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Group Wave Velocity |
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Group velocity is a dispersive characteristic where constructive patterns travel along the surface as wave packets. Group velocities can be used to determine the upper crustal structure because they are directly controlled by it. Geologic features such as mountain ranges and continental shields have faster group velocities than features such as basins where the energy is more attenuated. Measuring group and phase velocities involves several steps that require information from seismograms. First, the quality of the earthquake data must be checked to insure a reasonable signal-to-noise ratio of the seismogram. Background "noise" may be other energy (e.g. body waves) that arrives at the same time as the surface wave. Next, the instrument response must be removed from the seismogram from the seismogram by deconvolution. In SAC, four frequency values define a cosine window applied to the instrument deconvolution to reduce long and short-period noise amplified by spectral division. Once displacements are computed, a multiple-filter analysis is performed to estimate the group velocities for the 26 events. A Gaussian filter with peak amplitude centered at the desired period is applied to the seismogram in the frequency domain. The peak of the envelope of the corresponding time domain signal is used to estimate the group travel time. The time of the peak is estimated by fitting a quadratic curve to the largest three values (allowing interpolation between time samples). In practice, the true period represented in the filtered signal may not correspond to the Gaussian filter's center period. To account for possible bias produced by changing spectral amplitude, an instantaneous period is measured at the time of the envelope peak. The group velocity for a given period is estimated by dividing the distance between the station and the source by the group arrival time. The process is repeated for each period in a specific range and is plotted verses group velocity. Once a group velocities have been estimated, a mode isolation filter can be constructed and applied to the signal to isolate the fundamental mode from the signal-generated and ambient Earth noise. Mode-isolation provides smooth, stable spectral amplitudes and eases estimation of signal phase and in turn phase velocities. Below is a screen shot of the program SWMFA (left) that was used to estimate the group velocities and a the smoothed spectral amplitudes created by the mode-isolation filter. |
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