User Guide: Ground Motion Prediction Equations

Information

The complex model is 

The model takes into account successively increase of GM parameter along the increase of source size, non-linear source influence, non-elastic damping, non-linear geometric scattering, influence of site effect at station. The model can be customized by choosing by selecting any parts.
The Ordinary one-stage regression method is used.

This application is prepared in 3 steps and in two of them model can be improved.  

Step by Step

1. Preparation of the data - GM parameters Catalog is needed.
   To prepare GM parameters Catalog as the 1st input file is a a Seismic Catalog and the 2nd input file is Ground Motion Catalog from the same Episode (AH EPISODES). Thus choose a catalog and GM Catalog from a selected episode. Then run Ground Motion Parameters Catalog builder, as a result will be GM parameters Catalog. The part of the GM parameters Catalog can be used with Catalog filter. It is worth to remove smal values of PGA ef <=0.03 m/s²
   
   
2. Selection of the model parameters (STEP 1 of analysis)
   After the User adds the Application into his/her personal workspace, the following window appear on the screen (Figure 1), and the user is now requested to fill the fields shown on Figure 1:
   GM Parameters: The user may choose from all available ground motion parameters which were available in GM Catalog.
   Source characteristic parameter: The user may choose from all available source parameter which were available in Catalog. The model may contain M, M², both or none of them. Recommended is to choose both and check their statistical significance in results. When coefficients or one of them is insignificant can be remove from the model.
   Path characteristic: The model may contain R, logR, both or none of them. Additionally epicentral distance may be calculated with fixed depth ('h' parameter in the model). 'h' parameter can be estimated (then option Estimate depth with model should be chosen) or can be type (the value is given in kilometer). Recommended is to choose estimation of fix depth with model and choose both coefficients and check their statistical significance in results. When coefficients or one of them is insignificant can be remove from the model.
   Site characteristic: Site characteristic depend on station position.
   
   
   Figure 1. Input window of Ground Motion Prediction Equations: GMPE calculation
   

3. After defining the aforementioned parameters, the user shall click on the  button (Figure 1) and the calculations are performed. The output is soon to be created.

   The output results include:

   gmpe_model_report
   
   Figure 2. Ground Motion Prediction Equations model report.
   
   R2 - (R-squared value) - coefficient of determination is the proportion of the variance in the dependent variable that is predictable from the independent variable(s). It shows in how many %  the model explains the variability in the response.
   Root Mean Square Error (RMSE) - is a frequently used measure of the differences between values (sample or population values) predicted by a model or an estimator and the values observed.
   p - probability o F-statistic for testing statistical significance of the model.
   
   SEE chart (when 'h' chosen as one of coefficient)
   
   Figure 3. SEE plot. 
   
   Additional results:
   gmpe_dataset.mat - mat file with chosen parameters based on GM Parameters Catalog for which GMPE is calculeted.
   gmpe_model_residuals.mat -  mat file with residuals of the model,
   gmpe_model_step1.mat - mat file with results of 1. step.
   
   
4. Improving the model:
   According to the result - especially statistical significance of coefficients and its physical correctness - the model can be improve. To improve the model click on the . 
   In this case R coefficient of distance will be remove because is non-negative.
   
   
   Figure 4. Input window of recalculation of GMPE.
   
   the result:
   
   Figure 5. Result of recalculated model.
   
   
5. As a additionally result, after the improving the model, comparison of previous vs current model parameter appear.
   
   The  new model is better when SEE is smaller, R2 is bigger, F is bigger and p is smaller.
   This model not need improving. All coefficient are proper and statistically significant. Recalculation can be done so many time until the results are satisfactory.
    
6. Residual Analysis
   After receiving the satisfying model the residual analysis can be perform (STEP2 of analysis). To start choose .
   
   
   
   
   Figure 6. Plot of residuals.
   
   
   Figure 7. Input window of remove residuals step.
   
   the results:
   
   
   Figure 8. Results of the model after the removing outlieres.
7. According to the result - especially spreading of outliers - the analysis can be repeated. To repeat choose . Recalculation can be done so many times until the results are satisfactory. 
8. Summary
   After receiving the satisfying model the final model can be perform (STEP3 of analysis). To calculate the final model with additional plots please select .
   The final output results include:
   gmpe_model_raport, gmpe_model_dataset, figures (Normal probability plot of residuals, box plot - residuals according the station, Mw vs residuals, r vs residuals).
   There is also possibility to configure selected figures based n used and estimated parameters.
   

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