Peer review paper: Radiocarbon dating of fossil microatolls indicates a gradual fall of sea level over this period
Well, not in the Cocos (Keeling) Islands according to Woodroffe et al (https://doi.org/10.1016/S0025-3227(99)00009-2) Here is their abstract:
Reef islands around the margin of coral atolls generally comprise unconsolidated Holocene sands and gravels, overlying a reef flat or cemented conglomerate platform. Such islands have accreted within the last 3000–4000 years, since sea level has reached a level close to present and the reef flat and conglomerate platform have formed. Island morphology consists of an oceanward ridge, a less distinct lagoonward ridge, and low-lying central depression. Several alternative models of how such reef islands might have developed are examined in relation to chronology and sediment provenance, particularly in the context of the Cocos (Keeling) Islands where this issue has been debated since Darwin visited the atoll. Which of these models appears most appropriate for an elongate reef island on the atoll margin is assessed using conventional radiocarbon dating of coral shingle and accelerator mass spectrometry (AMS) radiocarbon dating of individual sand grains from pits across West Island. The dating results suggest that both coral clasts and individual grains of various components are generally reliable and replicable indicators of the chronology of island accumulation, implying rapid transport of skeletal material, after death of the contributing organisms, across the reef flat zone, and relatively little reworking. The central part of West Island appears to have formed first, with oceanward accretion up until about 2000 years BP. Gradual oceanward accretion with lesser lagoonward extension has continued beyond 2000 years BP at the northern and southern ends of the island, and a sequence of lagoonward recurving spits has formed adjacent to the inter-island passage at the southern end of the island. Radiocarbon dating of fossil microatolls indicates a gradual fall of sea level over this period which appears to have had little effect on the pattern of island accretion.