ShakyGround

The choice of the seismogram length and the digitization frequency requires some care. From the viewpoint of computing time and numerical exactness it is desirable to work with short seismogram length and, on the other hand, with high digitization frequencies. The attempt to match both demands at the same time, however, may cause problems due to an effect known as “wrap around effect” or “alias in the time domain”. The “wrap around effect” resides in the periodicity of the Fast Fourier Transform. It happens if the duration of the signal is longer than the time window given by the seismogram length divided by the digitization frequency. The parts of the signal, which would fall outside the time window, appear at its beginning, interfering with the signals occurring there for true physical reasons.The effect of wrap around may occur essentially for two reasons: First, the duration of the Green’s function is longer than the selected time window. This typically happens if the sources are distant from the receiver, i. e., the traveltime of the direct signal becomes longer than the time window. You can backtrace this effect from the “eventcode” produced by SHAKYGROUNDs numerical kernel. The eventcode is reported in the file “simul.log”. A further reason for wrap around may be the choice of seismic source moment and global stress drop yielding a large source with a low corner frequency and a long source duration. Actually this phenomenon is not reported by SHAKYGROUNDs eventcode, but can be easily identified by comparing the “Strong motion duration” to the seismogram length. If the strong motion duration is close to the seismogram length then you should indeed suspect the presence of “wrap around effect”. You can convince yourself about the validity of your choice writing the single synthetic seismograms to disk and visualizing them one by one.

Select now the “General” sheet with your mouse. Your screen should look like Fig. below. This sheet is organized in 5 logical units, which are the parameters for the synthetic “Seismogram Information”, the “Simulation Parameters”, the “Statistics [of] Source” parameters, “Statistics [of] Layer” parameters, and the “Absorption mode”.

The General Sheet with the parameters controlling the nmerical calculus.

The “Seismogram Information” concerns the “Length” of the synthetic seismograms given in points. For internal reasons of this number must be a power of 2. The second item of interest is the “Digitization frequency” given in Hz. If you select for example 200 Hz the spacing of points in the synthetic seismograms will be 0.005 s. With a length of 4096 points the seismogram length expressed in seconds or, in other words, the time window will be 4096/200 = 20.48 s. Limits imposed by SHAKYGROUND are 16384 points for the seismogram length and 1000 Hz for the digitization frequency.
In the field “Simulation parameters” you have two boxes where you select the “Number of Simulations” to perform during a run, and the “Seed Value..” for the “..Random Gen[erator]“. The seed value should be an integer. It initializes the random generator at the beginning of a SHAKYGROUND session. The number of simulations are important for the degree of statistical stability of your simulations. A good compromise between the needs of short computing times and statistical stability of SHAKYGROUNDs output parameters can be 50 simulations. In this case SHAKYGROUND will perform 50 simulations with the model parameters specified by the user,varying them according to the choices explained above, then produce a statistics of a number of output parameters and of the response spectra. For testing purposes you may select a small number of simulations, such as 3 which is the default. A choice of less than 2 simulations is blocked by SHAKYGROUND, since otherwise the standard deviation would not be defined any longer.The next two fields “Statistics Source” and “Statistics Layers” concern the manner of how to perform the random parameter variation. You may choose a “Uniform Distribution” where all values within a given range have the same probability. The uniform distribution has finite limits, i. e., certain values cannot be exceeded. In the gaussian distribution the average values have the highest probability of occrurence, however, in theory there is no upper or lower limit of possible values. For the sake of numerical stability SHAKYGROUND limits in any case the parameter variation with respect to its lower boundary in the sense that a value less than 5% of the average is not permitted.
The last field “Absorption mode” you have the choice between an “acausal” or “causal”, absorption model. The acausal absorption model causes the appearance of a little amount of signal energy before the seismic signals physical arrival time. The reason for this phenomenon resides in the fact that the acausal absorption model is zero-phase, in other words there is no phase shift since the seismic velocities are assumed independent of frequency. In the causal mode a velocity dispersion is assumed according to a model developed by Futterman (1962). Even though appearing more reasonable from a theoretical viewpoint one could argue the causal absorption model objecting that the true phase shifts cannot be described correctly neither by a zero-phase nor by Futterman’s model. After all, as experience has shown the results in most cases are affected only to a minor degree by the choice of the absoprtion mode.