126 



the dynamic free surface boundary condition (f^), 



f"" = ^ + ^{u^ + v^ + w')+gV-B = at z = rj (6.4) 



the BernoulH equation (/ 



B) 



cB ^V , ^ , 2 , 2 , 2\ , Pd -^ 



/ - ix + o (^ +v' + w') + ^-B = (6.5) 



ot z p 



with the Bernoulli constant (B) defined as: 



In order to apply the free surface boundary conditions, the location of the free 

 surface must be found, together with the potential function, in each window. In 

 order to locate the free surface, the water surface is defined at M nodes, located at 

 the horizontal location of the center of the array, and equidistantly spaced in time 

 throughout the window. The elevation of these nodes is unknown, and will be sought 

 as part of the solution. 



6.2 Formulation of the Optimization 



The formulation of the optimization for the LFI method as applied to the inter- 

 pretation of an array of pressure measurements has a great deal in common with the 

 formulation for an array of water surface measurements and the formulation for a sub- 

 surface pressure record (chapters 3 and 5). Only the framework is presented, together 

 with any additional information unique to the application to a pressure array. 



Observational Equations The observational equations are the equations that con- 

 fine the solution to fit the measured records. The predicted subsurface pressure is 

 available from the Bernoulli equation, Eq. 6.5, which is applied at the location of the 

 gauges in the array to define the observational equations. The error in the Bernoulli 

 equation is the diff'erence between the measured dynamic pressure at the given lo- 

 cation and time and the dynamic pressure predicted from the kinematics defined by 



