Compensation of vertical displacement components in marine seismic applications using the coupled heave and pitch model

The developments of a realistic model that incorporates vertical motions of a towed body is considered. Inclusion of the pitch dynamics results in two-coupled second-order equations in the heave and pitch components. The conventional hydrodynamic equations are reviewed, and a state-space model for representing the vertical displacement dynamics is derived. The model is of the fourth order and is of a form suitable for Kalman filtering implementation. The application of a standard Kalman filter to estimate the vertical displacement component on the basis of this higher-order model is also discussed