During run time the numerical kernel of SHAKYGROUND performs a number of checks in order to ensure a proper processing of the model parameters. As quite normal in numerical processing, the formulae are valid only within certain ranges and may become unstable it these limits are violated. In most cases the limits are wide enough to cover the user’s demands, nevertheless it may happen that users try to overstretch the underlying concept, or, for unfortunate combination of model parameters the numerical instability is encountered in an unforeseen manner. In order to limit problems due to numerical instabilities which may even cause program failure SHAKYGROUND tries to fix the possible reasons adjusting the critical parameters in a suitable way. SHAKYGROUND reports the critical situations encountered during run time writing an integer number, the so-called “Message Code”to the file “simul.log”. The single events are coded as follows:

1 = correction of layer thickness (happens if thickness of layer stack is less than focal depth)

2 = danger of numerical overflow in absorption terms

4 = overcritical reflection encountered

8 = time window probably too short

16 = upper frequency limit of response spectrum calculation adjusted.

Since the single events can occur simultaneously the final message code reported by SHAKYGROUND is given by the sum of the codes of the single events. For example a message code of 17, which occurs quite often, corresponds to a “correction of layer thickness” (1) plus the adjustment of the upper frequency limit of the response spectrum calculation (16).

You have now completed the editing of your input sheets. Click now the “Space Shuttle” icon on the tool bar. SHAKYGROUND asks for your patience and after some time of processing displays the standard output screen (see Fig. 14). The graphics show three response spectra, i. e., the average obtained over all simulations, the spectrum corresponding to the average plus one standard deviation (often referred to as “84%-spectra”) and the peak-hold spectra, which represent the highest values encountered during the whole number of simulations. Note that due to the stochastic source model there always be a statistical fluctuation of the response spectra even if the model parameters were not subjected to a random fluctuation.

Together with this graphics a table is presented reporting the most important signal parameters as maximum and RMS-values of ground acceleration, velocity and displacement. The strong motion duration is defined in terms of a HUSID plot, and corresponds to the time window where

of the total signal power, and a(t) is the acceleration time series (see Fig. 15).
Finally two magnitude values are given. MS is the surface wave magnitude deduced from the seismic moment after Geller (1976). MWA is the WOOD-ANDERSON magnitude and corresponds roughly to Ml as obtained on common short period recordings. MWA is estimated on the base of the synthetic traces, MS on the other hand on the base of an input parameter, i. e., the seismic moment. Similar to the response spectra the average of these signal parameters is given together with the values of average +one standard deviation and the peak hold values. For the reason explained earlier there will be always a statistical fluctuation of these values (besides MS) even if no random fluctuation was applied to the input parameters of the model.
On the right hand side of your screen you note two buttons labeled “Save Results” and “View Results”. Clicking “Save Results” the contents of the screen are saved to the model data base, for examples “Simul.mdb”. You can also choose to “Save [the]Results in ASCII”. SHAKYGROUND writes the spectra and the contents of the table with the signal parameters to a textfile in your current working directory. This which can be edited with any editor and easily imported to other programs like EXCEL for further processing. Choosing this option SHAKYGROUND asks you to specify the filename; if it alraedy exists you may either overwrite it or append your actually produced results to former ones.
Selecting “View Results” you have the possibility to scroll through the actually created time series and response spectra. Your screen should look like Fig. 16. Note the list-box with the arrow on its right. Use the arrow to get a list of available traces. SHAKYGROUND shows the numbers and you may click one of them in order visualize the corresponding traces.

Fig. 14. SHAKYGROUND’s standard output screen.

Then select the type of traces you wish to see clicking the flip-flop boxes. You may also select the length of the time window you want to see. SHAKYGROUND suggests a default value which should permit you to see all significant parts of the signal. You may choose to see the a longer or shorter window by specifying a corresponding number of points in the box labeled with “Time window”. You can choose the part of the visualized response spectra in a similar way specifying the number of points in the box labeled “RS Window”.

Now click the field with the traces or the response spectrum shown on your screen. The graphic routines used in SHAKYGROUND permit to select the field and to adjust its size. You also may click the strings like “Acceleration (m/s^2)”, “Displacement (m)” and so on and move them around on the field. If you desire to export some graphics to an other application, (e. g., MS Word where you are processing a document) select the area of interest, then press the “Print” key on your keyboard. Doing so you copy the graph to the clipboard of your computer. Now move to your application and point the mouse to the place where you wish to paste the graph.

Fig. 15. Visualizing Synthetic traces (acceleration, speed, displacement)

If there are no created traces or response spectra SHAKYGROUND prompts you a message. Return to the previous screen clicking the little X in the upper right corner of the screen (attention: use the X on the same row as the Strings “Input” and “Output”, otherwise you terminate the SHAKYGROUND session).

Clicking the “Response Spectrum” sheet your screen should display something similar to Fig. 10. You will note three fields, i. e. “Frequencies” “Type of Response Spectrum”, and “Damping”. In the “Frequency” field you indicate the highest and lowest frequency of the response spectrum together with the stepwidth of response spectrum calculation. Note that SHAKYGROUND cuts down the upper frequency limit to a value corresponding to 1/6 of the digitization frequency. If you specify, for example, a digitization frequency of 200 Hz (see the “General” sheet) the uppermost possible value of the response spectrum will be 33¹3Hz. This limit has been introduced for reasons of numerical stability. You can rise this limit by choosing a higher digitization frequency together with a larger number of points of the synthetic seismogram. For more details about how to choose the digitization frequency and seismogram length see the paragraph concerning the “General” sheet.

The Response Spectrum Sheet.

The choice of the “Type of Response Spectrum” to be calculated is quite simple. Just click the box of your desired response spectrum type. Choose the damping value of the response spectrum using the box named “Damping” at the bottom of the sheet. The damping is understood in fractions of 1 instead of %. For a 5% response spectrum choose a value of 0.05 in the “Damping” box.

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.

In this sheet (Fig.below) you may access the specification concerning the receiver position both with respect to its coordinates as well as to its position within the layer stack. The coordinates are entered in the frame named “Receiver position”. There are two text boxes where the coordinated expresses in UTMX and UTMY can be edited. As in the “Source” sheet, UTMX and UTMY are metric coordinates as in systems like, e. g, Gauß-Krüger or Gauß-Boaga.  SHAKYGROUND calculates the epicentral distance of the receiver and displays it in the frame “Epicentral distance” in the box labeled with “Calculated (m)”. Since the epicentral distance results automatically from the source and receiver coordinates it cannot be edited. What can be done, however, is to subject the epicentral distance to a random fluctuation in the same way as is done for the source and layer parameters. In the spin-box (box with the double horizontal arrow) the user specifies the bandwidth of the random fluctuation in percent of the value calculated. In other words, if the calculated epicentral distance is 10,000 m and the user specifies a random fluctuation of 15% then the actual epicentral distance used during the simulations will float around the calculated one according to a standard deviation of ± 1500 m. SHAKYGROUND reports the absolute value of the fluctuation in a text-box, where, however, editing is disabled. Note that in the concept of SHAKYGROUND the receiver position is linked with the layer stack which are actually present on the “Strata” sheet. If a geological model is loaded from the catalog, SHAKYGROUND automatically loads also the corresponding receiver position linked to that layers. If you wish to save the receiver coordinates (and its vertical position within the layer stack) you have to do this using the “Strata” sheet (click the “Strata” sheet then “Save in Catalog”). Or you may use the option to save the whole model, i. e., the whole bunch of the 6 sheets, by clicking the floppy-disk icon on the toolbar underneath the title “Models”.

Finally SHAKYGROUND offers on option to consider the wave field in some depth instead of a position directly on the earth’s surface. This option can be useful if the foundations of a building are situated at some depth. The seismic loading at depth is often lower due to destructive interference of upgoing and downgoing waves. In the frame “Receiver position within layer stack” SHAKYGROUND permits to pose the receiver at one of the layer interface of the geological model. SHAKYGROUND displays the model schematically. The first position is the “Surface” which is also the default. Clicking one of the subsequent layer names moves the receiver to the lower boundary of that layer. At a first glance there seems to be a limitation since the receiver position is linked to a layer boundary. This limit, however, can be easily circumvented by the creation of a virtual layer subdividing an existing layer into two layers with identical impedance and Q values, and choosing the thicknesses appropriately. Note again that the receiver position can be saved totgether with the layer parameters using the “Strata” sheet, or by saving the “Mode”, i. e. the whole stack of SHAKYGROUNDs input sheets.

The Receiver Sheet with coordinates, and the vertical position within the layer stack.

Having concluded the numerical processing of the model SHAKYGROUND should now what kind of output you would like to have. If you do not touch the “Output” sheet SHAKYGROUND provides you a standard output in graphical whose numerical contents may be saved to the model data base. This standard output concerns the average signal parameters, the average response spectrum plus their statistical fluctuation expressed by the standard deviations and peak hold values. You may also wish to access the results of single simulations. For this purpose click the sheet named “Output” to see a sheet as depicted in Fig. 13. SHAKYGROUND offers an option to scroll over all simulated seismograms and response spectra at the end of model processing.
Click the small white flip-flop boxes to activate or disactivate the salvation of time series and reponse-spectra. All files will be written to the subdirectory “Elaboration”. If you decided to write the single times series to disk SHAKYGROUND creates plain ASCII files with the single traces in terms of acceleration, velocity, displacement, and WOOD-ANDERSON response. The files are assigned names with respect to their type and an ID indicating the simulation during which the trace has been created. The accelerogram generated during the 36th simulation is written to the file named “acc.036″, the corresponding velocity and displacement seismograms are saved in files named “vel.036″ and “disp.036″, finally the corresponding WOOD-ANDERSON seismogram is found in the file “wa_sim.036″. Similarly, if you decided to save the single response spectra by clicking the corresponding flip-flop box SHAKYGROUND creates plain ASCII files containing the single response spectra. The file names are created as before. For instance, the 36th response spectrum is saved to a file named “rsp.036″. Since all files contain solely one column with the values it becomes very easy to export them to any other program and to perform further processing if desired. SHAKYGROUND itself allows to visualize them graphically (we shall return to this point when we explain how to launch SHAKYGROUND). Note that the necessary information for this visualization is stored in two header files, i. e. S_Info (for the seismograms) and R_info (for the response-spectra).

Out Sheet -  Specifying the Results you wish to have from SHAKYGROUND.

If you wish to conserve these files please copy them to a separate subdirectory IMMEDIATELY after processing. Otherwise you will loose them because SHAKYGROUND cancels all files on its working directory “Elaboration” every time you’re starting a simulation. We have adopted this rather cruel method in order to prevent users from creating unconsciously chaos on the “Elaboration” directory and to avoid the accumulation of mega- and gigabytes of garbage.

It is very important to Note that the layer models stored in the catalog are georeferenced. If you click the “Receiver” sheet you will find two boxes UTMX and UTMY. You can edit this values in order to obtain your desired epicentral distance. The receiver coordinates will be saved in the catalog when you click the “Save in Catalog” button on the “Strata” sheet. The receiver with its specifications on the “Receiver” sheet and the layer model form a logical unit which we may call “site”

Click now the “Strata” sheet in order to see a screen similar to the one shown in Fig. below. The “Strata” sheet is subdivided in three parts. The first part close to the title is labeled “Strata in Catalog”.

The layer parameters

The second part of the “Strata” sheet is devoted for editing the layer parameters. First note the text box “Strata Name” which reports the name of the layer model you are actually working on. It will be the same as the one indicated above in the textbox “Name” if you accessed a layer model from the catalog. You must change the name in “Strata Name” if you wish to create a new entry in the catalog. Use the button “Save in Catalog” to the right to save the new layer parameters to the catalog. Of course, if SHAKYGROUND finds an already existing layer model in the catalog which has the same name as indicated in the box “Strata Name” you’ll be asked whether to overwrite the layer model in the catalog.
Below the textbox “Strata Name” you find on the left hand side of the sheet a column of text boxes related to the single layers of the layer model. The first reports the layer name, the subsequent ones the various geotechnical parameters, i. e., the thickness of the layers, their shear wave velocity, their density and the quality factor Q. Similar to the “Source” sheet the geotechnical parameters reported in the textbox on the right hand side of the layer sheet represent average values. These average values can be subjected to a random fluctuation, whose bandwidth in % is specified with a column of spinboxes. The definition of the bandwidth of the random fluctuation is the same as the one applied to the source parameters. For example, if the random fluctuation of a layer thickness of 300 m has been selected as 10%, then this parameter will be varied in each simulation with a standard deviation of 30 m, that is ± 10% or a bandwidth of 20 %. The 3rd column of boxes on the right hand side report the bandwidth of the random parameter variation in absolute values. Note that these boxes cannot be used for changing the bandwidth of random parameter variation.
In the lowermost part you find a box which reports all layernames of the layer model together with their geotechnical parameters and the corresponding bandwidth of random variation. Additionally the layers are assigned with colors. This box, lets call it “Overall Box”, contains all information about the layer model and must be accessed if you want to edit the parameters of a layer. The “Overall Box” is rather large, so that you may not see it entirely on your screen. Use the horizontal arrow at its base in order to scroll it. Now click the color or the name of the layer you want to access. SHAKYGROUND reports the parameters of this layer in the central part of the sheet, i. e. in the textboxes related to name and parameters of the single layer and the subsequent columns of boxes reporting the random parameter variation. Use these boxes to make your changes. You now have two options to make your changes active in the layer model. For this purpose use the buttons on the left hand side in the lowermost part of the layer sheet. Clicking the “Next” button will append a layer with your new parameter set at the base of the layer stack. With “Insert” this layer will be copied above the previously selected layer. Finally, if desired, select once more the layer you edited and press the “Delete” button. If you don’t do so you simply augment your layer stack.
The creation of new layers and layer models can be performed in a straight forward manner, just using the tools described. First specify a new name in the “Strata Name” Box. If you don’t like the model which you may find in the “Overall Box” click the layers there and delete them one by one, until your “Overall Box” is empty. Now specify the layer name in the “Layer name” box and enter the parameters in the subsequent boxes. Use the spinboxes if you wish to vary your layer parameters randomly. Then “Insert” the layer. Repeat this procedure for every desired layer. Recall that for insertion of the layer in the layer stack you have two possibilities, i. e., to insert it above the previous one with the “Insert” button or to append it at the base of the layer stack with “Next”button. Be aware of the fact that what finally counts for the simulation are the contents of the “Overall” box. Your insertion of layer parameters is completed when you have clicked either the “Insert” or the “Next” button.
The “Up” and “Down” buttons above the “Next” button represent an additional tool for the manipulation of layer models. Click a layer in the “Overall Box” then click the “Up” or “Down” button. SHAKYGROUND interchanges the position of the selected layer with the upper or lower neighboring one according to the button you have selected. This action becomes available if there already a layer model of at least two layers.

Here we should talk in more detail about SHAKYGROUNDs input philosophy. As mentioned earlier, we understand “models” as an entire set of input parameters, in other words a complete stack of our electronic sheets consisting of the “Source” sheet, the “Strata” sheet, the “General sheet” the “Response Spectrum” sheet, the “Receiver” sheet and the “Output” sheet. If you save a “model” to the model data base, the entire stack will be stored there. You can retrieve a previous model as explained above, that is you load all sheets belonging to the chosen model. You may now understand, by the way, what SHAKYGROUNDs catalogs are good for. The catalogs are the place where the information of single sheets, in particular the “Source” and “Strata” sheets, are stored. Since you can access single sheets from the catalog it is possible, for example, to create a number of source models during a session, store them to the catalog and recall them later. This particularly useful if you don’t want to change the parameters in the other sheets, like the geological model in the “Strata” sheet, general parameters for the seismogram generation (sheet “General”) etc. We’ve adopted the same strategy for the parameters on the “Strata”sheet. It is thus possible to recombine source parameters and geological models in a very easy and effective way. If you want to change the source parameters in a in a seismic zoning project with 100 sites you have to edit the”Source” sheet only once in order to be ready to process 100 new models. Without the possibility to retrieve single sheets from the catalog you had to edit every single of the 100 models in order to consider the new source. If the user desires he can work only with the catalogs without accessing the model data base. In large seismic zoning projects this can be of advantage since the use of disk space is considerably reduced.