49 



Window Width Choice of window width is a balance between including sufficient 

 curvature in the record to identify the local wave response while minimizing the extent 

 of the locally steady approximation. Another factor to be considered is the sampling 

 rate of the data. The LFI method employs a cubic spline for interpolation among 

 the measured points. This approach allows the selection window widths and sampling 

 locations without being restricted by the data sampling locations. While this freedom 

 is very useful, it can be deceiving, as the data are not truly continuous. As the data 

 are not continuous, it is important to be sure that the window width chosen includes 

 sufficient measured data points to justify the order being used. Unfortunately, field 

 data are often sampled at a frequency of as low as IHz. In this case, a window width 

 of one tenth the mean zero crossing might be on order of 1 second. This would provide 

 a maximum of two actual data points in each window. It may not be appropriate 

 to attempt a high order solution with such little hard data. Ideally, the LFI method 

 should be used with data sampled at a higher rate. If that isn't possible, wider 

 windows, and perhaps lower order solutions, should be used. 



In the case of the theoretical records used in the previous section, the data sam- 

 pling rate could be arbitrarily high. Without being restricted by measurement fre- 

 quency, some guidelines for window width have been determined. A primary window 

 width of one tenth the zero crossing period provides a good starting point. Using 

 a smaller window often did not allow convergence of the solution. It was necessary 

 to occasionally increase window width at some locations on the record, as discussed 

 in section 3.3.2. When a primary window width is determined that works for most 

 of the record, while needing to be increased at a only a few locations, the optimum 

 width has been found. 



In the case of the shallow water wave discussed in the previous section, a window 

 width of O.ir, was successful for up to a fourth order solution. Unfortunately, the 

 fourth order solution did not fully capture the sharp crest of the wave. When a higher 

 order solution was attempted, the optimization would not converge with the given 

 window width. A wider window had to be used in order to obtain a solution of high 

 enough order to capture the sharp crest of the wave, and thus a window width of 0.2r^ 

 was used in that example. In general, it has been necessary to use wider windows for 



