the response of a geophone to a transient signal (such as a tap on the top of the case). The horizontal axis is time measured in units equal to periods at the resonant frequency. For example, if the resonant frequency is 10 Hz, the units on the axis are 100 ms=1.0. The response with no damping is continuous oscillation at the resonant frequency with no change in amplitude.

With increased damping, the oscillation dies with time, until at critical damping the response is never negative: it rises rapidly to a maximum then decays exponentially. The problem with critical damping is that the maximum is only about 36% of the response for an undamped geophone.

The practical solution is to use geophones with a damping factor of about 0.7 critical.This increases the response to 45% and improves the frequency response.

The amplitude of the geophone response is theoretically infinite at the resonant frequency, levelling off to a flat response about 3 octaves above the resonant frequency, if the geophone is undamped. As the damping increases, the peak at the resonant frequency decreases in amplitude, and disappears completely at 0.7 critical damping.Increased damping reduces the response at low frequencies. At 0.7, the response is down 3 dB at the resonant frequency, and drops at about 12 dB/octave. For 1.0 critical, the response is down 6 db at the resonant frequency.

Phase response is a further problem. As the figure to the right shows , the phase of the signal from a geophone rotates 180 degrees as it goes through the resonant frequency. For little damping, the phase change is abrupt and occurs at the resonant frequency. For large damping factors, the phase change is more gradual, and is spread over several octaves.

#### What causes damping

As mentioned above, damping is caused by some factor taking energy out of the system. In practice, this means converting the mechanical energy of the coil movement into heat. There are three practical techniques, two of which are commonly used:

• The coil can be immersed in a viscous fluid.
• The coil can be wound on a conductive base, so that energy is absorbed in eddy currents.
• Electrical current can be drawn from the geophone by a load resistance, so that resistive heating of the geophone coil and the load dissipates energy.

#### Interpretation Considerations

The interpreter needs to consider what the variations in amplitude and phase response around the resonant frequency might do to any calculations using amplitudes or phase differences.