# Questions

## Peak Distance (Diffusion Distance)

As a planewave propagates through the Earth, the location of its maximum amplitude (peak amplitude) propagates along with the signal. Begin by setting the time and conductivity to \(t\) = 0.60 s and \(\sigma\) = 10 S/m, respectively.

Looking at the app, what is the peak distance?

Now calculate the peak distance using this formula. How does your answer compare with the previous one?

Reduce the time to 0.1 s. What happens to the peak distance? Is this behaviour supported by the formula?

Reduce the conductivity to 1 S/m. What happens to the peak distance? Is this behaviour supported by the formula?

## Peak Time

The peak time is the time at which the maximum signal amplitude is observed at a particular location. Begin by setting the time and conductivity to \(t\) = 0.01 s and \(\sigma\) = 1 S/m, respectively.

Gradually increase the time until the peak amplitude is at a depth of 400 m. Using \(z\) = 400 m and \(\sigma\) = 1 S/m, calculate the peak time with this formula. How do the results compare.

Now increase the conductivity to \(\sigma\) = 4 S/m. Adjust the time until the peak amplitude is at a depth of 400 m. Thus at the same depth, is the peak time earlier/later in more conductive media?

## Peak Velocity

Begin by setting the time and conductivity to \(t\) = 0.01 s and \(\sigma\) = 1 S/m, respectively.

Adjust the time and determine how long it took for the peak amplitude to be at a depth of 400 m. Now increase the conductivity to 10 S/m and determine how long it took for the peak amplitude to be at a depth of 400 m. Based on these two experiments, do planewaves propagate faster in more conductive or resistive media? Is your answer supported by the formula for peak velocity?

Reset the time and conductivity to 0.01 s and 1 S/m, respectively. Determine the time it takes for peak amplitude to reach 400 m. Now determine the additional time required for the peak amplitude to reach 800 m. Based on this, does the peak velocity increase or decrease over time? Is your answer supported by the formula for peak velocity?