Example Rayleigh Wave Processing: Synthetic Seismogram

A synthetic Rayleigh wave vertical component seismogram was created for the following 1D-layered model.


{showmdl}
     point      depth (m)    Vs (m/s)    Vp (m/s)   Density
         1        0.0          125.        312.     2000.0
         2        1.6          153.        382.     2000.0
         3        3.2          217.        542.     2000.0
         4        6.6          165.        412.     2000.0
         5       16.0          387.        967.     2000.0
showmdl


The above model specifies points of control. Between the control, the elastic moduli are linearly interpolated in steps set by a incremental layer thickness. Here, the step size was 0.1 meters. A graphical display of this model is shown in Figure 42. Note the curved interpolation of velocity when elastic constants are linearly interpolated. One starts the process with program gendis which interactively prompts the user for the depths, velocities, and densities. The result is a namelist file, disper.d, that is then read by program disper. Program disper computes the phase velocity dispersion, creating as an output a dispersion file, (earth.crv in this case) and a plot of phase velocity as shown in Figure 43

Figure 42: Example Rayleigh wave model with 0.1 meter step interpolation between control. The interpolation is linear in elastic modulus or density. See section 7.3.2 for additional details.
\includegraphics[scale=.55]{FigureHH}

Figure 43: Phase velocity computed by program disper for the model of Figure 42.
\includegraphics[scale=.55]{FigureII}

We compute a synthetic seismogram using the program, waves. Program genwav prompts the user for parameters like trace spacing, maximum time, component of motion, and produces output file waves.d. Program waves reads waves.d and the dispersion curve saved in output file earth.crv from the disper run. Here we will use a source moment tensor for a vertical impact source, a spectral band from 1 to 50 Hz (the total available from the earth.crv file). Offsets will range from 1 to 48 meters, with 1 meter trace spacing. The program waves employs a minimum phase wavelet with bandwidth reduced somewhat from the range of frequencies specified (to avoid an abrupt transition from the available source spectrum). The source wavelet used in the synthetic seismogram is shown in Figure 44.

Figure 44: Source wavelet for synthetic Rayleigh wave seismogram, model of Figure 42.
\includegraphics[scale=.55]{FigureJJ}

Program waves (see section 7.3.6) computes the actual waveforms for a synthetic seismogram. Signals of particle displacement, vertical component, are shown in Figure 45.

Figure 45: Synthetic vertical component Rayleigh wave seismogram, model of Figure 42. See section 7.3.6 for further details.
\includegraphics[scale=.55]{FigureKK}