A method is provided for sequestration of a greenhouse gas in a water-laden formation by injection of a fluid comprising greenhouse gas (GHG) into a formation under conditions suitable for generating an unstable front of said greenhouse gas within the formation. The injection may comprise a first stage wherein a gas phase comprising CO2 is injected into the formation, followed by a second stage comprising injecting an aqueous liquid into the formation, to thereby generate an unstable front within the formation that results in relatively rapid dissolution of the injected CO2 within the formation water. The cyclic nature of the injection, alternating between GHG and water injection, can be repeated for a number of times until the carrying capacity of the formation is deemed to have been reached.