Speaker: Dr. Mathieu Perton; CONACYT Research Fellow at the Universidad Nacional Autónoma de México
The equipartition theorem is generally badly understood and has been recently strongly criticized. However, we used this theorem to compute Green's functions (GF) and results have been validated by comparing with other well-known methods. This approach is very promising since it increases significantly the GF calculation efficiency. The main idea is to send plane waves in all the possible directions and to make the correlations of the resulting displacement fields at two points to obtain the GF, exactly as for ambient noise correlations. First, I will discuss the details of the method for several canonical cases (a full space, a half space, a layered medium and for a heterogeneity inside a layered medium).
Then, I will demonstrate that in the particular case where the two points are superimposed, the energy is related to the auto-correlation of the displacement field. From this observation, the H/V technique, which is the ratio of the Horizontal energies on the Vertical energy, has gained a new insight and has been reformulated. While H/V are traditionally used to determine a simple shallow velocity model (i.e. one layer over a half-space) and the dominant frequency site response, I will show that complex and deep velocity structures can be inferred from such low-cost measurements.