Phase Shift The phase parameters, cxi and 0-2 are set for the phase of the global 

 segment of the record used. The local time in each window is set so that i = at 

 the center of the window. The initial estimate for the phase in each window must be 

 shifted to accommodate the change in the time reference frame. 



a„ = -UnAt + a„,giobai (5.23) 



where A^ is the difference between the time in the two reference frames. 



Nonlinear Optimization in Windows 



Once the global solution is computed, it is used as the first guess for the parameters 

 in each window, and these parameters are refined by solving Eq. 5.6 with a standard 

 nonlinear optimization routine. For the results given, the Levenberg-Marquardt algo- 

 rithm was used as implemented by the Matlab Optimization Tool Box (Grace 1992). 

 If the optimization successfully converges to a minimum, the solution is checked to 

 see if it is a clearly spurious solution. Spurious solutions can be identified by the same 

 criteria used in chapter 3: 



• Very large or systematically variable errors. 



• First order amplitude smaller than one of the higher order amplitudes. 



• Unrealistically large or small frequency or wave number. 



• Large discontinuity between the windows in the predicted kinematics. 



As in chapter 3, it is unusual for the routine to converge to a spurious solution. It is 

 far more common for the routine not to converge at all. 



If no solution or a spurious solution is found, it is necessary to revise the pa- 

 rameters of the solution as was discussed in section 3.3.2. These revisions include 

 increasing the width of the window, and if that is not successful, decreasing the order 

 of the solution. If neither of these adjustments result in an acceptable solution, the 

 window is skipped, and future analysis must be interpolated through that point. As 

 with the analysis of a point pressure measurement, these adjustments are most likely 



