Dispersive swell source inversion ($t=t_0+4\pi L/(gT)$)

For an impulsive distant source of deep-water gravity waves, a component of period $T$ travels at group velocity $gT/(4\pi )$. Its arrival at distance $L$ obeys the displayed law, so inverse period increases linearly with arrival time. Two arrivals determine both $L$ and $t_0$. Finite source duration, currents, refraction and passage through sea ice can invalidate the simple inversion.