Surface wave holography

Abstract

Surface waves have proven to be very useful in determining the properties of the Earth’s crust and mantle. The traditional surface wave analysis consists of two steps. First, from surface wave recordings, dispersion data (phase velocities or group velocities) are retrieved for each source receiver pair (Dziewonski and Hales, 1972; Nolet, 1977). Next, the information for different frequencies and many source receiver pairs is combined to yield an image of the Earth’s interior (e.g. Woodhouse and Dziewonski, 1984; Montagner, 1986; Nataf et al., 1986). These methods implicitly use ray theory by resorting to the “great circle theorem” (Backus, 1964; Jordan, 1978; Dahlen, 1979). This theorem states that for a sufficiently smooth medium the surface wave data are only influenced by the structure under the great circle joining the source and the receiver. The great circle theorem is acceptable provided the inhomogeneity varies little on the scale of the wavelength of the surface waves.