Greetings,
The plates are quite thick and the water, oil and gas deposits are within the crust. There can be local subsidence where the deposits are removed, especially if they are shallow. The plates are moving constantly and basically are driven by convection currents in the soft mantle below them and basically float on the latter. As you likely know there is a destructive plate margin or subduction zone of the east coast of the North Island which drives the earthquake and volcanic activity in the North Island.
Regards Grandpamac.
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