Converted phases and receiver functions

The converted phase and receiver function methods use conversions from a P-wave to a S-wave, or vice versa, at the discontinuities. Mostly, conversions beneath the receiver are used, but some studies also use conversions within the source region (Vidale and Benz, 1992) or conversions between source and receiver in combination with migration techniques (Castle and Creager, 1999).
The P $\rightarrow$ S converted phases (Ps) (Vinnik, 1977) are weak onsets within the P coda. In single seismograms, these phases are difficult to detect. Therefore, different array techniques and stacking techniques are used (Vinnik, 1977; Stammler, 1992). The Ps phases of the main upper mantle discontinuities arrive at $\sim$40s (400km) and at $\sim$65s (660 km) after the P-onset.
The S $\rightarrow$ P (Sp) converted phases can be detected as precursors to the S arrival in the seismogram. They reach the seismometer about 50 to 80 s ahead of S, depending on the depth of the conversion between 400 km and 700 km (Faber and Müller, 1980; Bock, 1991). Again, these phases are too weak to be identified in a single seismogram and similar methods as for the Ps-phases are used to detect Sp.
The depth of the conversion is resolved by the S - Sp (Ps - P) differential travel times. Additional information on the velocity contrast across the discontinuity is given by the amplitude ratio Sp/S (Ps/P). An estimate of the thickness of the discontinuity can be given by studying the spectral content of the converted phase with respect to the direct wave (Stammler, 1992).
A method often used to study converted phases are the so called Receiver Functions (RF). Receiver functions enable the determination of the velocity structure of the crust and upper mantle directly beneath a seismic station. This requires the isolation of the response of this structure from other factors, which interact to form the observed seismograms recorded at teleseismic distances (Owens et al., 1984).
For this purpose the recorded 3-component seismograms with the components Z, N, and E are rotated into the ray coordinate system L, Q, and T (Kind et al., 1995).

Figure 3.2: Rotation of coordinate system for the use with Receiver Functions. The incident ray is indicated by the dashed line. The Z, R, T components point perpendicular to the surface, along the great circle path and perpendicular to these two directions. The L, Q, T point to the vertical incidence angle, perpendicular to L and perpendicular to the horizontal incidence angle.

The different coordinate systems used are shown in Figure 3.2.
The L-component points into the direction of the ray. The Q-component is perpendicular to L and T and the T-component is perpendicular to the horizontal incident angle. The rotation separates the different types of waves, P, SV (vertically polarized shear wave), and SH (horizontally polarized shear wave), to the different components of the local ray system, L, Q, and T, respectively. The converted phases can be found on the Q-component, only. To remove source effects and to normalize the Q-component seismograms of different sources, the Q-component is deconvolved with the vertical Z-component (Langston, 1979). This procedure produces horizontal receiver functions that are very similar even for events with quite different source functions.
To study different regions, conversion depths or the azimuthal dependence of the discontinuity depth, RF of many events recorded at the station can be calculated by stacking according to different conversion regions (Duecker and Sheehan, 1997), different conversion depths (Vinnik, 1977) or different backazimuths (Li et al., 2000).