If a single disturbance some unknown distance away sends out both transverse and longitudinal waves that travel with distinctly different speeds in the medium, such as in the ground during earthquakes, how could the distance to the disturbance be determined? How could the location of the disturbance be determined?

To calculate distance, you measure the difference in waves as they arrive.

To determine location, you find the point of intersection.

Explanation:

This single disturbance sends out both transverse and longitudinal waves and since both waves have different speeds.

To determine the distance:

You measure the time difference in the waves as they arrive. If the difference in time is large then the distance is larger.

To determine the location of the disturbance:

If you were to call two people from different locations who have made measurements of this same event on a telephone call. Their circles can be transferred to your map. The location of the disturbance can then be determined by the point of intersection of the 3 circles.