Dynamics of submergence and uplift of a sedimentary basin underlain by a phase-change boundary

A procedure is given for calculating the evolution of a sedimentary basin underlain by a phase-change boundary that is in isostatic equilibrium. The equation of motion of the water depth w(t) as a function of the water depth and as a function of the sedimentation rate ds/dt is Q_w(w) dw/dt + Q_s ds/dt + (1 - ρ_1/ρ_2) dl/dt = 0 where l(t) is the lag of the phase boundary behind the transient equilibrium position. Numerically precise integrals of this equation are given for different time regimes by use of certain approximations for the temperature field that determine dl/dt. Solutions are demonstrated that are attenuated, explosive, or near periodic, depending on the physical parameters used. The results clearly show the possibility of depositing very thick sedimentary sections and the existence of self-sustained oscillations (above and below sea level) for a sedimentary basin of this type.