Seismic sources usually excite a continuous spectrum of surface-wave periods. Each harmonic component has a velocity, c(w), called a phase velocity where w=2pf ( radian frequency) depends on the medium parameters (layer thickness, P and/or S velocities, etc). Phase velocity is also know as the "carrier" velocity. Phase velocity is usually measured using the one or two-station method. Each method requires proir knowledge about the source (i.e. depth estimates and moment tensor) as wells as origin time and the distance traveled. The observed phase of a seismic surface wave can be expressed as an initial phase from the source acted upon by a set of linear filters. Source phase, f_s(w), and pobserved phase f_o(w), are related by

f_o(w) = f_s(w) + f_p(w) + f_i(w)

where w=2pf ( radian frequency), f_i(w) is the instrument phase, and f_p(w) is the propagation phase. To calculate the initial phase, the faulting mechanism and source depth must be known. The instrument response is known and already removed when the seismogram is deconvolved to recover ground displacement. Constrained moment-tensor solutions provide good source correction estiamtes. The propagation phase term depends on the phase velocity of the structure. Solving for the phase velocity introduces a 2pN uncertainty without changing the observed waveform. The 2pN term represents the periodicity of the harmonic term in the phase velocities and is estimated using long-period observations, which should converge to globally averaged values at long-periods. Below is a picture of the output from the phase velocity determination program showing the reference curves, observed group velocities and 2pN branches (N = +1 is the correct branch in this case).

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