Forward Computation
Radial and vertical components of synthetic seismograms are calculated using the Propagator Matrix method of Thomson and Haskell. In the case of offshore setting, we adopt a boundary condition that requires zero traction on the seafloor. Also, we use equations of acoustic wave propagation rather than imitating the acoustic waves by setting Vs ~ 0 on the equations of elastic waves.
Radial component records are deconvolved by the corresponding vertical components. Water-level deconvolution is used for the deconvolution.
A Gaussian low-pass filter is applied to the deconvolved seismograms:
where a is a tuning parameter.
The synthetic receiver functions are normalized such that the amplitude of the direct P arrival on the vertical component of becomes unity. The normalization constant, c, is as follows:
where a is the parameter for Gaussian low-pass filter, N is the number of element in the time series, and \Delta t is the sampling interval.