Source code of analytical solution

Existing analytical models for tidal wave propagation in coastal leaky aquifers remain limited to one- or two-layer systems with either homogeneity or oversimplified heterogeneityrepresentations. Complex heterogeneity patterns, such as the prevalent occurrence of aquitard preferential conduits in multilayered systems, have not been addressed analytically. This study develops a generalized analytical model that accommodatesan arbitrary number ofvertically stratified aquifer and aquitard layers and horizontally segmented zones with distinct hydraulic properties. The model’s generality is enhanced by incorporating four key features, including the finite lateral extent representation, mixed-form lateral boundary conditions, zone-specific tidal forcing at the top boundary, and zone-specific tidal loading effects on both aquifer and aquitard layers. Analytical solution development begins with the establishment of a coupled system of ordinary differential equations governing zone-specific steady-state and periodic components of tidal wave propagation in aquifer layers.The solution is derived by employing matrix eigenvalue analysis to obtain the zone-specific general solution, followed by the recursive formulation implementation to enforce hydraulic head and flux continuity across aquifer zone interfaces.Under equivalent boundary conditions and system configurations, the newly derived analytical solution is shown to subsume multiple existing analytical solutions as special cases. Theoretical investigations reveal that aquitard preferential conduits can reverse the typical landward amplitude decay and phase shift increase in the less permeable adjacent aquifer. Such a reversed tidal wave propagation pattern is pronounced with strong aquifer permeability contrasts, high conduit-to-aquitard permeability ratios, and sizable conduit widths, and exhibits remarkable period dependence. For conduit identification through multi-frequency tidal analysis, greater weight should be assigned to higher-frequency components.