Extracting the earth response from noise and complex earthquake data.
ABSTRACT Theory shows that when random noise is generated in proportion to the local dissipation rate, one can extract the response of a system from correlations of field measurements of such noise. Such a condition of equilibrium is rarely satisfied for elastic waves of the earth. Yet the earth response can be extracted from measured noise. We show examples of the retrieval of P-waves and of S-waves. The latter type of waves are retrieved from traffic noise in an urban environment. Since the traffic noise is excited by localized sources (road and railroads), it displays strong amplitude variations. In order to compensate for such amplitude variations, we use cross-coherence rather than cross-correlations for the data processing. We also analyze complicated waveforms excited by earthquakes to create maps of the shear-wave velocity in Japan and show that the shear wave velocity changes with time; this velocity drops throughout northeastern Japan with about 5% after the recent Tohoku-Oki earthquake. Our measurements show that the shallow subsurface in Japan weakens after the earthquake over a region about 1 200 km wide.