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In this paper, we propose a novel method for autonomously seeking out sparsely distributed targets in an unknown underwater environment. Our Sparse Adaptive Search and Sample (SASS) algorithm mixes low-altitude observations of discrete targets with high-altitude observations of the surrounding substrates. By using prior information about the distribution of targets across substrate types in combination with belief modelling over these substrates in the environment, high-altitude observations provide information that allows SASS to quickly guide the robot to areas with high target densities. A maximally informative path is autonomously constructed online using Monte Carlo Tree Search with a novel acquisition function to guide the search to maximise observations of unique targets. We demonstrate our approach in a set of simulated trials using a novel generative species model. SASS consistently outperforms the canonical boustrophedon planner by up to 36% in seeking out unique targets in the first 75 - 90% of time it takes for a boustrophedon survey. Additionally, we verify the performance of SASS on two real world coral reef datasets.