 He is also a member of the National Academy of Sciences.He studied the relation of Earth tides and earthquakes - finding only the strongest tides noticeably effect the timing of earthquakes, earthquake swarms - finding they are a more general phenomenon than he previously suspected, the inner core - discovering high-frequency seismic waves scattered therein that offer a second line of evidence it is rotating about 0.2 degrees per year, the stronger than expected healing of fault zones after an earthquake, and various details of the seismic structure of the mantle.Vidale also contributed an improved method of ray tracing which relied on a finite-difference approximation of the eikonal equation and which has been used widely in both earthquake and reflection seismology.