Marine microfossils provide a useful record of the Earth's resources and prehistory via biostratigraphy. To study Hydrocarbon reservoirs and prehistoric climate, geoscientists visually identify the species of microfossils found in core samples. Because microfossil identification is labour intensive, automation has been investigated since the 1980s. With the initial rule-based systems, users still had to examine each specimen under a microscope. While artificial neural network systems showed more promise for reducing expert labour, they also did not displace manual identification for a variety of reasons, which we aim to overcome. In our human-based computation approach, the most difficult step, namely taxon identification is outsourced via a frontend website to human volunteers. A backend algorithm, called dynamic hierarchical identification, uses unsupervised, supervised, and dynamic learning to accelerate microfossil identification. Unsupervised learning clusters specimens so that volunteers need not identify every specimen during supervised learning. Dynamic learning means interim computation outputs prioritize subsequent human inputs. Using a dataset of microfossils identified by an expert, we evaluated correct and incorrect genus and species rates versus simulated time, where each specimen identification defines a moment. The proposed algorithm accelerated microfossil identification effectively, especially compared to benchmark results obtained using a k-nearest neighbour method.