How Math Could Help Map Earth’s Interior #geometry

Via Scientific American

Mathematicians say that they have solved a major, decades-old problem in geometry: how to reconstruct the inner structure of a mystery object ‘X’ from knowing only how fast waves travel between any two points on its boundary.

The work has implications in real-world situations, such as for geophysicists who use seismic waves to analyse the structure of Earth’s interior.

“Without destroying ‘X’, can we figure out what’s inside?” asked mathematician András Vasy of Stanford University in California, when he presented the work in a talk at University College London (UCL) last week. “One way to do it is to send waves through it,” he said, and measure their properties.

Now, Vasy and two of his collaborators say that they have proved that this information alone is sufficient to reveal an object’s internal structure.

Read more.