Spatio-temporal imaging of ruptures and the discrete-time dependent inverse source problem for the wave equation

We first introduce and present an analysis of seismic waves starting
from the system of elastic-gravitational equations describing the free
oscillations of the earth. We establish an existence and uniqueness
result to a weak formulation under minimal regularity assumptions. We
then briefly describe the extraction of surface waves and body waves
using techniques from semi-classical analysis. We finally discuss the
discrete-time dependent inverse source problem and present an explicit
reconstruction of microseisms and ruptures from body-wave data under
certain conditions derived from local energy decay.