The geophysics problems that must be solved in order for us to reliably monitor subsurface change, without disruption or prohibitive cost, have pushed researchers into new and fascinating areas in inverse theory, optimization, acquisition design, and AI. In this presentation I will summarize some recent computational, laboratory, and field experiences our group has had while chasing these solutions. But equally beguiling have been the strange geophysical phenomena uncovered along the way. In the second half of the presentation I will discuss the observation of some peculiar transient seismic responses to fluid injection, an equally peculiar possible explanation for them, and the finding of statistical phase transitions in a famous model for seismic wave propagation through thin layers.

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